Husain, Viqar
2012-03-01
Research on quantum gravity from a non-perturbative 'quantization of geometry' perspective has been the focus of much research in the past two decades, due to the Ashtekar-Barbero Hamiltonian formulation of general relativity. This approach provides an SU(2) gauge field as the canonical configuration variable; the analogy with Yang-Mills theory at the kinematical level opened up some research space to reformulate the old Wheeler-DeWitt program into what is now known as loop quantum gravity (LQG). The author is known for his work in the LQG approach to cosmology, which was the first application of this formalism that provided the possibility of exploring physical questions. Therefore the flavour of the book is naturally informed by this history. The book is based on a set of graduate-level lectures designed to impart a working knowledge of the canonical approach to gravitation. It is more of a textbook than a treatise, unlike three other recent books in this area by Kiefer [1], Rovelli [2] and Thiemann [3]. The style and choice of topics of these authors are quite different; Kiefer's book provides a broad overview of the path integral and canonical quantization methods from a historical perspective, whereas Rovelli's book focuses on philosophical and formalistic aspects of the problems of time and observables, and gives a development of spin-foam ideas. Thiemann's is much more a mathematical physics book, focusing entirely on the theory of representing constraint operators on a Hilbert space and charting a mathematical trajectory toward a physical Hilbert space for quantum gravity. The significant difference from these books is that Bojowald covers mainly classical topics until the very last chapter, which contains the only discussion of quantization. In its coverage of classical gravity, the book has some content overlap with Poisson's book [4], and with Ryan and Shepley's older work on relativistic cosmology [5]; for instance the contents of chapter five of the
Signature change from Schutz's canonical quantum cosmology and its classical analogue
International Nuclear Information System (INIS)
Pedram, Pouria; Jalalzadeh, Shahram
2008-01-01
We study the signature change in a perfect fluid Friedmann-Robertson-Walker quantum cosmological model. In this work the Schutz's variational formalism is applied to recover the notion of time. This gives rise to a Schroedinger-Wheeler-DeWitt equation with arbitrary ordering for the scale factor. We use the eigenfunctions in order to construct wave packets and evaluate the time-dependent expectation value of the scale factor which coincides with the ontological interpretation. We show that these solutions exhibit signature transitions from a finite Euclidean to a Lorentzian domain. Moreover, such models are equivalent to a classical system where, besides the perfect fluid, a repulsive fluid is present
International Nuclear Information System (INIS)
Hawking, S.W.
1984-01-01
The subject of these lectures is quantum effects in cosmology. The author deals first with situations in which the gravitational field can be treated as a classical, unquantized background on which the quantum matter fields propagate. This is the case with inflation at the GUT era. Nevertheless the curvature of spacetime can have important effects on the behaviour of the quantum fields and on the development of long-range correlations. He then turns to the question of the quantization of the gravitational field itself. The plan of these lectures is as follows: Euclidean approach to quantum field theory in flat space; the extension of techniques to quantum fields on a curved background with the four-sphere, the Euclidean version of De Sitter space as a particular example; the GUT era; quantization of the gravitational field by Euclidean path integrals; mini superspace model. (Auth.)
International Nuclear Information System (INIS)
Coule, D H
2005-01-01
We contrast the initial condition requirements of various contemporary cosmological models including inflationary and bouncing cosmologies. Canonical quantization of general relativity is used, as a first approximation to full quantum gravity, to determine whether suitable initial conditions are present. Various proposals such as Hartle-Hawking's 'no boundary' or tunnelling boundary conditions are assessed on grounds of naturalness and fine tuning. Alternatively, a quiescent initial state or an initial closed timelike curve 'time machine' is considered. Possible extensions to brane models are also addressed. Further ideas about universe creation from a meta-universe are outlined. Semiclassical and time asymmetry requirements of cosmology are briefly discussed and contrasted with the black-hole final-state proposal. We compare the recent loop quantum cosmology of Bojowald and co-workers with these earlier schemes. A number of possible difficulties and limitations are outlined. (topical review)
Page, Don N.
2006-01-01
A complete model of the universe needs at least three parts: (1) a complete set of physical variables and dynamical laws for them, (2) the correct solution of the dynamical laws, and (3) the connection with conscious experience. In quantum cosmology, item (2) is the quantum state of the cosmos. Hartle and Hawking have made the `no-boundary' proposal, that the wavefunction of the universe is given by a path integral over all compact Euclidean 4-dimensional geometries and matter fields that hav...
Modern Canonical Quantum General Relativity
Thiemann, Thomas
2008-11-01
Preface; Notation and conventions; Introduction; Part I. Classical Foundations, Interpretation and the Canonical Quantisation Programme: 1. Classical Hamiltonian formulation of general relativity; 2. The problem of time, locality and the interpretation of quantum mechanics; 3. The programme of canonical quantisation; 4. The new canonical variables of Ashtekar for general relativity; Part II. Foundations of Modern Canonical Quantum General Relativity: 5. Introduction; 6. Step I: the holonomy-flux algebra [P]; 7. Step II: quantum-algebra; 8. Step III: representation theory of [A]; 9. Step IV: 1. Implementation and solution of the kinematical constraints; 10. Step V: 2. Implementation and solution of the Hamiltonian constraint; 11. Step VI: semiclassical analysis; Part III. Physical Applications: 12. Extension to standard matter; 13. Kinematical geometrical operators; 14. Spin foam models; 15. Quantum black hole physics; 16. Applications to particle physics and quantum cosmology; 17. Loop quantum gravity phenomenology; Part IV. Mathematical Tools and their Connection to Physics: 18. Tools from general topology; 19. Differential, Riemannian, symplectic and complex geometry; 20. Semianalytical category; 21. Elements of fibre bundle theory; 22. Holonomies on non-trivial fibre bundles; 23. Geometric quantisation; 24. The Dirac algorithm for field theories with constraints; 25. Tools from measure theory; 26. Elementary introduction to Gel'fand theory for Abelean C* algebras; 27. Bohr compactification of the real line; 28. Operatir -algebras and spectral theorem; 29. Refined algebraic quantisation (RAQ) and direct integral decomposition (DID); 30. Basics of harmonic analysis on compact Lie groups; 31. Spin network functions for SU(2); 32. + Functional analytical description of classical connection dynamics; Bibliography; Index.
Modern Canonical Quantum General Relativity;
International Nuclear Information System (INIS)
Kiefer, Claus
2008-01-01
The open problem of constructing a consistent and experimentally tested quantum theory of the gravitational field has its place at the heart of fundamental physics. The main approaches can be roughly divided into two classes: either one seeks a unified quantum framework of all interactions or one starts with a direct quantization of general relativity. In the first class, string theory (M-theory) is the only known example. In the second class, one can make an additional methodological distinction: while covariant approaches such as path-integral quantization use the four-dimensional metric as an essential ingredient of their formalism, canonical approaches start with a foliation of spacetime into spacelike hypersurfaces in order to arrive at a Hamiltonian formulation. The present book is devoted to one of the canonical approaches-loop quantum gravity. It is named modern canonical quantum general relativity by the author because it uses connections and holonomies as central variables, which are analogous to the variables used in Yang-Mills theories. In fact, the canonically conjugate variables are a holonomy of a connection and the flux of a non-Abelian electric field. This has to be contrasted with the older geometrodynamical approach in which the metric of three-dimensional space and the second fundamental form are the fundamental entities, an approach which is still actively being pursued. It is the author's ambition to present loop quantum gravity in a way in which every step is formulated in a mathematically rigorous form. The formal Leitmotiv of loop quantum gravity is background independence. Non-gravitational theories are usually quantized on a given non-dynamical background. In contrast, due to the geometrical nature of gravity, no such background exists in quantum gravity. Instead, the notion of a background is supposed to emerge a posteriori as an approximate notion from quantum states of geometry. As a consequence, the standard ultraviolet divergences of
Classical and quantum cosmology
Calcagni, Gianluca
2017-01-01
This comprehensive textbook is devoted to classical and quantum cosmology, with particular emphasis on modern approaches to quantum gravity and string theory and on their observational imprint. It covers major challenges in theoretical physics such as the big bang and the cosmological constant problem. An extensive review of standard cosmology, the cosmic microwave background, inflation and dark energy sets the scene for the phenomenological application of all the main quantum-gravity and string-theory models of cosmology. Born of the author's teaching experience and commitment to bridging the gap between cosmologists and theoreticians working beyond the established laws of particle physics and general relativity, this is a unique text where quantum-gravity approaches and string theory are treated on an equal footing. As well as introducing cosmology to undergraduate and graduate students with its pedagogical presentation and the help of 45 solved exercises, this book, which includes an ambitious bibliography...
Finite canonical measure for nonsingular cosmologies
International Nuclear Information System (INIS)
Page, Don N.
2011-01-01
The total canonical (Liouville-Henneaux-Gibbons-Hawking-Stewart) measure is finite for completely nonsingular Friedmann-Lemaître-Robertson-Walker classical universes with a minimally coupled massive scalar field and a positive cosmological constant. For a cosmological constant very small in units of the square of the scalar field mass, most of the measure is for nearly de Sitter solutions with no inflation at a much more rapid rate. However, if one restricts to solutions in which the scalar field energy density is ever more than twice the equivalent energy density of the cosmological constant, then the number of e-folds of rapid inflation must be large, and the fraction of the measure is low in which the spatial curvature is comparable to the cosmological constant at the time when it is comparable to the energy density of the scalar field. The measure for such classical FLRWΛ-φ models with both a big bang and a big crunch is also finite. Only the solutions with a big bang that expand forever, or the time-reversed ones that contract from infinity to a big crunch, have infinite measure
Inflation and quantum cosmology
International Nuclear Information System (INIS)
Linde, A.
1991-01-01
In this article a review of the present status of inflationary cosmology is given. We start with a discussion of the simplest version of the chaotic inflation scenario. Then we discuss some recent develoments in the inflationary cosmology, including the theory of a self-reproducing inflationary universe (eternal chaotic inflation). We do it with the help of stochastic approach to inflation. The results obtained within this approach are compared with the results obtained in the context of Euclidean quantum cosmology. (WL)
International Nuclear Information System (INIS)
Padmanabhan, T.
1989-01-01
Quantum cosmology is to quantum gravity what the Bohr model is to the full quantum mechanical description of the hydrogen atom. In quantum cosmology one attempts to give a quantum-mechanical meaning to classical solutions of general relativity. This is discussed in this chapter. The approach is illustrated by quantizing only the conformal degree of freedom of the gravitational field, in particular the Friedmann-Robertson-Walker models. And, as in the hydrogen atom, the classical singularity of general relativity is avoided and one has analogous stationary states in the quantum Universe. The chapter ends with a model of the fundamental role that the Planck length may play as the universal cutoff in all field theories, thus ridding the theory of ultra-violet divergences. Two appendices introduce field theory in the Schroedinger representation and the Schroedinger equation for quantum gravity, namely the Wheeler-De Wit equation. (author). 38 refs.; 2 figs.; 1 tab
Modern canonical quantum general relativity
Thiemann, Thomas
2007-01-01
This is an introduction to the by now fifteen years old research field of canonical quantum general relativity, sometimes called "loop quantum gravity". The term "modern" in the title refers to the fact that the quantum theory is based on formulating classical general relativity as a theory of connections rather than metrics as compared to in original version due to Arnowitt, Deser and Misner. Canonical quantum general relativity is an attempt to define a mathematically rigorous, non-perturbative, background independent theory of Lorentzian quantum gravity in four spacetime dimensions in the continuum. The approach is minimal in that one simply analyzes the logical consequences of combining the principles of general relativity with the principles of quantum mechanics. The requirement to preserve background independence has lead to new, fascinating mathematical structures which one does not see in perturbative approaches, e.g. a fundamental discreteness of spacetime seems to be a prediction of the theory provi...
Quantum gravity and quantum cosmology
Papantonopoulos, Lefteris; Siopsis, George; Tsamis, Nikos
2013-01-01
Quantum gravity has developed into a fast-growing subject in physics and it is expected that probing the high-energy and high-curvature regimes of gravitating systems will shed some light on how to eventually achieve an ultraviolet complete quantum theory of gravity. Such a theory would provide the much needed information about fundamental problems of classical gravity, such as the initial big-bang singularity, the cosmological constant problem, Planck scale physics and the early-time inflationary evolution of our Universe. While in the first part of this book concepts of quantum gravity are introduced and approached from different angles, the second part discusses these theories in connection with cosmological models and observations, thereby exploring which types of signatures of modern and mathematically rigorous frameworks can be detected by experiments. The third and final part briefly reviews the observational status of dark matter and dark energy, and introduces alternative cosmological models. ...
Quantum cosmology - science of Genesis
International Nuclear Information System (INIS)
Padmanabhan, Thanu
1987-01-01
Quantum cosmology, the marriage between the theories of the microscopic and macroscopic Universe, is examined in an attempt to explain the birth of the Universe in the 'big bang'. A quantum cosmological model of the Universe does not exist, but a rough approximation, or 'poor man's' version of quantum cosmology has been developed. The idea is to combine the theory of quantum mechanics with the classical cosmological solutions to obtain a quantum mechanical version of cosmology. Such a model of quantum cosmology is described -here the quantum universe behaves like a hydrogen atom with the Planck length replacing the Bohr radius. Properties of quantum cosmologies and the significance of the Planck length are both discussed. (UK)
Bojowald, Martin
2008-01-01
Quantum gravity is expected to be necessary in order to understand situations in which classical general relativity breaks down. In particular in cosmology one has to deal with initial singularities, i.e., the fact that the backward evolution of a classical spacetime inevitably comes to an end after a finite amount of proper time. This presents a breakdown of the classical picture and requires an extended theory for a meaningful description. Since small length scales and high curvatures are involved, quantum effects must play a role. Not only the singularity itself but also the surrounding spacetime is then modified. One particular theory is loop quantum cosmology, an application of loop quantum gravity to homogeneous systems, which removes classical singularities. Its implications can be studied at different levels. The main effects are introduced into effective classical equations, which allow one to avoid the interpretational problems of quantum theory. They give rise to new kinds of early-universe phenomenology with applications to inflation and cyclic models. To resolve classical singularities and to understand the structure of geometry around them, the quantum description is necessary. Classical evolution is then replaced by a difference equation for a wave function, which allows an extension of quantum spacetime beyond classical singularities. One main question is how these homogeneous scenarios are related to full loop quantum gravity, which can be dealt with at the level of distributional symmetric states. Finally, the new structure of spacetime arising in loop quantum gravity and its application to cosmology sheds light on more general issues, such as the nature of time. Supplementary material is available for this article at 10.12942/lrr-2008-4.
Directory of Open Access Journals (Sweden)
Bojowald Martin
2008-07-01
Full Text Available Quantum gravity is expected to be necessary in order to understand situations in which classical general relativity breaks down. In particular in cosmology one has to deal with initial singularities, i.e., the fact that the backward evolution of a classical spacetime inevitably comes to an end after a finite amount of proper time. This presents a breakdown of the classical picture and requires an extended theory for a meaningful description. Since small length scales and high curvatures are involved, quantum effects must play a role. Not only the singularity itself but also the surrounding spacetime is then modified. One particular theory is loop quantum cosmology, an application of loop quantum gravity to homogeneous systems, which removes classical singularities. Its implications can be studied at different levels. The main effects are introduced into effective classical equations, which allow one to avoid the interpretational problems of quantum theory. They give rise to new kinds of early-universe phenomenology with applications to inflation and cyclic models. To resolve classical singularities and to understand the structure of geometry around them, the quantum description is necessary. Classical evolution is then replaced by a difference equation for a wave function, which allows an extension of quantum spacetime beyond classical singularities. One main question is how these homogeneous scenarios are related to full loop quantum gravity, which can be dealt with at the level of distributional symmetric states. Finally, the new structure of spacetime arising in loop quantum gravity and its application to cosmology sheds light on more general issues, such as the nature of time.
Bojowald, Martin
2015-02-01
In quantum cosmology, one applies quantum physics to the whole universe. While no unique version and no completely well-defined theory is available yet, the framework gives rise to interesting conceptual, mathematical and physical questions. This review presents quantum cosmology in a new picture that tries to incorporate the importance of inhomogeneity. De-emphasizing the traditional minisuperspace view, the dynamics is rather formulated in terms of the interplay of many interacting 'microscopic' degrees of freedom that describe the space-time geometry. There is thus a close relationship with more-established systems in condensed-matter and particle physics even while the large set of space-time symmetries (general covariance) requires some adaptations and new developments. These extensions of standard methods are needed both at the fundamental level and at the stage of evaluating the theory by effective descriptions.
Quantum Gravity Effects in Cosmology
Directory of Open Access Journals (Sweden)
Gu Je-An
2018-01-01
Full Text Available Within the geometrodynamic approach to quantum cosmology, we studied the quantum gravity effects in cosmology. The Gibbons-Hawking temperature is corrected by quantum gravity due to spacetime fluctuations and the power spectrum as well as any probe field will experience the effective temperature, a quantum gravity effect.
Directory of Open Access Journals (Sweden)
Bojowald Martin
2005-12-01
Full Text Available Quantum gravity is expected to be necessary in order to understand situations where classical general relativity breaks down. In particular in cosmology one has to deal with initial singularities, i.e., the fact that the backward evolution of a classical space-time inevitably comes to an end after a finite amount of proper time. This presents a breakdown of the classical picture and requires an extended theory for a meaningful description. Since small length scales and high curvatures are involved, quantum effects must play a role. Not only the singularity itself but also the surrounding space-time is then modified. One particular realization is loop quantum cosmology, an application of loop quantum gravity to homogeneous systems, which removes classical singularities. Its implications can be studied at different levels. Main effects are introduced into effective classical equations which allow to avoid interpretational problems of quantum theory. They give rise to new kinds of early universe phenomenology with applications to inflation and cyclic models. To resolve classical singularities and to understand the structure of geometry around them, the quantum description is necessary. Classical evolution is then replaced by a difference equation for a wave function which allows to extend space-time beyond classical singularities. One main question is how these homogeneous scenarios are related to full loop quantum gravity, which can be dealt with at the level of distributional symmetric states. Finally, the new structure of space-time arising in loop quantum gravity and its application to cosmology sheds new light on more general issues such as time.
Cosmology from quantum potential
Energy Technology Data Exchange (ETDEWEB)
Farag Ali, Ahmed, E-mail: ahmed.ali@fsc.bu.edu.eg [Center for Fundamental Physics, Zewail City of Science and Technology, Giza, 12588 (Egypt); Dept. of Physics, Faculty of Sciences, Benha University, Benha, 13518 (Egypt); Das, Saurya, E-mail: saurya.das@uleth.c [Department of Physics and Astronomy, University of Lethbridge, 4401 University Drive, Lethbridge, Alberta, T1K 3M4 (Canada)
2015-02-04
It was shown recently that replacing classical geodesics with quantal (Bohmian) trajectories gives rise to a quantum corrected Raychaudhuri equation (QRE). In this article we derive the second order Friedmann equations from the QRE, and show that this also contains a couple of quantum correction terms, the first of which can be interpreted as cosmological constant (and gives a correct estimate of its observed value), while the second as a radiation term in the early universe, which gets rid of the big-bang singularity and predicts an infinite age of our universe.
Canonical quantum gravity and consistent discretizations
Indian Academy of Sciences (India)
Abstract. This paper covers some developments in canonical quantum gravity that ... derstanding the real Ashtekar variables four dimensionally [4], or the recent work ... Traditionally, canonical formulations of general relativity considered as canonical variables the metric on a spatial slice qab and a canonically conjugate.
Higher dimensional loop quantum cosmology
International Nuclear Information System (INIS)
Zhang, Xiangdong
2016-01-01
Loop quantum cosmology (LQC) is the symmetric sector of loop quantum gravity. In this paper, we generalize the structure of loop quantum cosmology to the theories with arbitrary spacetime dimensions. The isotropic and homogeneous cosmological model in n + 1 dimensions is quantized by the loop quantization method. Interestingly, we find that the underlying quantum theories are divided into two qualitatively different sectors according to spacetime dimensions. The effective Hamiltonian and modified dynamical equations of n + 1 dimensional LQC are obtained. Moreover, our results indicate that the classical big bang singularity is resolved in arbitrary spacetime dimensions by a quantum bounce. We also briefly discuss the similarities and differences between the n + 1 dimensional model and the 3 + 1 dimensional one. Our model serves as a first example of higher dimensional loop quantum cosmology and offers the possibility to investigate quantum gravity effects in higher dimensional cosmology. (orig.)
International Nuclear Information System (INIS)
Amsterdamski, P.
1986-01-01
The standard cosmological model is reviewed and shown not to be self-sufficient in that it requires initial conditions most likely to be supplied by quantum cosmology. The possible approaches to the issue of initial conditions for cosmology are then discussed. In this thesis, the author considers three separate problems related to this issue. First, the possibility of inflation is investigated in detail by analyzing the evolution of metric perturbations and fluctuations in the expectation value of a scalar field prior to a phase transition; finite temperature effects are also included. Since the inhomogeneities were damped well before the onset of a phase transition. It is concluded that an inflation was possible. Next, the effective action of neutrino and photon fields is calculated for homogeneous spacetimes with small anisotropy; it is shown that quantum corrections to the action due to these fields influence the evolution of an early Universe in the Same way as do the analogous correction terms arising from a conformally invariant scalar which has been previously studied. Finally, the question of an early anisotropy is also discussed in a framework of Hartle-Hawking wave function of the Universe. A wave function of a Bianchi IX type Universe is calculated in a semiclassical approximation
Inflation and quantum cosmology
International Nuclear Information System (INIS)
Linde, A.
1990-01-01
We investigate an interplay between elementary particle physics, quantum cosmology and inflation. These results obtained within this approach are compared with the results obtained in the context of Euclidean quantum cosmology. In particular, we discuss relations between the stochastic approach to inflationary cosmology and the approaches based on the investigation of the Hartle-Hawking and tunneling wave functions of the universe. We argue that neither of these wave functions can be used for a complete description of the inflationary universe, but in certain cases they can be used for a description of some particular stages of inflation. It is shown that if the present vacuum energy density ρ υ exceeds some extremely small critical value ρ c (ρ c ∼ 10 -107 ) g cm -3 for chaotic inflation in the theory 1/2m 2 φ 2 ), then the lifetime of mankind in the inflationary universe should be finite, even though the universe as a whole will exist without end. A possible way to justify the anthropic principle in the context of the baby universe theory and to apply it to the evaluation of masses of elementary particles, of their coupling constants and of the vacuum energy density is also discussed. (author)
Perturbations in loop quantum cosmology
International Nuclear Information System (INIS)
Nelson, W; Agullo, I; Ashtekar, A
2014-01-01
The era of precision cosmology has allowed us to accurately determine many important cosmological parameters, in particular via the CMB. Confronting Loop Quantum Cosmology with these observations provides us with a powerful test of the theory. For this to be possible, we need a detailed understanding of the generation and evolution of inhomogeneous perturbations during the early, quantum gravity phase of the universe. Here, we have described how Loop Quantum Cosmology provides a completion of the inflationary paradigm, that is consistent with the observed power spectra of the CMB
Decoherence in quantum cosmology
International Nuclear Information System (INIS)
Halliwell, J.J.
1989-01-01
We discuss the manner in which the gravitational field becomes classical in quantum cosmology. This involves two steps. First, one must show that the quantum state of the gravitational field becomes strongly peaked about a set of classical configurations. Second, one must show that the system is in one of a number of states of a relatively permanent nature that have negligible interference with each other. This second step involves decoherence---destruction of the off-diagonal terms in the density matrix, representing interference. To introduce the notion of decoherence, we discuss it in the context of the quantum theory of measurement, following the environment-induced superselection approach of Zurek. We then go on to discuss the application of these ideas to quantum cosmology. We show, in a simple homogeneous isotropic model, that the density matrix of the Universe will decohere if the long-wavelength modes of an inhomogeneous massless scalar field are traced out. These modes effectively act as an environment which continuously ''monitors'' the scale factor. The coherence width is very small except in the neighborhood of a classical bounce. This means that one cannot really say that a classical solution bounces because the notion of classical spacetime does not apply. The coherence width decreases as the scale factor increases, which has implications for the arrow of time. We also show, using decoherence arguments, that the WKB component of the wave function of the Universe which represents expanding universes has negligible interference with the collapsing component. This justifies the usual assumption that they may be treated separately
Cosmological quantum entanglement
International Nuclear Information System (INIS)
Martín-Martínez, Eduardo; Menicucci, Nicolas C
2012-01-01
We review recent literature on the connection between quantum entanglement and cosmology, with an emphasis on the context of expanding universes. We discuss recent theoretical results reporting on the production of entanglement in quantum fields due to the expansion of the underlying spacetime. We explore how these results are affected by the statistics of the field (bosonic or fermionic), the type of expansion (de Sitter or asymptotically stationary), and the coupling to spacetime curvature (conformal or minimal). We then consider the extraction of entanglement from a quantum field by coupling to local detectors and how this procedure can be used to distinguish curvature from heating by their entanglement signature. We review the role played by quantum fluctuations in the early universe in nucleating the formation of galaxies and other cosmic structures through their conversion into classical density anisotropies during and after inflation. We report on current literature attempting to account for this transition in a rigorous way and discuss the importance of entanglement and decoherence in this process. We conclude with some prospects for further theoretical and experimental research in this area. These include extensions of current theoretical efforts, possible future observational pursuits, and experimental analogues that emulate these cosmic effects in a laboratory setting. (paper)
Quantum cosmology on the worldsheet
International Nuclear Information System (INIS)
Cooper, A.R.; Susskind, L.; Thorlacius, L.
1991-08-01
Two-dimensional quantum gravity coupled to conformally invariant matter central c > 25 provides a toy model for quantum gravity in four dimensions. Two-dimensional quantum cosmology can thus be studied in terms of string theory in background fields. The large scale cosmological constant depends on non-linear dynamics in the string theory target space and does not appear to be suppressed by wormhole effects. 13 refs
International Nuclear Information System (INIS)
Hartle, J.B.
1990-01-01
Our observations of the world give us specific facts. Here, there is a galaxy; there is none. Today, there is a supernova explosion; yesterday, there was a star. Here, there are fission fragments; before, there was a uranium nucleus. The task of physics is to compress the message which describes these facts into a shorter form -to compress it, in particular, to a form where the message consists of just a few observed facts together with simple universal laws of nature from which the rest can be deduced. In the past, physics has concentrated on finding dynamical laws which correlate facts at different times. Such laws predict later evolution given observed initial conditions. However, there is no logical reason why we could not look for laws which correlate facts at the same time. Such laws would be, in effect, laws of initial conditions. It was the limited nature of our observations which led to our focus on dynamical laws. Now, however, in cosmology, in the observations of the early universe and even on familiar scales, it is possible to discern regularities of the world which may find a compressed expression in a simple, testable, theory of the initial conditions of the universe as a whole. The search for this law of the initial conditions is the subject of quantum cosmology and the subject whose recent development is reviewed. (author)
Evolution in bouncing quantum cosmology
International Nuclear Information System (INIS)
Mielczarek, Jakub; Piechocki, Włodzimierz
2012-01-01
We present the method of describing an evolution in quantum cosmology in the framework of the reduced phase space quantization of loop cosmology. We apply our method to the flat Friedmann-Robertson-Walker model coupled to a massless scalar field. We identify the physical quantum Hamiltonian that is positive-definite and generates globally a unitary evolution of the considered quantum system. We examine the properties of expectation values of physical observables in the process of the quantum big bounce transition. The dispersion of evolved observables is studied for the Gaussian state. Calculated relative fluctuations enable an examination of the semi-classicality conditions and possible occurrence of the cosmic forgetfulness. Preliminary estimations based on the cosmological data suggest that there was no cosmic amnesia. Presented results are analytical, and numerical computations are only used for the visualization purposes. Our method may be generalized to sophisticated cosmological models including the Bianchi-type universes. (paper)
HAWKING'S Theory of Quantum Cosmology
Zhi, Fang Li; Chao, Wu Zhong
The most important problem in cosmology is the birth of the universe. Recently Hartle and Hawking put forward a ground state proposal for the quantum state of the universe which incorporates the idea that the universe must come from nothing. Many models have been discussed in quantum cosmology with this boundary condition. It has been shown that every model is a step towards to a realistic universe, i.e. a 4-dimensional isotropic universe with a long inflationary stage.
Quantum cosmology and baby universes
International Nuclear Information System (INIS)
Grishchuk, L.P.
1990-01-01
The contributed papers presented to the workshop on ''Quantum Cosmology and Baby Universes'' have demonstrated the great interest in, and rapid development of, the field of quantum cosmology. In my view, there are at least three areas of active research at present. The first area can be defined as that of practical calculations. Here researchers are dealing with the basic quantum cosmological equation, which is the Wheeler-DeWitt equation. They try to classify all possible solutions to the Wheeler-DeWitt equation or seek a specific integration contour in order to select one particular wave function or generalize the simple minisuperspace models to more complicated cases, including various inhomogeneities, anisotropies, etc. The second area of research deals with the interpretational issues of quantum cosmology. There are still many questions about how to extract the observational consequences from a given cosmological wave function, the role of time in quantum cosmology, and how to reformulate the rules of quantum mechanics in such a way that they could be applicable to the single system which is our Universe. The third area of research is concerned with the so-called ''third quantization'' of gravity. In this approach a wave function satisfying the Wheeler-DeWitt equation becomes an operator acting on a Wave Function of the many-universes system. Within this approach one operates with Euclidean worm-holes joining different Lorentzian universes. (author)
Thermodynamics in Loop Quantum Cosmology
International Nuclear Information System (INIS)
Li, L.F.; Zhu, J.Y.
2009-01-01
Loop quantum cosmology (LQC) is very powerful to deal with the behavior of early universe. Moreover, the effective loop quantum cosmology gives a successful description of the universe in the semiclassical region. We consider the apparent horizon of the Friedmann-Robertson-Walker universe as a thermodynamical system and investigate the thermodynamics of LQC in the semiclassical region. The effective density and effective pressure in the modified Friedmann equation from LQC not only determine the evolution of the universe in LQC scenario but also are actually found to be the thermodynamic quantities. This result comes from the energy definition in cosmology (the Misner-Sharp gravitational energy) and is consistent with thermodynamic laws. We prove that within the framework of loop quantum cosmology, the elementary equation of equilibrium thermodynamics is still valid.
Chaos, decoherence and quantum cosmology
International Nuclear Information System (INIS)
Calzetta, Esteban
2012-01-01
In this topical review we discuss the connections between chaos, decoherence and quantum cosmology. We understand chaos as classical chaos in systems with a finite number of degrees of freedom, decoherence as environment induced decoherence and quantum cosmology as the theory of the Wheeler-DeWitt equation or else the consistent history formulation thereof, first in mini super spaces and later through its extension to midi super spaces. The overall conclusion is that consideration of decoherence is necessary (and probably sufficient) to sustain an interpretation of quantum cosmology based on the wavefunction of the Universe adopting a Wentzel-Kramers-Brillouin form for large Universes, but a definitive account of the semiclassical transition in classically chaotic cosmological models is not available in the literature yet. (topical review)
Large numbers hypothesis. IV - The cosmological constant and quantum physics
Adams, P. J.
1983-01-01
In standard physics quantum field theory is based on a flat vacuum space-time. This quantum field theory predicts a nonzero cosmological constant. Hence the gravitational field equations do not admit a flat vacuum space-time. This dilemma is resolved using the units covariant gravitational field equations. This paper shows that the field equations admit a flat vacuum space-time with nonzero cosmological constant if and only if the canonical LNH is valid. This allows an interpretation of the LNH phenomena in terms of a time-dependent vacuum state. If this is correct then the cosmological constant must be positive.
Loop quantum cosmology and singularities.
Struyve, Ward
2017-08-15
Loop quantum gravity is believed to eliminate singularities such as the big bang and big crunch singularity. This belief is based on studies of so-called loop quantum cosmology which concerns symmetry-reduced models of quantum gravity. In this paper, the problem of singularities is analysed in the context of the Bohmian formulation of loop quantum cosmology. In this formulation there is an actual metric in addition to the wave function, which evolves stochastically (rather than deterministically as the case of the particle evolution in non-relativistic Bohmian mechanics). Thus a singularity occurs whenever this actual metric is singular. It is shown that in the loop quantum cosmology for a homogeneous and isotropic Friedmann-Lemaître-Robertson-Walker space-time with arbitrary constant spatial curvature and cosmological constant, coupled to a massless homogeneous scalar field, a big bang or big crunch singularity is never obtained. This should be contrasted with the fact that in the Bohmian formulation of the Wheeler-DeWitt theory singularities may exist.
Multiple choices of time in quantum cosmology
International Nuclear Information System (INIS)
Małkiewicz, Przemysław
2015-01-01
It is often conjectured that a choice of time function merely sets up a frame for the quantum evolution of the gravitational field, meaning that all choices should be in some sense compatible. In order to explore this conjecture (and the meaning of compatibility), we develop suitable tools for determining the relation between quantum theories based on different time functions. First, we discuss how a time function fixes a canonical structure on the constraint surface. The presentation includes both the kinematical and the reduced perspective, and the relation between them. Second, we formulate twin theorems about the existence of two inequivalent maps between any two deparameterizations, a formal canonical and a coordinate one. They are used to separate the effects induced by choice of clock and other factors. We show, in an example, how the spectra of quantum observables are transformed under the change of clock and prove, via a general argument, the existence of choice-of-time-induced semiclassical effects. Finally, we study an example, in which we find that the semiclassical discrepancies can in fact be arbitrarily large for dynamical observables. We conclude that the values of critical energy density or critical volume in the bouncing scenarios of quantum cosmology cannot in general be at the Planck scale, and always need to be given with reference to a specific time function. (paper)
Quantum propagation across cosmological singularities
Gielen, Steffen; Turok, Neil
2017-05-01
The initial singularity is the most troubling feature of the standard cosmology, which quantum effects are hoped to resolve. In this paper, we study quantum cosmology with conformal (Weyl) invariant matter. We show that it is natural to extend the scale factor to negative values, allowing a large, collapsing universe to evolve across a quantum "bounce" into an expanding universe like ours. We compute the Feynman propagator for Friedmann-Robertson-Walker backgrounds exactly, identifying curious pathologies in the case of curved (open or closed) universes. We then include anisotropies, fixing the operator ordering of the quantum Hamiltonian by imposing covariance under field redefinitions and again finding exact solutions. We show how complex classical solutions allow one to circumvent the singularity while maintaining the validity of the semiclassical approximation. The simplest isotropic universes sit on a critical boundary, beyond which there is qualitatively different behavior, with potential for instability. Additional scalars improve the theory's stability. Finally, we study the semiclassical propagation of inhomogeneous perturbations about the flat, isotropic case, at linear and nonlinear order, showing that, at least at this level, there is no particle production across the bounce. These results form the basis for a promising new approach to quantum cosmology and the resolution of the big bang singularity.
Twistor Cosmology and Quantum Space-Time
International Nuclear Information System (INIS)
Brody, D.C.; Hughston, L.P.
2005-01-01
The purpose of this paper is to present a model of a 'quantum space-time' in which the global symmetries of space-time are unified in a coherent manner with the internal symmetries associated with the state space of quantum-mechanics. If we take into account the fact that these distinct families of symmetries should in some sense merge and become essentially indistinguishable in the unified regime, our framework may provide an approximate description of or elementary model for the structure of the universe at early times. The quantum elements employed in our characterisation of the geometry of space-time imply that the pseudo-Riemannian structure commonly regarded as an essential feature in relativistic theories must be dispensed with. Nevertheless, the causal structure and the physical kinematics of quantum space-time are shown to persist in a manner that remains highly analogous to the corresponding features of the classical theory. In the case of the simplest conformally flat cosmological models arising in this framework, the twistorial description of quantum space-time is shown to be effective in characterising the various physical and geometrical properties of the theory. As an example, a sixteen-dimensional analogue of the Friedmann-Robertson-Walker cosmologies is constructed, and its chronological development is analysed in some detail. More generally, whenever the dimension of a quantum space-time is an even perfect square, there exists a canonical way of breaking the global quantum space-time symmetry so that a generic point of quantum space-time can be consistently interpreted as a quantum operator taking values in Minkowski space. In this scenario, the breakdown of the fundamental symmetry of the theory is due to a loss of quantum entanglement between space-time and internal quantum degrees of freedom. It is thus possible to show in a certain specific sense that the classical space-time description is an emergent feature arising as a consequence of a
Decoherence in quantum mechanics and quantum cosmology
Hartle, James B.
1992-01-01
A sketch of the quantum mechanics for closed systems adequate for cosmology is presented. This framework is an extension and clarification of that of Everett and builds on several aspects of the post-Everett development. It especially builds on the work of Zeh, Zurek, Joos and Zeh, and others on the interactions of quantum systems with the larger universe and on the ideas of Griffiths, Omnes, and others on the requirements for consistent probabilities of histories.
Quantum transitions through cosmological singularities
Energy Technology Data Exchange (ETDEWEB)
Bramberger, Sebastian F.; Lehners, Jean-Luc [Max Planck Institute for Gravitational Physics (Albert Einstein Institute), 14476 Potsdam-Golm (Germany); Hertog, Thomas; Vreys, Yannick, E-mail: sebastian.bramberger@aei.mpg.de, E-mail: thomas.hertog@kuleuven.be, E-mail: jlehners@aei.mpg.de, E-mail: yannick.vreys@kuleuven.be [Institute for Theoretical Physics, KU Leuven, 3001 Leuven (Belgium)
2017-07-01
In a quantum theory of cosmology spacetime behaves classically only in limited patches of the configuration space on which the wave function of the universe is defined. Quantum transitions can connect classical evolution in different patches. Working in the saddle point approximation and in minisuperspace we compute quantum transitions connecting inflationary histories across a de Sitter like throat or a singularity. This supplies probabilities for how an inflating universe, when evolved backwards, transitions and branches into an ensemble of histories on the opposite side of a quantum bounce. Generalising our analysis to scalar potentials with negative regions we identify saddle points describing a quantum transition between a classically contracting, crunching ekpyrotic phase and an inflationary universe.
Quantum transitions through cosmological singularities
International Nuclear Information System (INIS)
Bramberger, Sebastian F.; Lehners, Jean-Luc; Hertog, Thomas; Vreys, Yannick
2017-01-01
In a quantum theory of cosmology spacetime behaves classically only in limited patches of the configuration space on which the wave function of the universe is defined. Quantum transitions can connect classical evolution in different patches. Working in the saddle point approximation and in minisuperspace we compute quantum transitions connecting inflationary histories across a de Sitter like throat or a singularity. This supplies probabilities for how an inflating universe, when evolved backwards, transitions and branches into an ensemble of histories on the opposite side of a quantum bounce. Generalising our analysis to scalar potentials with negative regions we identify saddle points describing a quantum transition between a classically contracting, crunching ekpyrotic phase and an inflationary universe.
Conformal constraint in canonical quantum gravity
t Hooft, G.
2010-01-01
Perturbative canonical quantum gravity is considered, when coupled to a renormalizable model for matter fields. It is proposed that the functional integral over the dilaton field should be disentangled from the other integrations over the metric fields. This should generate a conformally invariant
From quantum cosmology to quantum gravity
International Nuclear Information System (INIS)
Englert, F.
1983-01-01
A theory is proposed which solves the problem of the acausal character of the hot big bang cosmology in general relativity. The initial thermal state is stabilized by constructing a semi-classical solution to the coupled graviation and matter system with zero cosmological constant. This solution is an expanding deSitter in which black holes are created by a quantum process out of the expansion energy. It is argued that the initial nucleation process originates from a quantum metric fluctuation. Universe-like configurations must be added over the path integral metrics. This stabilizes the path integral and saturates it with a ''foam of universes'' where the nonrenormalizability of gravity can be seen as the manifestation of long range interactions within a universe. This description introduces indeterminacy into quantum field theory and suggests that 4-D space-time should be explained by new concepts
New ekpyrotic quantum cosmology
Energy Technology Data Exchange (ETDEWEB)
Lehners, Jean-Luc, E-mail: jlehners@aei.mpg.de
2015-11-12
Ekpyrotic instantons describe the emergence of classical contracting universes out of the no-boundary quantum state. However, up to now these instantons ended in a big crunch singularity. We remedy this by adding a higher-derivative term, allowing a ghost condensate to form. This causes a smooth, non-singular bounce from the contracting phase into an expanding, kinetic-dominated phase. Remarkably, and although there is a non-trivial evolution during the bounce, the wavefunction of the universe is “classical” in a WKB sense just as much after the bounce as before. These new non-singular instantons can thus form the basis for a fully non-singular and calculable ekpyrotic history of the universe, from creation until now.
New ekpyrotic quantum cosmology
Directory of Open Access Journals (Sweden)
Jean-Luc Lehners
2015-11-01
Full Text Available Ekpyrotic instantons describe the emergence of classical contracting universes out of the no-boundary quantum state. However, up to now these instantons ended in a big crunch singularity. We remedy this by adding a higher-derivative term, allowing a ghost condensate to form. This causes a smooth, non-singular bounce from the contracting phase into an expanding, kinetic-dominated phase. Remarkably, and although there is a non-trivial evolution during the bounce, the wavefunction of the universe is “classical” in a WKB sense just as much after the bounce as before. These new non-singular instantons can thus form the basis for a fully non-singular and calculable ekpyrotic history of the universe, from creation until now.
Cosmological footprints of loop quantum gravity.
Grain, J; Barrau, A
2009-02-27
The primordial spectrum of cosmological tensor perturbations is considered as a possible probe of quantum gravity effects. Together with string theory, loop quantum gravity is one of the most promising frameworks to study quantum effects in the early universe. We show that the associated corrections should modify the potential seen by gravitational waves during the inflationary amplification. The resulting power spectrum should exhibit a characteristic tilt. This opens a new window for cosmological tests of quantum gravity.
Time evolution in quantum cosmology
International Nuclear Information System (INIS)
Lawrie, Ian D.
2011-01-01
A commonly adopted relational account of time evolution in generally covariant systems, and more specifically in quantum cosmology, is argued to be unsatisfactory, insofar as it describes evolution relative to observed readings of a clock that does not exist as a bona fide observable object. A modified strategy is proposed, in which evolution relative to the proper time that elapses along the worldline of a specific observer can be described through the introduction of a ''test clock,'' regarded as internal to, and hence unobservable by, that observer. This strategy is worked out in detail in the case of a homogeneous cosmology, in the context of both a conventional Schroedinger quantization scheme, and a 'polymer' quantization scheme of the kind inspired by loop quantum gravity. Particular attention is given to limitations placed on the observability of time evolution by the requirement that a test clock should contribute only a negligible energy to the Hamiltonian constraint. It is found that suitable compromises are available, in which the clock energy is reasonably small, while Dirac observables are reasonably sharply defined.
Quantum canonical ensemble: A projection operator approach
Magnus, Wim; Lemmens, Lucien; Brosens, Fons
2017-09-01
Knowing the exact number of particles N, and taking this knowledge into account, the quantum canonical ensemble imposes a constraint on the occupation number operators. The constraint particularly hampers the systematic calculation of the partition function and any relevant thermodynamic expectation value for arbitrary but fixed N. On the other hand, fixing only the average number of particles, one may remove the above constraint and simply factorize the traces in Fock space into traces over single-particle states. As is well known, that would be the strategy of the grand-canonical ensemble which, however, comes with an additional Lagrange multiplier to impose the average number of particles. The appearance of this multiplier can be avoided by invoking a projection operator that enables a constraint-free computation of the partition function and its derived quantities in the canonical ensemble, at the price of an angular or contour integration. Introduced in the recent past to handle various issues related to particle-number projected statistics, the projection operator approach proves beneficial to a wide variety of problems in condensed matter physics for which the canonical ensemble offers a natural and appropriate environment. In this light, we present a systematic treatment of the canonical ensemble that embeds the projection operator into the formalism of second quantization while explicitly fixing N, the very number of particles rather than the average. Being applicable to both bosonic and fermionic systems in arbitrary dimensions, transparent integral representations are provided for the partition function ZN and the Helmholtz free energy FN as well as for two- and four-point correlation functions. The chemical potential is not a Lagrange multiplier regulating the average particle number but can be extracted from FN+1 -FN, as illustrated for a two-dimensional fermion gas.
Newtonian cosmology with a quantum bounce
Energy Technology Data Exchange (ETDEWEB)
Bargueno, P.; Bravo Medina, S.; Nowakowski, M. [Universidad de los Andes, Departamento de Fisica, Bogota (Colombia); Batic, D. [University of West Indies, Department of Mathematics, Kingston 6 (Jamaica)
2016-10-15
It has been known for some time that the cosmological Friedmann equation deduced from general relativity can also be obtained within the Newtonian framework under certain assumptions. We use this result together with quantum corrections to the Newtonian potentials to derive a set a of quantum corrected Friedmann equations. We examine the behavior of the solutions of these modified cosmological equations paying special attention to the sign of the quantum corrections. We find different quantum effects crucially depending on this sign. One such a solution displays a qualitative resemblance to other quantum models like Loop quantum gravity or non-commutative geometry. (orig.)
Canonical Quantum Teleportation of Two-Particle Arbitrary State
Institute of Scientific and Technical Information of China (English)
HAO Xiang; ZHU Shi-Qun
2005-01-01
The canonical quantum teleportation of two-particle arbitrary state is realized by means of phase operator and number operator. The maximally entangled eigenstates between the difference of phase operators and the sum of number operators are considered as the quantum channels. In contrast to the standard quantum teleportation, the different unitary local operation of canonical teleportation can be simplified by a general expression.
Kato expansion in quantum canonical perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Nikolaev, Andrey, E-mail: Andrey.Nikolaev@rdtex.ru [Institute of Computing for Physics and Technology, Protvino, Moscow Region, Russia and RDTeX LTD, Moscow (Russian Federation)
2016-06-15
This work establishes a connection between canonical perturbation series in quantum mechanics and a Kato expansion for the resolvent of the Liouville superoperator. Our approach leads to an explicit expression for a generator of a block-diagonalizing Dyson’s ordered exponential in arbitrary perturbation order. Unitary intertwining of perturbed and unperturbed averaging superprojectors allows for a description of ambiguities in the generator and block-diagonalized Hamiltonian. We compare the efficiency of the corresponding computational algorithm with the efficiencies of the Van Vleck and Magnus methods for high perturbative orders.
Kato expansion in quantum canonical perturbation theory
International Nuclear Information System (INIS)
Nikolaev, Andrey
2016-01-01
This work establishes a connection between canonical perturbation series in quantum mechanics and a Kato expansion for the resolvent of the Liouville superoperator. Our approach leads to an explicit expression for a generator of a block-diagonalizing Dyson’s ordered exponential in arbitrary perturbation order. Unitary intertwining of perturbed and unperturbed averaging superprojectors allows for a description of ambiguities in the generator and block-diagonalized Hamiltonian. We compare the efficiency of the corresponding computational algorithm with the efficiencies of the Van Vleck and Magnus methods for high perturbative orders.
Horizon-preserving dualities and perturbations in non-canonical scalar field cosmologies
International Nuclear Information System (INIS)
Geshnizjani, Ghazal; Kinney, William H.; Dizgah, Azadeh Moradinezhad
2012-01-01
We generalize the cosmological duality between inflation and cyclic contraction under the interchange a↔H to the case of non-canonical scalar field theories with varying speed of sound. The single duality in the canonical case generalizes to a family of three dualities constructed to leave the cosmological acoustic horizon invariant. We find three classes of models: (I) DBI inflation, (II) the non-canonical generalization of cyclic contraction, and (III) a new cosmological solution with rapidly decreasing speed of sound and relatively slowly growing scale factor, which we dub stalled cosmology. We construct dual analogs to the inflationary slow roll approximation, and solve for the curvature perturbation in all three cases. Both cyclic contraction and stalled cosmology predict a strongly blue spectrum for the curvature perturbations inconsistent with observations
Canonical transformations in problems of quantum statistical mechanics
International Nuclear Information System (INIS)
Sankovich, D.P.
1985-01-01
The problem of general canonical transformations in quantum systems possessing a classical analog is considered. The main role plays the Weyl representation of dynamic variables of the quantum system considered. One managed to build a general diagram of canonical transformations in a quantum case and to develop a method for reducing one or another operator to the simplest canonical form. In this case the procedure, being analogous to the Poincare-Birkhof normalization based on the Lie series theory, occurs
Wave packets in quantum cosmology and the cosmological constant
International Nuclear Information System (INIS)
Kiefer, C.
1990-01-01
Wave packets are constructed explicitly in minisuperspace of quantum gravity corresponding to a Friedmann universe containing a conformally coupled scalar field with and without a cosmological constant. The construction is performed in close analogy to the case of constructing coherent states in quantum mechanics. Various examples are also depicted numerically. The corresponding lorentzian path integrals are evaluated for some cases. It is emphasized that the new concept of time in quantum gravity demands the imposition of a kind of boundary conditions not encountered in quantum gravity demands the imposition of a kind of boundary conditions not encountered in quantum mechanics. Connection is also made to recent investigations predicting a vanishing cosmological constant. It is shown that the fact of whether this result is generic or not depends on where the boundary conditions are imposed in the configuration space. (orig.)
Nonlocal Quantum Effects in Cosmology
Directory of Open Access Journals (Sweden)
Yurii V. Dumin
2014-01-01
Full Text Available Since it is commonly believed that the observed large-scale structure of the universe is an imprint of quantum fluctuations existing at the very early stage of its evolution, it is reasonable to pose the question: do the effects of quantum nonlocality, which are well established now by the laboratory studies, manifest themselves also in the early universe? We try to answer this question by utilizing the results of a few experiments, namely, with the superconducting multi-Josephson-junction loops and the ultracold gases in periodic potentials. Employing a close analogy between the above-mentioned setups and the simplest one-dimensional Friedmann-Robertson-Walker cosmological model, we show that the specific nonlocal correlations revealed in the laboratory studies might be of considerable importance also in treating the strongly nonequilibrium phase transitions of Higgs fields in the early universe. Particularly, they should substantially reduce the number of topological defects (e.g., domain walls expected due to independent establishment of the new phases in the remote spatial regions. This gives us a hint on resolving a long-standing problem of the excessive concentration of topological defects, inconsistent with observational constraints. The same effect may be also relevant to the recent problem of the anomalous behavior of cosmic microwave background fluctuations at large angular scales.
Quantum Gravity and Cosmology: an intimate interplay
Sakellariadou, Mairi
2017-08-01
I will briefly discuss three cosmological models built upon three distinct quantum gravity proposals. I will first highlight the cosmological rôle of a vector field in the framework of a string/brane cosmological model. I will then present the resolution of the big bang singularity and the occurrence of an early era of accelerated expansion of a geometric origin, in the framework of group field theory condensate cosmology. I will then summarise results from an extended gravitational model based on non-commutative spectral geometry, a model that offers a purely geometric explanation for the standard model of particle physics.
Topics in quantum field theory and cosmology
International Nuclear Information System (INIS)
Brandenberger, R.H.
1983-01-01
This thesis contains a study of topics in quantum field theory and cosmology in the context of the new inflationary universe scenario. It presents a review of the quantum field theory methods used in the new cosmological models. The following chapters are a detailed study of energy density fluctuations in the early universe. Hawking radiation is derived as the source of initial perturbations in two complementary ways. The following section presents a new gauge invariant framework to study the growth of fluctuations outside the horizon. This framework is applied to the new inflationary universe in the final chapter. The introduction gives a brief outline of the new cosmological models
Nonsingular cosmology from evolutionary quantum gravity
Cianfrani, Francesco; Montani, Giovanni; Pittorino, Fabrizio
2014-11-01
We provide a cosmological implementation of the evolutionary quantum gravity, describing an isotropic Universe, in the presence of a negative cosmological constant and a massive (preinflationary) scalar field. We demonstrate that the considered Universe has a nonsingular quantum behavior, associated to a primordial bounce, whose ground state has a high occupation number. Furthermore, in such a vacuum state, the super-Hamiltonian eigenvalue is negative, corresponding to a positive emerging dust energy density. The regularization of the model is performed via a polymer quantum approach to the Universe scale factor and the proper classical limit is then recovered, in agreement with a preinflationary state of the Universe. Since the dust energy density is redshifted by the Universe de Sitter phase and the cosmological constant does not enter the ground state eigenvalue, we get a late-time cosmology, compatible with the present observations, endowed with a turning point in the far future.
Quantum cosmology and late-time singularities
International Nuclear Information System (INIS)
Kamenshchik, A Yu
2013-01-01
The development of dark energy models has stimulated interest to cosmological singularities, which differ from the traditional Big Bang and Big Crunch singularities. We review a broad class of phenomena connected with soft cosmological singularities in classical and quantum cosmology. We discuss the classification of singularities from the geometrical point of view and from the point of view of the behavior of finite size objects, crossing such singularities. We discuss in some detail quantum and classical cosmology of models based on perfect fluids (anti-Chaplygin gas and anti-Chaplygin gas plus dust), of models based on the Born–Infeld-type fields and of the model of a scalar field with a potential inversely proportional to the field itself. We dwell also on the phenomenon of the phantom divide line crossing in the scalar field models with cusped potentials. Then we discuss the Friedmann equations modified by quantum corrections to the effective action of the models under considerations and the influence of such modification on the nature and the existence of soft singularities. We review also quantum cosmology of models, where the initial quantum state of the universe is presented by the density matrix (mixed state). Finally, we discuss the exotic singularities arising in the braneworld cosmological models. (topical review)
2-point functions in quantum cosmology
International Nuclear Information System (INIS)
Gielen, Steffen
2012-01-01
We discuss the path-integral formulation of quantum cosmology with a massless scalar field as a sum-over-histories, with particular reference to loop quantum cosmology. Exploiting the analogy with the relativistic particle, we give a complete overview of the possible two-point functions, deriving vertex expansions and composition laws they satisfy. We clarify the tie between definitions using a group averaging procedure and those in a deparametrised framework. We draw some conclusions about the physics of a single quantum universe and multiverse field theories where the role of these sectors and the inner product are reinterpreted.
Loop quantum cosmology of the Bianchi I model: complete quantization
International Nuclear Information System (INIS)
Martín-Benito, M; Garay, L J; Mena Marugán, G A; Wilson-Ewing, E
2012-01-01
We complete the canonical quantization of the vacuum Bianchi I model within the improved dynamics scheme of loop quantum cosmology, characterizing the Hilbert structure of the physical states and providing a complete set of observables acting on them. In order to achieve this task, it has been essential to determine the structure of the separable superselection sectors that arise owing to the polymeric quantization, and to prove that the initial value problem obtained when regarding the Hamiltonian constraint as an evolution equation, interpreting the volume as the evolution parameter, is well-posed.
Time and prediction in quantum cosmology
International Nuclear Information System (INIS)
Hartle, J.B.
1989-01-01
In this paper a generalized quantum mechanics for cosmological spacetimes is suggested in which no variable plays the special role of the time of familiar quantum mechanics. In this generalization the central role of time in familiar quantum mechanics arises, not at a fundamental aspect of the formalism, but rather as an approximation appropriate to those initial conditions of the universe which lead to classical spacetime when it is large
Cosmological perturbation theory and quantum gravity
Energy Technology Data Exchange (ETDEWEB)
Brunetti, Romeo [Dipartimento di Matematica, Università di Trento,Via Sommarive 14, 38123 Povo TN (Italy); Fredenhagen, Klaus [II Institute für Theoretische Physik, Universität Hamburg,Luruper Chaussee 149, 22761 Hamburg (Germany); Hack, Thomas-Paul [Institute für Theoretische Physik, Universität Leipzig,Brüderstr. 16, 04103 Leipzig (Germany); Pinamonti, Nicola [Dipartimento di Matematica, Università di Genova,Via Dodecaneso 35, 16146 Genova (Italy); INFN, Sezione di Genova,Via Dodecaneso 33, 16146 Genova (Italy); Rejzner, Katarzyna [Department of Mathematics, University of York,Heslington, York YO10 5DD (United Kingdom)
2016-08-04
It is shown how cosmological perturbation theory arises from a fully quantized perturbative theory of quantum gravity. Central for the derivation is a non-perturbative concept of gauge-invariant local observables by means of which perturbative invariant expressions of arbitrary order are generated. In particular, in the linearised theory, first order gauge-invariant observables familiar from cosmological perturbation theory are recovered. Explicit expressions of second order quantities are presented as well.
Canonical methods in classical and quantum gravity: An invitation to canonical LQG
Reyes, Juan D.
2018-04-01
Loop Quantum Gravity (LQG) is a candidate quantum theory of gravity still under construction. LQG was originally conceived as a background independent canonical quantization of Einstein’s general relativity theory. This contribution provides some physical motivations and an overview of some mathematical tools employed in canonical Loop Quantum Gravity. First, Hamiltonian classical methods are reviewed from a geometric perspective. Canonical Dirac quantization of general gauge systems is sketched next. The Hamiltonian formultation of gravity in geometric ADM and connection-triad variables is then presented to finally lay down the canonical loop quantization program. The presentation is geared toward advanced undergradute or graduate students in physics and/or non-specialists curious about LQG.
Quantum cosmology with R + R sup 2 gravity
Sanyal, A K
2002-01-01
Canonical quantization of an action containing a curvature-squared term requires the introduction of an auxiliary variable. Boulware and coworkers prescribed a technique to choose such a variable, by taking the derivative of the action with respect to the highest derivative of the field variable, present in the action. It has been shown that this technique can even be applied in situations where the introduction of auxiliary variables is not required, leading to the wrong Wheeler-De Witt equation. It has also been pointed out that Boulware's prescription should be taken up only after removing all possible total derivative terms from the action. Once this is done only a unique description of quantum dynamics would emerge. For the curvature-squared term this technique yields, for the first time, a quantum mechanical probability interpretation of quantum cosmology, and an effective potential whose extremization leads to Einstein's equation. We conclude that the Einstein-Hilbert action should essentially be modif...
Dilaton quantum cosmology in two dimensions
International Nuclear Information System (INIS)
Mazzitelli, F.D.; Russo, J.G.
1992-11-01
We consider a renormalizable two-dimensional model of dilaton gravity coupled to a set of conformal fields as a toy model for quantum cosmology. We discuss the cosmological solutions of the model and study the effect of including the back reaction due to quantum corrections. As a result, when the matter density is below some threshold new singularities form in a weak coupling region, which suggests that they will not be removed in full quantum theory. We also solve the Wheeler-DeWitt equation. Depending on the quantum state of the Universe, the singularities may appear in a quantum region where the wave function is not oscillatory, i.e., when there is not a well defined notion of classical spacetime. (author). 29 refs, 4 figs
Canonical quantum theory of gravitational field with higher derivatives, 3
International Nuclear Information System (INIS)
Kawasaki, Shoichiro; Kimura, Tadahiko
1983-01-01
A formulation which is invariant under an additional BRS transformation with nilpotency of order two is presented for the canonical theory of the renormalizable quantum gravity with higher derivatives. The canonical quantization is carried out and various equal time (anti-) commutation relations are derived. The asymptotic fields are reanalyzed. The physical particle contents are just the same as those obtained in previous papers. (author)
Canonical ensembles and nonzero density quantum chromodynamics
International Nuclear Information System (INIS)
Hasenfratz, A.; Toussaint, D.
1992-01-01
We study QCD with nonzero chemical potential on 4 4 lattices by averaging over the canonical partition functions, or sectors with fixed quark number. We derive a condensed matrix of size 2x3xL 3 whose eigenvalues can be used to find the canonical partition functions. We also experiment with a weight for configuration generation which respects the Z(3) symmetry which forces the canonical partition function to be zero for quark numbers that are not multiples of three. (orig.)
Observational constraints on loop quantum cosmology.
Bojowald, Martin; Calcagni, Gianluca; Tsujikawa, Shinji
2011-11-18
In the inflationary scenario of loop quantum cosmology in the presence of inverse-volume corrections, we give analytic formulas for the power spectra of scalar and tensor perturbations convenient to compare with observations. Since inverse-volume corrections can provide strong contributions to the running spectral indices, inclusion of terms higher than the second-order runnings in the power spectra is crucially important. Using the recent data of cosmic microwave background and other cosmological experiments, we place bounds on the quantum corrections.
Loop quantum cosmology: a status report
International Nuclear Information System (INIS)
Ashtekar, Abhay; Singh, Parampreet
2011-01-01
Loop quantum cosmology (LQC) is the result of applying principles of loop quantum gravity (LQG) to cosmological settings. The distinguishing feature of LQC is the prominent role played by the quantum geometry effects of LQG. In particular, quantum geometry creates a brand new repulsive force which is totally negligible at low spacetime curvature but rises very rapidly in the Planck regime, overwhelming the classical gravitational attraction. In cosmological models, while Einstein's equations hold to an excellent degree of approximation at low curvature, they undergo major modifications in the Planck regime: for matter satisfying the usual energy conditions, any time a curvature invariant grows to the Planck scale, quantum geometry effects dilute it, thereby resolving singularities of general relativity. Quantum geometry corrections become more sophisticated as the models become richer. In particular, in anisotropic models, there are significant changes in the dynamics of shear potentials which tame their singular behavior in striking contrast to older results on anisotropies in bouncing models. Once singularities are resolved, the conceptual paradigm of cosmology changes and one has to revisit many of the standard issues-e.g. the 'horizon problem'-from a new perspective. Such conceptual issues as well as potential observational consequences of the new Planck scale physics are being explored, especially within the inflationary paradigm. These considerations have given rise to a burst of activity in LQC in recent years, with contributions from quantum gravity experts, mathematical physicists and cosmologists. The goal of this review is to provide an overview of the current state of the art in LQC for three sets of audiences: young researchers interested in entering this area; the quantum gravity community in general and cosmologists who wish to apply LQC to probe modifications in the standard paradigm of the early universe. In this review, effort has been made to
Cosmological constant in the quantum multiverse
International Nuclear Information System (INIS)
Larsen, Grant; Nomura, Yasunori; Roberts, Hannes L. L.
2011-01-01
Recently, a new framework for describing the multiverse has been proposed which is based on the principles of quantum mechanics. The framework allows for well-defined predictions, both regarding global properties of the universe and outcomes of particular experiments, according to a single probability formula. This provides complete unification of the eternally inflating multiverse and many worlds in quantum mechanics. In this paper, we elucidate how cosmological parameters can be calculated in this framework, and study the probability distribution for the value of the cosmological constant. We consider both positive and negative values, and find that the observed value is consistent with the calculated distribution at an order of magnitude level. In particular, in contrast to the case of earlier measure proposals, our framework prefers a positive cosmological constant over a negative one. These results depend only moderately on how we model galaxy formation and life evolution therein.
Quantum cosmology and the early universe
International Nuclear Information System (INIS)
Hartle, J.B.
1983-01-01
Despite the absence of a complete and manageable quantum theory of gravity, it is shown that considerable progress has been made in constructing cosmological models displaying the possible implications such a theory might have for the structure and dynamics of the very early universe. (U.K.)
Consistent probabilities in loop quantum cosmology
International Nuclear Information System (INIS)
Craig, David A; Singh, Parampreet
2013-01-01
A fundamental issue for any quantum cosmological theory is to specify how probabilities can be assigned to various quantum events or sequences of events such as the occurrence of singularities or bounces. In previous work, we have demonstrated how this issue can be successfully addressed within the consistent histories approach to quantum theory for Wheeler–DeWitt-quantized cosmological models. In this work, we generalize that analysis to the exactly solvable loop quantization of a spatially flat, homogeneous and isotropic cosmology sourced with a massless, minimally coupled scalar field known as sLQC. We provide an explicit, rigorous and complete decoherent-histories formulation for this model and compute the probabilities for the occurrence of a quantum bounce versus a singularity. Using the scalar field as an emergent internal time, we show for generic states that the probability for a singularity to occur in this model is zero, and that of a bounce is unity, complementing earlier studies of the expectation values of the volume and matter density in this theory. We also show from the consistent histories point of view that all states in this model, whether quantum or classical, achieve arbitrarily large volume in the limit of infinite ‘past’ or ‘future’ scalar ‘time’, in the sense that the wave function evaluated at any arbitrary fixed value of the volume vanishes in that limit. Finally, we briefly discuss certain misconceptions concerning the utility of the consistent histories approach in these models. (paper)
From Classical to Quantum: New Canonical Tools for the Dynamics of Gravity
Höhn, P. A.
2012-05-01
second part of this thesis, the paradigm of relational dynamics is considered. Dynamical observables in gravity are relational. Unfortunately, their construction and evaluation is notoriously difficult, especially in the quantum theory. An effective canonical framework is devised which permits to evaluate the semiclassical relational dynamics of constrained quantum systems by sidestepping technical problems associated with explicit constructions of physical Hilbert spaces. This effective approach is well-geared for addressing the concept of relational evolution in general quantum cosmological models since it (i) allows to depart from idealized relational `clock references’ and, instead, to employ generic degrees of freedom as imperfect relational `clocks’, (ii) enables one to systematically switch between different such `clocks’ and (iii) yields a consistent (temporally) local time evolution with transient observables so long as semiclassicality holds. These techniques are illustrated by toy models and, finally, are applied to a non-integrable cosmological model. It is argued that relational evolution is generically only a transient and semiclassical phenomenon
Inhomogenous loop quantum cosmology with matter
International Nuclear Information System (INIS)
Martín-de Bias, D; Mena Marugán, G A; Martín-Benito, M
2012-01-01
The linearly polarized Gowdy T 3 model with a massless scalar field with the same symmetries as the metric is quantized by applying a hybrid approach. The homogeneous geometry degrees of freedom are loop quantized, fact which leads to the resolution of the cosmological singularity, while a Fock quantization is employed for both matter and gravitational inhomogeneities. Owing to the inclusion of the massless scalar field this system allows us to modelize flat Friedmann-Robertson-Walker cosmologies filled with inhomogeneities propagating in one direction. It provides a perfect scenario to study the quantum back-reaction between the inhomogeneities and the polymeric homogeneous and isotropic background.
Zhou, Chi-Chun; Dai, Wu-Sheng
2018-02-01
In statistical mechanics, for a system with a fixed number of particles, e.g. a finite-size system, strictly speaking, the thermodynamic quantity needs to be calculated in the canonical ensemble. Nevertheless, the calculation of the canonical partition function is difficult. In this paper, based on the mathematical theory of the symmetric function, we suggest a method for the calculation of the canonical partition function of ideal quantum gases, including ideal Bose, Fermi, and Gentile gases. Moreover, we express the canonical partition functions of interacting classical and quantum gases given by the classical and quantum cluster expansion methods in terms of the Bell polynomial in mathematics. The virial coefficients of ideal Bose, Fermi, and Gentile gases are calculated from the exact canonical partition function. The virial coefficients of interacting classical and quantum gases are calculated from the canonical partition function by using the expansion of the Bell polynomial, rather than calculated from the grand canonical potential.
Quantum cosmology and stationary states
International Nuclear Information System (INIS)
Padmanabhan, T.
1983-01-01
A model for quantum gravity, in which the conformal part of the metric is quantized using the path integral formalism, is presented. Einstein's equations can be suitably modified to take into account the effects of quantum conformal fluctuations. A closed Friedman model can be described in terms of well-defined stationary states. The ''ground state'' sets a lower bound (at Planck length) to the scale factor preventing the collapse. A possible explanation for matter creation and quantum nature of matter is suggested. (author)
Covariant entropy bound and loop quantum cosmology
International Nuclear Information System (INIS)
Ashtekar, Abhay; Wilson-Ewing, Edward
2008-01-01
We examine Bousso's covariant entropy bound conjecture in the context of radiation filled, spatially flat, Friedmann-Robertson-Walker models. The bound is violated near the big bang. However, the hope has been that quantum gravity effects would intervene and protect it. Loop quantum cosmology provides a near ideal setting for investigating this issue. For, on the one hand, quantum geometry effects resolve the singularity and, on the other hand, the wave function is sharply peaked at a quantum corrected but smooth geometry, which can supply the structure needed to test the bound. We find that the bound is respected. We suggest that the bound need not be an essential ingredient for a quantum gravity theory but may emerge from it under suitable circumstances.
Quantum cosmological relational model of shape and scale in 1D
International Nuclear Information System (INIS)
Anderson, Edward
2011-01-01
Relational particle models are useful toy models for quantum cosmology and the problem of time in quantum general relativity. This paper shows how to extend existing work on concrete examples of relational particle models in 1D to include a notion of scale. This is useful as regards forming a tight analogy with quantum cosmology and the emergent semiclassical time and hidden time approaches to the problem of time. This paper shows furthermore that the correspondence between relational particle models and classical and quantum cosmology can be strengthened using judicious choices of the mechanical potential. This gives relational particle mechanics models with analogues of spatial curvature, cosmological constant, dust and radiation terms. A number of these models are then tractable at the quantum level. These models can be used to study important issues (1) in canonical quantum gravity: the problem of time, the semiclassical approach to it and timeless approaches to it (such as the naive Schroedinger interpretation and records theory) and (2) in quantum cosmology, such as in the investigation of uniform states, robustness and the qualitative understanding of the origin of structure formation.
Bouncing cosmologies from quantum gravity condensates
Oriti, Daniele; Sindoni, Lorenzo; Wilson-Ewing, Edward
2017-02-01
We show how the large-scale cosmological dynamics can be obtained from the hydrodynamics of isotropic group field theory condensate states in the Gross-Pitaevskii approximation. The correct Friedmann equations are recovered in the classical limit for some choices of the parameters in the action for the group field theory, and quantum gravity corrections arise in the high-curvature regime causing a bounce which generically resolves the big-bang and big-crunch singularities.
Positive Cosmological Constant and Quantum Theory
Directory of Open Access Journals (Sweden)
Felix M. Lev
2010-11-01
Full Text Available We argue that quantum theory should proceed not from a spacetime background but from a Lie algebra, which is treated as a symmetry algebra. Then the fact that the cosmological constant is positive means not that the spacetime background is curved but that the de Sitter (dS algebra as the symmetry algebra is more relevant than the Poincare or anti de Sitter ones. The physical interpretation of irreducible representations (IRs of the dS algebra is considerably different from that for the other two algebras. One IR of the dS algebra splits into independent IRs for a particle and its antiparticle only when Poincare approximation works with a high accuracy. Only in this case additive quantum numbers such as electric, baryon and lepton charges are conserved, while at early stages of the Universe they could not be conserved. Another property of IRs of the dS algebra is that only fermions can be elementary and there can be no neutral elementary particles. The cosmological repulsion is a simple kinematical consequence of dS symmetry on quantum level when quasiclassical approximation is valid. Therefore the cosmological constant problem does not exist and there is no need to involve dark energy or other fields for explaining this phenomenon (in agreement with a similar conclusion by Bianchi and Rovelli.
Orbifolds, quantum cosmology, and nontrivial topology
International Nuclear Information System (INIS)
Fagundes, Helio V.; Vargas, Teofilo
2006-01-01
In order to include nontrivial topologies in the problem of quantum creation of a universe, it seems to be necessary to generalize the sum over compact, smooth 4-manifolds to a sum over finite-volume, compact 4-orbifolds. We consider in detail the case of a 4-spherical orbifold with a cone-point singularity. This allows for the inclusion of a nontrivial topology into the semiclassical path integral approach to quantum cosmology, in the context of a Robertson-Walker minisuperspace. (author)
Loop quantum cosmology: Recent progress
Indian Academy of Sciences (India)
Aspects of the full theory of loop quantum gravity can be studied in a simpler .... group) 1-forms and vector fields and Λ is an SO(3)-matrix indicating the internal ... are p and c which are related to the more familiar scale factor by the relations.
Decoherent histories analysis of minisuperspace quantum cosmology
Energy Technology Data Exchange (ETDEWEB)
Halliwell, J J, E-mail: j.halliwell@imperial.ac.uk [Blackett Laboratory Imperial College London SW7 2BZ (United Kingdom)
2011-07-08
Recent results on the decoherent histories quantization of simple cosmological models (minisuperspace models) are described. The most important issue is the construction, from the wave function, of a probability distribution answering various questions of physical interest, such as the probability of the system entering a given region of configuration space at any stage in its entire history. A standard but heuristic procedure is to use the flux of (components of) the wave function in a WKB approximation as the probability. This gives sensible semiclassical results but lacks an underlying operator formalism. Here, we supply the underlying formalism by deriving probability distributions linked to the Wheeler-DeWitt equation using the decoherent histories approach to quantum theory, building on the generalized quantum mechanics formalism developed by Hartle. The key step is the construction of class operators characterizing questions of physical interest. Taking advantage of a recent decoherent histories analysis of the arrival time problem in non-relativistic quantum mechanics, we show that the appropriate class operators in quantum cosmology are readily constructed using a complex potential. The class operator for not entering a region of configuration space is given by the S-matrix for scattering off a complex potential localized in that region. We thus derive the class operators for entering one or more regions in configuration space. The class operators commute with the Hamiltonian, have a sensible classical limit and are closely related to an intersection number operator. The corresponding probabilities coincide, in a semiclassical approximation, with standard heuristic procedures.
Decoherent histories analysis of minisuperspace quantum cosmology
International Nuclear Information System (INIS)
Halliwell, J J
2011-01-01
Recent results on the decoherent histories quantization of simple cosmological models (minisuperspace models) are described. The most important issue is the construction, from the wave function, of a probability distribution answering various questions of physical interest, such as the probability of the system entering a given region of configuration space at any stage in its entire history. A standard but heuristic procedure is to use the flux of (components of) the wave function in a WKB approximation as the probability. This gives sensible semiclassical results but lacks an underlying operator formalism. Here, we supply the underlying formalism by deriving probability distributions linked to the Wheeler-DeWitt equation using the decoherent histories approach to quantum theory, building on the generalized quantum mechanics formalism developed by Hartle. The key step is the construction of class operators characterizing questions of physical interest. Taking advantage of a recent decoherent histories analysis of the arrival time problem in non-relativistic quantum mechanics, we show that the appropriate class operators in quantum cosmology are readily constructed using a complex potential. The class operator for not entering a region of configuration space is given by the S-matrix for scattering off a complex potential localized in that region. We thus derive the class operators for entering one or more regions in configuration space. The class operators commute with the Hamiltonian, have a sensible classical limit and are closely related to an intersection number operator. The corresponding probabilities coincide, in a semiclassical approximation, with standard heuristic procedures.
Gauge-invariant perturbations in hybrid quantum cosmology
Energy Technology Data Exchange (ETDEWEB)
Gomar, Laura Castelló; Marugán, Guillermo A. Mena [Instituto de Estructura de la Materia, CSIC, Serrano 121, 28006 Madrid (Spain); Martín-Benito, Mercedes, E-mail: laura.castello@iem.cfmac.csic.es, E-mail: m.martin@hef.ru.nl, E-mail: mena@iem.cfmac.csic.es [Institute for Mathematics, Astrophysics and Particle Physics, Radboud University Nijmegen, Heyendaalseweg 135, NL-6525 AJ Nijmegen (Netherlands)
2015-06-01
We consider cosmological perturbations around homogeneous and isotropic spacetimes minimally coupled to a scalar field and present a formulation which is designed to preserve covariance. We truncate the action at quadratic perturbative order and particularize our analysis to flat compact spatial sections and a field potential given by a mass term, although the formalism can be extended to other topologies and potentials. The perturbations are described in terms of Mukhanov-Sasaki gauge invariants, linear perturbative constraints, and variables canonically conjugate to them. This set is completed into a canonical one for the entire system, including the homogeneous degrees of freedom. We find the global Hamiltonian constraint of the model, in which the contribution of the homogeneous sector is corrected with a term quadratic in the perturbations, that can be identified as the Mukhanov-Sasaki Hamiltonian in our formulation. We then adopt a hybrid approach to quantize the model, combining a quantum representation of the homogeneous sector with a more standard field quantization of the perturbations. Covariance is guaranteed in this approach inasmuch as no gauge fixing is adopted. Next, we adopt a Born-Oppenheimer ansatz for physical states and show how to obtain a Schrödinger-like equation for the quantum evolution of the perturbations. This evolution is governed by the Mukhanov-Sasaki Hamiltonian, with the dependence on the homogeneous geometry evaluated at quantum expectation values, and with a time parameter defined also in terms of suitable expectation values on that geometry. Finally, we derive effective equations for the dynamics of the Mukhanov-Sasaki gauge invariants, that include quantum contributions, but have the same ultraviolet limit as the classical equations. They provide the master equation to extract predictions about the power spectrum of primordial scalar perturbations.
Gauge-invariant perturbations in hybrid quantum cosmology
International Nuclear Information System (INIS)
Gomar, Laura Castelló; Marugán, Guillermo A. Mena; Martín-Benito, Mercedes
2015-01-01
We consider cosmological perturbations around homogeneous and isotropic spacetimes minimally coupled to a scalar field and present a formulation which is designed to preserve covariance. We truncate the action at quadratic perturbative order and particularize our analysis to flat compact spatial sections and a field potential given by a mass term, although the formalism can be extended to other topologies and potentials. The perturbations are described in terms of Mukhanov-Sasaki gauge invariants, linear perturbative constraints, and variables canonically conjugate to them. This set is completed into a canonical one for the entire system, including the homogeneous degrees of freedom. We find the global Hamiltonian constraint of the model, in which the contribution of the homogeneous sector is corrected with a term quadratic in the perturbations, that can be identified as the Mukhanov-Sasaki Hamiltonian in our formulation. We then adopt a hybrid approach to quantize the model, combining a quantum representation of the homogeneous sector with a more standard field quantization of the perturbations. Covariance is guaranteed in this approach inasmuch as no gauge fixing is adopted. Next, we adopt a Born-Oppenheimer ansatz for physical states and show how to obtain a Schrödinger-like equation for the quantum evolution of the perturbations. This evolution is governed by the Mukhanov-Sasaki Hamiltonian, with the dependence on the homogeneous geometry evaluated at quantum expectation values, and with a time parameter defined also in terms of suitable expectation values on that geometry. Finally, we derive effective equations for the dynamics of the Mukhanov-Sasaki gauge invariants, that include quantum contributions, but have the same ultraviolet limit as the classical equations. They provide the master equation to extract predictions about the power spectrum of primordial scalar perturbations
Anisotropy dissipation in quantum cosmology
International Nuclear Information System (INIS)
Calzetta, E.; Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellon I, 1428 Buenos Aires, Argentina)
1991-01-01
We study the issue of decoherence and dissipation in the wave function of the Universe for a Bianchi type-I universe with classical and quantum matter. We obtain a coarse-grained description by tracing over the matter degrees of freedom. Provided that for small universes the wave function of the universe is concentrated on a neighborhood of the isotropic configuration, then the coarse-grained density matrix of the universe will show an even more marked peak around isotropy for large universes. In this sense we can say that, while decoherence makes the reduced density matrix of the universe diagonal, dissipation causes the universe to be isotropic with a high probability for large radii
Inflationary cosmology from quantum conformal gravity
International Nuclear Information System (INIS)
Jizba, Petr; Kleinert, Hagen; Scardigli, Fabio
2015-01-01
We analyze the functional integral for quantum conformal gravity and show that, with the help of a Hubbard-Stratonovich transformation, the action can be broken into a local quadratic-curvature theory coupled to a scalar field. A one-loop effective-action calculation reveals that strong fluctuations of the metric field are capable of spontaneously generating a dimensionally transmuted parameter which, in the weak-field sector of the broken phase, induces a Starobinsky-type f(R)-model with a gravi-cosmological constant. A resulting non-trivial relation between Starobinsky's parameter and the gravi-cosmological constant is highlighted and implications for cosmic inflation are briefly discussed and compared with the recent PLANCK and BICEP2 data. (orig.)
Quantum unitary dynamics in cosmological spacetimes
International Nuclear Information System (INIS)
Cortez, Jerónimo; Mena Marugán, Guillermo A.; Velhinho, José M.
2015-01-01
We address the question of unitary implementation of the dynamics for scalar fields in cosmological scenarios. Together with invariance under spatial isometries, the requirement of a unitary evolution singles out a rescaling of the scalar field and a unitary equivalence class of Fock representations for the associated canonical commutation relations. Moreover, this criterion provides as well a privileged quantization for the unscaled field, even though the associated dynamics is not unitarily implementable in that case. We discuss the relation between the initial data that determine the Fock representations in the rescaled and unscaled descriptions, and clarify that the S-matrix is well defined in both cases. In our discussion, we also comment on a recently proposed generalized notion of unitary implementation of the dynamics, making clear the difference with the standard unitarity criterion and showing that the two approaches are not equivalent.
Quantum unitary dynamics in cosmological spacetimes
Energy Technology Data Exchange (ETDEWEB)
Cortez, Jerónimo, E-mail: jacq@ciencias.unam.mx [Departamento de Física, Facultad de Ciencias, Universidad Nacional Autónoma de México, México D.F. 04510 (Mexico); Mena Marugán, Guillermo A., E-mail: mena@iem.cfmac.csic.es [Instituto de Estructura de la Materia, IEM-CSIC, Serrano 121, 28006 Madrid (Spain); Velhinho, José M., E-mail: jvelhi@ubi.pt [Departamento de Física, Faculdade de Ciências, Universidade da Beira Interior, R. Marquês D’Ávila e Bolama, 6201-001 Covilhã (Portugal)
2015-12-15
We address the question of unitary implementation of the dynamics for scalar fields in cosmological scenarios. Together with invariance under spatial isometries, the requirement of a unitary evolution singles out a rescaling of the scalar field and a unitary equivalence class of Fock representations for the associated canonical commutation relations. Moreover, this criterion provides as well a privileged quantization for the unscaled field, even though the associated dynamics is not unitarily implementable in that case. We discuss the relation between the initial data that determine the Fock representations in the rescaled and unscaled descriptions, and clarify that the S-matrix is well defined in both cases. In our discussion, we also comment on a recently proposed generalized notion of unitary implementation of the dynamics, making clear the difference with the standard unitarity criterion and showing that the two approaches are not equivalent.
Affine histories in quantum gravity: introduction and the representation for a cosmological model
International Nuclear Information System (INIS)
Kessari, Smaragda
2007-01-01
It is shown how consistent histories quantum cosmology can be realized through Isham's histories projection operator consistent histories scheme. This is done by using an affine algebra instead of a canonical one and also by using cocycle representations. A regularization scheme allows us to find a history Hamiltonian which exists as a proper self-adjoint operator. The role of a cocycle choice is also discussed
Geometry of real and complex canonical transformations in quantum mechanics
International Nuclear Information System (INIS)
Grossmann, A.
1977-08-01
Quantum mechanics of finitely many particles involves the group of linear (and affine) canonical transformations. A well-defined ray representation of this group acts in the space of states of any quantum-mechanical system with finitely many degrees of freedom and plays a central role in many different contexts. This representation appears quite naturally in quantum mechanics over phase space (Weyl-Wigner correspondence), that it becomes, when suitably written, just a matter of looking at one object from different symplectic reference frames. This is particularly interesting for complex canonical transformations which are represented by unbounded operators. The list of references gives an idea of the variety of motivations and points of view in the subject
Stepping out of homogeneity in loop quantum cosmology
International Nuclear Information System (INIS)
Rovelli, Carlo; Vidotto, Francesca
2008-01-01
We explore the extension of quantum cosmology outside the homogeneous approximation using the formalism of loop quantum gravity. We introduce a model where some of the inhomogeneous degrees of freedom are present, providing a tool for describing general fluctuations of quantum geometry near the initial singularity. We show that the dynamical structure of the model reduces to that of loop quantum cosmology in the Born-Oppenheimer approximation. This result corroborates the assumptions that ground loop cosmology sheds some light on the physical and mathematical relation between loop cosmology and full loop quantum gravity, and on the nature of the cosmological approximation. Finally, we show that the non-graph-changing Hamiltonian constraint considered in the context of algebraic quantum gravity provides a viable effective dynamics within this approximation
Coherent semiclassical states for loop quantum cosmology
International Nuclear Information System (INIS)
Corichi, Alejandro; Montoya, Edison
2011-01-01
The spatially flat Friedmann-Robertson-Walker cosmological model with a massless scalar field in loop quantum cosmology admits a description in terms of a completely solvable model. This has been used to prove that: (i) the quantum bounce that replaces the big bang singularity is generic; (ii) there is an upper bound on the energy density for all states, and (iii) semiclassical states at late times had to be semiclassical before the bounce. Here we consider a family of exact solutions to the theory, corresponding to generalized coherent Gaussian and squeezed states. We analyze the behavior of basic physical observables and impose restrictions on the states based on physical considerations. These turn out to be enough to select, from all the generalized coherent states, those that behave semiclassical at late times. We study then the properties of such states near the bounce where the most 'quantum behavior' is expected. As it turns out, the states remain sharply peaked and semiclassical at the bounce and the dynamics is very well approximated by the ''effective theory'' throughout the time evolution. We compare the semiclassicality properties of squeezed states to those of the Gaussian semiclassical states and conclude that the Gaussians are better behaved. In particular, the asymmetry in the relative fluctuations before and after the bounce are negligible, thus ruling out claims of so-called 'cosmic forgetfulness'.
Towards cosmological dynamics from loop quantum gravity
Li, Bao-Fei; Singh, Parampreet; Wang, Anzhong
2018-04-01
We present a systematic study of the cosmological dynamics resulting from an effective Hamiltonian, recently derived in loop quantum gravity using Thiemann's regularization and earlier obtained in loop quantum cosmology (LQC) by keeping the Lorentzian term explicit in the Hamiltonian constraint. We show that quantum geometric effects result in higher than quadratic corrections in energy density in comparison to LQC, causing a nonsingular bounce. Dynamics can be described by the Hamilton or Friedmann-Raychaudhuri equations, but the map between the two descriptions is not one to one. A careful analysis resolves the tension on symmetric versus asymmetric bounce in this model, showing that the bounce must be asymmetric and symmetric bounce is physically inconsistent, in contrast to the standard LQC. In addition, the current observations only allow a scenario where the prebounce branch is asymptotically de Sitter, similar to a quantization of the Schwarzschild interior in LQC, and the postbounce branch yields the classical general relativity. For a quadratic potential, we find that a slow-roll inflation generically happens after the bounce, which is quite similar to what happens in LQC.
The quantum cosmology of an anisotropic universe
International Nuclear Information System (INIS)
Duncan, M.J.; Jensen, L.G.
1989-01-01
Surveys of the microwave background indicate that the universe is isotropic to more than one part in 10 5 . Due to the arbitrariness of the initial conditions of the universe at the big bang singularity one cannot predict this; it is usually put in by hand. We therefore construct the quantum cosmology of an anisotropic universe according to the 'no-boundary' prescription of Hartle and Hawking. Such a model has a well-defined behavior at the classical singularity. We then show it also implies that a large universe, such as ours, is isotropic. (orig.)
Quantum cosmology of an anisotropic universe
Energy Technology Data Exchange (ETDEWEB)
Duncan, M.J.; Jensen, L.G.
1989-01-23
Surveys of the microwave background indicate that the universe is isotropic to more than one part in 10/sup 5/. Due to the arbitrariness of the initial conditions of the universe at the big bang singularity one cannot predict this; it is usually put in by hand. We therefore construct the quantum cosmology of an anisotropic universe according to the 'no-boundary' prescription of Hartle and Hawking. Such a model has a well-defined behavior at the classical singularity. We then show it also implies that a large universe, such as ours, is isotropic.
Uncertainty principle in loop quantum cosmology by Moyal formalism
Perlov, Leonid
2018-03-01
In this paper, we derive the uncertainty principle for the loop quantum cosmology homogeneous and isotropic Friedmann-Lemaiter-Robertson-Walker model with the holonomy-flux algebra. The uncertainty principle is between the variables c, with the meaning of connection and μ having the meaning of the physical cell volume to the power 2/3, i.e., v2 /3 or a plaquette area. Since both μ and c are not operators, but rather the random variables, the Robertson uncertainty principle derivation that works for hermitian operators cannot be used. Instead we use the Wigner-Moyal-Groenewold phase space formalism. The Wigner-Moyal-Groenewold formalism was originally applied to the Heisenberg algebra of the quantum mechanics. One can derive it from both the canonical and path integral quantum mechanics as well as the uncertainty principle. In this paper, we apply it to the holonomy-flux algebra in the case of the homogeneous and isotropic space. Another result is the expression for the Wigner function on the space of the cylindrical wave functions defined on Rb in c variables rather than in dual space μ variables.
Quantum oscillators in the canonical coherent states
Energy Technology Data Exchange (ETDEWEB)
Rodrigues, R. de Lima [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil); Lima, A.F. de; Ferreira, K. de Araujo [Paraiba Univ., Campina Grande, PB (Brazil). Dept. de Fisica; Vaidya, A.N. [Universidade Federal, Rio de Janeiro, RJ (Brazil). Inst. de Fisica
2001-11-01
The main characteristics of the quantum oscillator coherent states including the two-particle Calogero interaction are investigated. We show that these Calogero coherent states are the eigenstates of the second-order differential annihilation operator which is deduced via Wigner-Heisenberg algebraic technique and correspond exactly to the pure uncharged-bosonic states. They posses the important properties of non-orthogonality and completeness. The minimum uncertainty relation for the Wigner oscillator coherent states are investigated. New sets of even and odd coherent states are point out. (author)
n-dimensional FLRW quantum cosmology
International Nuclear Information System (INIS)
Letelier, Patricio S.; Pitelli, Joao Paulo M.
2010-01-01
We introduce the formalism of quantum cosmology in a Friedmann-Lemaitre-Robertson-Walker (FLRW) universe of arbitrary dimension filled with a perfect fluid with p=αρ equation of state. First we show that the Schutz formalism, developed in four dimensions, can be extended to a n-dimensional universe. We compute the quantum representant of the scale factor a(t), in the Many-Worlds, as well as, in the de Broglie-Bohm interpretation of quantum mechanics. We show that the singularities, which are still present in the n-dimensional generalization of FLRW universe, are excluded with the introduction of quantum theory. We quantize, via the de Broglie-Bohm interpretation of quantum mechanics, the components of the Riemann curvature tensor in a tetrad basis in a n-dimensional FLRW universe filled with radiation (p=(1/n-1)ρ). We show that the quantized version of the Ricci scalar are perfectly regular for all time t. We also study the behavior of the energy density and pressure and show that the ratio L / L tends to the classical value 1/(n-1) only for n=4, showing that n=4 is somewhat privileged among the other dimensions. Besides that, as n→∞, L / L →1.
Non equilibrium quantum fields in cosmology
International Nuclear Information System (INIS)
Paz, J.P.
1991-01-01
The authors discuss the general framework used to construct a quantum mechanical model of the inflationary phase transition. The emer-gence of classical behavior in the longwavelength modes of the inflation is one of the facts that these models should address. For some toy examples (in which the inflation interacts with an environment consti-tuted by other fields) decoherence is shown of the modes with physical wavelength greater than the horizon. The authors use an approach based on a master equation. They take advantage of the similarities that exist between the master equation for the toy cosmological models and the one for the simple Quantum Brownian Motion. Recent results are discussed obtained for the general QBM problem (in which the environment has a generic spectral density). (author). 10 refs
Higher derivatives and renormalization in quantum cosmology
International Nuclear Information System (INIS)
Mazzitelli, F.D.
1991-10-01
In the framework of the canonical quantization of general relativity, quantum field theory on a fixed background formally arises in an expansion in powers of the Planck length. In order to renormalize the theory, quadratic terms in the curvature must be included in the gravitational action from the beginning. These terms contain higher derivatives which change the Hamiltonian structure of the theory completely, making the relation between the renormalized-theory and the original one not clear. We show that it is possible to avoid this problem. We replace the higher derivative theory by a second order one. The classical solutions of the latter are also solutions of the former. We quantize the theory, renormalize the infinities and show that there is a smooth limit between the classical and the renormalized theories. We work in a Robertson Walker minisuperspace with a quantum scalar field. (author). 32 refs
Algorithmic Complexity in Cosmology and Quantum Gravity
Directory of Open Access Journals (Sweden)
D. Singleton
2002-01-01
Full Text Available Abstract: In this article we use the idea of algorithmic complexity (AC to study various cosmological scenarios, and as a means of quantizing the ravitational interaction. We look at 5D and 7D cosmological models where the Universe begins as a higher dimensional Planck size spacetime which fluctuates between Euclidean and Lorentzian signatures. These fluctuations are overned by the AC of the two different signatures. At some point a transition to a 4D Lorentzian signature Universe occurs, with the extra dimensions becoming "frozen" or non-dynamical. We also apply the idea of algorithmic complexity to study composite wormholes, the entropy of black holes, and the path integral for quantum gravity. Some of the physical consequences of the idea presented here are:the birth of the Universe with a fluctuating metric signature; the transition from a fluctuating metric signature to Lorentzian one; "frozen" extra dimensions as a consequence of this transition; quantum handles in the spacetime foam as regions with multidimensional gravity.
Generalized quantum theory of recollapsing homogeneous cosmologies
International Nuclear Information System (INIS)
Craig, David; Hartle, James B.
2004-01-01
A sum-over-histories generalized quantum theory is developed for homogeneous minisuperspace type A Bianchi cosmological models, focusing on the particular example of the classically recollapsing Bianchi type-IX universe. The decoherence functional for such universes is exhibited. We show how the probabilities of decoherent sets of alternative, coarse-grained histories of these model universes can be calculated. We consider in particular the probabilities for classical evolution defined by a suitable coarse graining. For a restricted class of initial conditions and coarse grainings we exhibit the approximate decoherence of alternative histories in which the universe behaves classically and those in which it does not. For these situations we show that the probability is near unity for the universe to recontract classically if it expands classically. We also determine the relative probabilities of quasiclassical trajectories for initial states of WKB form, recovering for such states a precise form of the familiar heuristic 'J·dΣ' rule of quantum cosmology, as well as a generalization of this rule to generic initial states
Loop quantum cosmology with complex Ashtekar variables
International Nuclear Information System (INIS)
Achour, Jibril Ben; Grain, Julien; Noui, Karim
2015-01-01
We construct and study loop quantum cosmology (LQC) when the Barbero–Immirzi parameter takes the complex value γ=±i. We refer to this new approach to quantum cosmology as complex LQC. This formulation is obtained via an analytic continuation of the Hamiltonian constraint (with no inverse volume corrections) from real γ to γ=±i, in the simple case of a flat FLRW Universe coupled to a massless scalar field with no cosmological constant. For this, we first compute the non-local curvature operator (defined by the trace of the holonomy of the connection around a fundamental plaquette) evaluated in an arbitrary spin j representation, and find a new close formula for its expression. This allows us to define explicitly a one parameter family of regularizations of the Hamiltonian constraint in LQC, parametrized by the spin j. It is immediate to see that any spin j regularization leads to a bouncing scenario. Then, motivated in particular by previous results on black hole thermodynamics, we perform the analytic continuation of the Hamiltonian constraint to values of the Barbero–Immirzi parameter given by γ=±i and to spins j=(1/2)(−1+is) where s is real. Even if the area spectrum then becomes continuous, we show that the complex LQC defined in this way does also replace the initial big-bang singularity by a big-bounce. In addition to this, the maximal density and the minimal volume of the Universe are obviously independent of γ. Furthermore, the dynamics before and after the bounce is not symmetrical anymore, which makes a clear distinction between these two phases of the evolution of the Universe. (paper)
Canonical Drude Weight for Non-integrable Quantum Spin Chains
Mastropietro, Vieri; Porta, Marcello
2018-03-01
The Drude weight is a central quantity for the transport properties of quantum spin chains. The canonical definition of Drude weight is directly related to Kubo formula of conductivity. However, the difficulty in the evaluation of such expression has led to several alternative formulations, accessible to different methods. In particular, the Euclidean, or imaginary-time, Drude weight can be studied via rigorous renormalization group. As a result, in the past years several universality results have been proven for such quantity at zero temperature; remarkably, the proofs work for both integrable and non-integrable quantum spin chains. Here we establish the equivalence of Euclidean and canonical Drude weights at zero temperature. Our proof is based on rigorous renormalization group methods, Ward identities, and complex analytic ideas.
The Problem of Time in Quantum Cosmology: A Decoherent Histories View
International Nuclear Information System (INIS)
Christodoulakis, Theodosios; Wallden, Petros
2011-01-01
The problem of time in quantum gravity arises due to the diffeomorphisms invariance of the theory and appears via the Hamiltonian constraint, in the canonical quantizations. There is a need for a description where one can ask some timeless questions that still encode some sense of temporality. The decoherent histories approach to quantum theory, already at the kinematical level admits an internal time. Several alternative proposals for resolving the problem of time via the decoherent histories, exist, and in this contribution we focus on one particular and examine how it manifests itself at some simple cosmological models.
Black holes, quantum theory and cosmology
International Nuclear Information System (INIS)
Penrose, Roger
2009-01-01
Some reasons are given for believing that the rules of quantum (field) theory must be changed when general relativity becomes seriously involved. If full quantum mechanical respect is paid to the principle of equivalence, we find that a superposition of gravitational fields leads to an illegal superposition of different vacua, giving support to a proposal for spontaneous quantum state reduction made earlier by Diosi, and then independently by the author. A different line of attack involves the over-riding role of black holes in the total entropy content of the universe, and in the operation of the 2nd Law of thermodynamics. The author's proposal of conformal cyclic cosmology is reviewed in order to highlight a seeming paradox, according to which the entropy of the universe of the remote future seems to return to the small kind of value that it had at the big bang. The paradox is resolved when we take into account the information loss that, from this perspective, necessarily occurs in Hawking's black-hole evaporation, with the accompanying loss of unitarity.
Black holes, quantum theory and cosmology
Penrose, Roger
2009-06-01
Some reasons are given for believing that the rules of quantum (field) theory must be changed when general relativity becomes seriously involved. If full quantum mechanical respect is paid to the principle of equivalence, we find that a superposition of gravitational fields leads to an illegal superposition of different vacua, giving support to a proposal for spontaneous quantum state reduction made earlier by Diósi, and then independently by the author. A different line of attack involves the over-riding role of black holes in the total entropy content of the universe, and in the operation of the 2nd Law of thermodynamics. The author's proposal of conformal cyclic cosmology is reviewed in order to highlight a seeming paradox, according to which the entropy of the universe of the remote future seems to return to the small kind of value that it had at the big bang. The paradox is resolved when we take into account the information loss that, from this perspective, necessarily occurs in Hawking's black-hole evaporation, with the accompanying loss of unitarity.
Black holes, quantum theory and cosmology
Energy Technology Data Exchange (ETDEWEB)
Penrose, Roger, E-mail: rouse@maths.ox.ac.u [Mathematical Institute, 24-29 St Giles, Oxford OX1 3LB (United Kingdom)
2009-06-01
Some reasons are given for believing that the rules of quantum (field) theory must be changed when general relativity becomes seriously involved. If full quantum mechanical respect is paid to the principle of equivalence, we find that a superposition of gravitational fields leads to an illegal superposition of different vacua, giving support to a proposal for spontaneous quantum state reduction made earlier by Diosi, and then independently by the author. A different line of attack involves the over-riding role of black holes in the total entropy content of the universe, and in the operation of the 2nd Law of thermodynamics. The author's proposal of conformal cyclic cosmology is reviewed in order to highlight a seeming paradox, according to which the entropy of the universe of the remote future seems to return to the small kind of value that it had at the big bang. The paradox is resolved when we take into account the information loss that, from this perspective, necessarily occurs in Hawking's black-hole evaporation, with the accompanying loss of unitarity.
Loop quantum cosmology and spin foams
International Nuclear Information System (INIS)
Ashtekar, Abhay; Campiglia, Miguel; Henderson, Adam
2009-01-01
Loop quantum cosmology (LQC) is used to provide concrete evidence in support of the general paradigm underlying spin foam models (SFMs). Specifically, it is shown that: (i) the physical inner product in the timeless framework equals the transition amplitude in the deparameterized theory; (ii) this quantity admits a vertex expansion a la SFMs in which the M-th term refers just to M volume transitions, without any reference to the time at which the transition takes place; (iii) the exact physical inner product is obtained by summing over just the discrete geometries; no 'continuum limit' is involved; and, (iv) the vertex expansion can be interpreted as a perturbative expansion in the spirit of group field theory. This sum over histories reformulation of LQC also addresses certain other issues which are briefly summarized.
Singularity, initial conditions and quantum tunneling in modern cosmology
International Nuclear Information System (INIS)
Khalatnikov, I M; Kamenshchik, A Yu
1998-01-01
The key problems of modern cosmology, such as the cosmological singularity, initial conditions, and the quantum tunneling hypothesis, are discussed. The relationship between the latest cosmological trends and L D Landau's old ideas is analyzed. Particular attention is given to the oscillatory approach to singularity; quantum tunneling processes determining wave function of the Universe in the presence of a compex scalar field; and the role of quantum corrections in these processes. The classical dynamics of closed models with a real scalar field is investigated from the standpoint of chaotic, fractal, and singularity-avoiding properties. (special issue)
Quantum cosmology from the de Broglie–Bohm perspective
International Nuclear Information System (INIS)
Pinto-Neto, N; Fabris, J C
2013-01-01
We review the main results that have been obtained in quantum cosmology from the perspective of the de Broglie–Bohm quantum theory. As it is a dynamical theory of assumed objectively real trajectories in the configuration space of the physical system under investigation, this quantum theory is not essentially probabilistic and dispenses the collapse postulate, turning it suitable to be applied to cosmology. In the framework of minisuperspace models, we show how quantum cosmological effects in the de–Broglie-Bohm approach can avoid the initial singularity, and isotropize the Universe. We then extend minisuperspace in order to include linear cosmological perturbations. We present the main equations which govern the dynamics of quantum cosmological perturbations evolving in non-singular quantum cosmological backgrounds, and calculate some of their observational consequences. These results are not known how to be obtained in other approaches to quantum theory. In the general case of full superspace, we enumerate the possible structures of quantum space and time that emerge from the de Broglie–Bohm picture. Finally, we compare some of the results coming from the de Broglie–Bohm theory with other approaches, and discuss the physical reasons for some discrepancies that occur. (topical review)
TCP, quantum gravity, the cosmological constant and all that .
International Nuclear Information System (INIS)
Banks, T.
1985-01-01
We study cosmology from the point of view of quantum gravity. Some light is thrown on the nature of time, and it is suggested that the cosmological arrow of time is generated by a spontaneous breakdown of TCP. Conventional cosmological models in which quantum fields interact with a time-dependent gravitational field are shown to describe an approximation to the quantum gravitational wave function which is valid in the long-wavelength limit. Two problems with initial conditions are resolved in models in which a negative bare cosmological constant is cancelled by the classical excitation of a Bose field eta with a very flat potential. These models can also give a natural explanation for the observed value of the cosmological constant. (orig.)
Cosmic time gauge in quantum cosmology and chaotic inflation model
International Nuclear Information System (INIS)
Hosoya, A.
1986-01-01
The author proposes a cosmic time gauge formalism in quantum cosmology to get an equation for the Schrodinger type. Its application to the chaotic inflation scenario reveals that the uncertainty in the scale factor grows exponentially as the universe inflates
Quantum mechanics of Klein-Gordon-type fields and quantum cosmology
International Nuclear Information System (INIS)
Mostafazadeh, Ali
2004-01-01
dynamics. Our method is based on the central postulates of nonrelativistic quantum mechanics, especially the quest for a genuine probabilistic interpretation and a unitary Schroedinger time-evolution. It generalizes to arbitrary minisuperspace (spatially homogeneous) models and provides a way of unifying the two main approaches to the canonical quantum cosmology based on these models, namely quantization before and after imposing the Hamiltonian constraint
Quantum mechanics of Klein-Gordon-type fields and quantum cosmology
Mostafazadeh, Ali
2004-01-01
based on the central postulates of nonrelativistic quantum mechanics, especially the quest for a genuine probabilistic interpretation and a unitary Schrödinger time-evolution. It generalizes to arbitrary minisuperspace (spatially homogeneous) models and provides a way of unifying the two main approaches to the canonical quantum cosmology based on these models, namely quantization before and after imposing the Hamiltonian constraint.
International Nuclear Information System (INIS)
Yeon, Kyu Hwang; Hong, Suc Kyoung; Um, Chung In; George, Thomas F.
2006-01-01
With quantum operators corresponding to functions of the canonical variables, Schroedinger equations are constructed for systems corresponding to classical systems connected by a general point canonical transformation. Using the operator connecting quantum states between systems before and after the transformation, the quantum correction term and ordering parameter are obtained
Quantum cosmology of a conformal multiverse
Robles-Pérez, Salvador J.
2017-09-01
This paper studies the cosmology of a homogeneous and isotropic spacetime endorsed with a conformally coupled massless scalar field. We find six different solutions of the Friedmann equation that represent six different types of universes, and all of them are periodically distributed along the complex time axis. From a classical point of view, they are then isolated, separated by Euclidean regions that represent quantum mechanical barriers. Quantum mechanically, however, there is a nonzero probability for the state of the universes to tunnel out through a Euclidean instanton and suffer a sudden transition to another state of the spacetime. We compute the probability of transition for this and other nonlocal processes like the creation of universes in entangled pairs and, generally speaking, in multipartite entangled states. We obtain the quantum state of a single universe within the formalism of the Wheeler-DeWitt equation and give the semiclassical state of the universes that describes the quantum mechanics of a scalar field propagating in a de Sitter background spacetime. We show that the superposition principle of the quantum mechanics of matter fields alone is an emergent feature of the semiclassical description of the universe that is not valid, for instance, in the spacetime foam. We use the third quantization formalism to describe the creation of an entangled pair of universes with opposite signs of the momentum conjugated to the scale factor. Each universe of the entangled pair represents an expanding spacetime in terms of the Wentzel-Kramers-Brillouin (WKB) time experienced by internal observers in their particle physics experiments. We compute the effective value of the Friedmann equation of the background spacetime of the two entangled universes, and thus, the effect that the entanglement would have in their expansion rates. We analyze as well the effects of the interuniversal entanglement in the properties of the scalar fields that propagate in each
Classical and quantum cosmology of minimal massive bigravity
International Nuclear Information System (INIS)
Darabi, F.; Mousavi, M.
2016-01-01
In a Friedmann–Robertson–Walker (FRW) space–time background we study the classical cosmological models in the context of recently proposed theory of nonlinear minimal massive bigravity. We show that in the presence of perfect fluid the classical field equations acquire contribution from the massive graviton as a cosmological term which is positive or negative depending on the dynamical competition between two scale factors of bigravity metrics. We obtain the classical field equations for flat and open universes in the ordinary and Schutz representation of perfect fluid. Focusing on the Schutz representation for flat universe, we find classical solutions exhibiting singularities at early universe with vacuum equation of state. Then, in the Schutz representation, we study the quantum cosmology for flat universe and derive the Schrodinger–Wheeler–DeWitt equation. We find its exact and wave packet solutions and discuss on their properties to show that the initial singularity in the classical solutions can be avoided by quantum cosmology. Similar to the study of Hartle–Hawking no-boundary proposal in the quantum cosmology of de Rham, Gabadadze and Tolley (dRGT) massive gravity, it turns out that the mass of graviton predicted by quantum cosmology of the minimal massive bigravity is large at early universe. This is in agreement with the fact that at early universe the cosmological constant should be large.
Classical and quantum cosmology of minimal massive bigravity
Energy Technology Data Exchange (ETDEWEB)
Darabi, F., E-mail: f.darabi@azaruniv.edu; Mousavi, M., E-mail: mousavi@azaruniv.edu
2016-10-10
In a Friedmann–Robertson–Walker (FRW) space–time background we study the classical cosmological models in the context of recently proposed theory of nonlinear minimal massive bigravity. We show that in the presence of perfect fluid the classical field equations acquire contribution from the massive graviton as a cosmological term which is positive or negative depending on the dynamical competition between two scale factors of bigravity metrics. We obtain the classical field equations for flat and open universes in the ordinary and Schutz representation of perfect fluid. Focusing on the Schutz representation for flat universe, we find classical solutions exhibiting singularities at early universe with vacuum equation of state. Then, in the Schutz representation, we study the quantum cosmology for flat universe and derive the Schrodinger–Wheeler–DeWitt equation. We find its exact and wave packet solutions and discuss on their properties to show that the initial singularity in the classical solutions can be avoided by quantum cosmology. Similar to the study of Hartle–Hawking no-boundary proposal in the quantum cosmology of de Rham, Gabadadze and Tolley (dRGT) massive gravity, it turns out that the mass of graviton predicted by quantum cosmology of the minimal massive bigravity is large at early universe. This is in agreement with the fact that at early universe the cosmological constant should be large.
Emergence of a classical Universe from quantum gravity and cosmology.
Kiefer, Claus
2012-09-28
I describe how we can understand the classical appearance of our world from a universal quantum theory. The essential ingredient is the process of decoherence. I start with a general discussion in ordinary quantum theory and then turn to quantum gravity and quantum cosmology. There is a whole hierarchy of classicality from the global gravitational field to the fluctuations in the cosmic microwave background, which serve as the seeds for the structure in the Universe.
Quantum effects and regular cosmological models
International Nuclear Information System (INIS)
Gurovich, V.Ts.; Starobinskij, A.A.; AN SSSR, Moscow. Inst. Teoreticheskoj Fiziki)
1979-01-01
Allowance for the quantum nature of material fields and weak gravitational waves on the background of the classical metric of the cosmological model results in two basic effects: vacuum polarization and particle production. The first of the effects may be taken into account qualitatively by introducing into the lagrangian density of the gravitational field an additional term of the type A+BR 2 +CR 2 In|R/R 0 |; the second effect can be accounted for by prescribing a local rate of particle (graviton) production which is proportional to the square of the scalar curvature R 2 . It is shown that the taking into account of the combined effect of these phenomena on the evolution of a homogeneous anisotropic metric of the first Bianchi type removes the Einstein singularities. Asymptotic approach to the classical model, however, is attained only if additional assumptions are made. At the stage of compression the solution is close to the anisotropic vacuum Kasner solution; at the expansion stage it tends to the isotropic Friedman solution in which matter is produced by the gravitational field
Universal features of quantum bounce in loop quantum cosmology
Directory of Open Access Journals (Sweden)
Tao Zhu
2017-10-01
Full Text Available In this Letter, we study analytically the evolutions of the flat Friedmann–Lemaitre–Robertson–Walker (FLRW universe and its linear perturbations in the framework of the dressed metric approach in loop quantum cosmology (LQC. Assuming that the evolution of the background is dominated by the kinetic energy of the inflaton at the quantum bounce, we find that both evolutions of the background and its perturbations are independent of the inflationary potentials during the pre-inflationary phase. During this period the effective potentials of the perturbations can be well approximated by a Pöschl–Teller (PT potential, from which we find analytically the mode functions and then calculate the corresponding Bogoliubov coefficients at the onset of the slow-roll inflation, valid for any inflationary model with a single scalar field. Imposing the Bunch–Davies (BD vacuum in the contracting phase prior to the bounce when the modes are all inside the Hubble horizon, we show that particles are generically created due to the pre-inflation dynamics. Matching them to those obtained in the slow-roll inflationary phase, we investigate the effects of the pre-inflation dynamics on the scalar and tensor power spectra and find features that can be tested by current and forthcoming observations. In particular, to be consistent with the Planck 2015 data, we find that the universe must have expanded at least 141 e-folds since the bounce.
Cosmological applications of algebraic quantum field theory in curved spacetimes
Hack, Thomas-Paul
2016-01-01
This book provides a largely self-contained and broadly accessible exposition on two cosmological applications of algebraic quantum field theory (QFT) in curved spacetime: a fundamental analysis of the cosmological evolution according to the Standard Model of Cosmology; and a fundamental study of the perturbations in inflation. The two central sections of the book dealing with these applications are preceded by sections providing a pedagogical introduction to the subject. Introductory material on the construction of linear QFTs on general curved spacetimes with and without gauge symmetry in the algebraic approach, physically meaningful quantum states on general curved spacetimes, and the backreaction of quantum fields in curved spacetimes via the semiclassical Einstein equation is also given. The reader should have a basic understanding of General Relativity and QFT on Minkowski spacetime, but no background in QFT on curved spacetimes or the algebraic approach to QFT is required.
On the Convergence in Effective Loop Quantum Cosmology
International Nuclear Information System (INIS)
Corichi, Alejandro; Vukasinac, Tatjana; Zapata, Jose Antonio
2010-01-01
In Loop Quantum Cosmology (LQC) there is a discreteness parameter λ, that has been heuristically associated to a fundamental granularity of quantum geometry. It is also possible to consider λ as a regulator in the same spirit as that used in lattice field theory, where it specifies a regular lattice in the real line. A particular quantization of the k = 0 FLRW loop cosmological model yields a completely solvable model, known as solvable loop quantum cosmology(sLQC). In this contribution, we consider effective classical theories motivated by sLQC and study their λ-dependence, with a special interest on the limit λ→0 and the role of the evolution parameter in the convergence of such limit.
Cosmology from group field theory formalism for quantum gravity.
Gielen, Steffen; Oriti, Daniele; Sindoni, Lorenzo
2013-07-19
We identify a class of condensate states in the group field theory (GFT) formulation of quantum gravity that can be interpreted as macroscopic homogeneous spatial geometries. We then extract the dynamics of such condensate states directly from the fundamental quantum GFT dynamics, following the procedure used in ordinary quantum fluids. The effective dynamics is a nonlinear and nonlocal extension of quantum cosmology. We also show that any GFT model with a kinetic term of Laplacian type gives rise, in a semiclassical (WKB) approximation and in the isotropic case, to a modified Friedmann equation. This is the first concrete, general procedure for extracting an effective cosmological dynamics directly from a fundamental theory of quantum geometry.
Quantum cosmology of classically constrained gravity
International Nuclear Information System (INIS)
Gabadadze, Gregory; Shang Yanwen
2006-01-01
In [G. Gabadadze, Y. Shang, hep-th/0506040] we discussed a classically constrained model of gravity. This theory contains known solutions of General Relativity (GR), and admits solutions that are absent in GR. Here we study cosmological implications of some of these new solutions. We show that a spatially-flat de Sitter universe can be created from 'nothing'. This universe has boundaries, and its total energy equals to zero. Although the probability to create such a universe is exponentially suppressed, it favors initial conditions suitable for inflation. Then we discuss a finite-energy solution with a nonzero cosmological constant and zero space-time curvature. There is no tunneling suppression to fluctuate into this state. We show that for a positive cosmological constant this state is unstable-it can rapidly transition to a de Sitter universe providing a new unsuppressed channel for inflation. For a negative cosmological constant the space-time flat solutions is stable.
Symmetry groups of state vectors in canonical quantum gravity
International Nuclear Information System (INIS)
Witt, D.M.
1986-01-01
In canonical quantum gravity, the diffeomorphisms of an asymptotically flat hypersurface S, not connected to the identity, but trivial at infinity, can act nontrivially on the quantum state space. Because state vectors are invariant under diffeomorphisms that are connected to the identity, the group of inequivalent diffeomorphisms is a symmetry group of states associated with S. This group is the zeroth homotopy group of the group of diffeomorphisms fixing a frame of infinity on S. It is calculated for all hypersurfaces of the form S = S 3 /G-point, where the removed point is thought of as infinity on S and the symmetry group S is the zeroth homotopy group of the group of diffeomorphisms of S 3 /G fixing a point and frame, denoted π 0 Diff/sub F/(S 3 /G). Before calculating π 0 Diff/sub F/ (S 3 /G), it is necessary to find π 0 of the group of diffeomorphisms. Once π 0 Diff(S 3 /G) is known, π 0 Diff/sub x/ 0 (S 3 /G) is calculated using a fiber bundle involving Diff(S 3 /G), Diff/sub x/ 0 (S 3 /G), and S 3 /G. Finally, a fiber bundle involving Diff/sub F/(S 3 /G), Diff(S 3 /G), and the bundle of frames over S 3 /G is used along with π 0 Diff/sub x/ 0 (S 3 /G) to calculate π 0 Diff/sub F/(S 3 /G)
Quantum symmetry, the cosmological constant and Planck-scale phenomenology
International Nuclear Information System (INIS)
Amelino-Camelia, Giovanni; Smolin, Lee; Starodubtsev, Artem
2004-01-01
We present a simple algebraic mechanism for the emergence of deformations of Poincare symmetries in the low-energy limit of quantum theories of gravity. The deformations, called κ-Poincare algebras, are parametrized by a dimensional parameter proportional to the Planck mass, and imply modified energy-momentum relations of a type that may be observable in near future experiments. Our analysis assumes that the low energy limit of a quantum theory of gravity must also involve a limit in which the cosmological constant is taken very small with respect to the Planck scale, and makes use of the fact that in some quantum theories of gravity the cosmological constant results in the (anti)de Sitter symmetry algebra being quantum deformed. We show that deformed Poincare symmetries inevitably emerge in the small-cosmological-constant limit of quantum gravity in 2 + 1 dimensions, where geometry does not have local degrees of freedom. In 3 + 1 dimensions we observe that, besides the quantum deformation of the (anti)de Sitter symmetry algebra, one must also take into account that there are local degrees of freedom leading to a renormalization of the generators for energy and momentum of the excitations. At the present level of development of quantum gravity in 3 + 1 dimensions, it is not yet possible to derive this renormalization from first principles, but we establish the conditions needed for the emergence of a deformed low energy limit symmetry algebra also in the case of 3 + 1 dimensions
Wavepacket Evolution in Unimodular Quantum Cosmology
Directory of Open Access Journals (Sweden)
Natascha Riahi
2018-01-01
Full Text Available The unimodular theory of gravity admits a canonical quantization of minisuperspace models without the problem of time. We derive instead a kind of Schrödinger equation. We have found unitarily evolving wave packet solutions for the special case of a massless scalar field and a spatially flat Friedmann universe. We show that the longterm behaviour of the expectation values of the canonical quantities corresponds to the evolution of the classical variables. The solutions provided in an explicit example can be continued beyond the singularity at t = 0 , passing a finite minimal extension of the universe.
New Hamiltonians for loop quantum cosmology with arbitrary spin representations
Ben Achour, Jibril; Brahma, Suddhasattwa; Geiller, Marc
2017-04-01
In loop quantum cosmology, one has to make a choice of SU(2) irreducible representation in which to compute holonomies and regularize the curvature of the connection. The systematic choice made in the literature is to work in the fundamental representation, and very little is known about the physics associated with higher spin labels. This constitutes an ambiguity of which the understanding, we believe, is fundamental for connecting loop quantum cosmology to full theories of quantum gravity like loop quantum gravity, its spin foam formulation, or cosmological group field theory. We take a step in this direction by providing here a new closed formula for the Hamiltonian of flat Friedmann-Lemaître-Robertson-Walker models regularized in a representation of arbitrary spin. This expression is furthermore polynomial in the basic variables which correspond to well-defined operators in the quantum theory, takes into account the so-called inverse-volume corrections, and treats in a unified way two different regularization schemes for the curvature. After studying the effective classical dynamics corresponding to single and multiple-spin Hamiltonians, we study the behavior of the critical density when the number of representations is increased and the stability of the difference equations in the quantum theory.
International Nuclear Information System (INIS)
Raoelina Andriambololona; Ranaivoson, R.T.R.; Rakotoson, H.; Solofoarisina, W.C.
2015-04-01
We present a study on linear canonical transformation in the framework of a phase space representation of quantum mechanics that we have introduced in our previous work. We begin with a brief recall about the so called phase space representation. We give the definition of linear canonical transformation with the transformation law of coordinate and momentum operators. We establish successively the transformation laws of mean values, dispersions, basis state and wave functions.Then we introduce the concept of isodispersion linear canonical transformation.
Summary of session D2: quantum aspects of cosmology
International Nuclear Information System (INIS)
Bojowald, Martin
2008-01-01
This is a summary of talks about quantum aspects of cosmology. Topics involve the properties of quantum matter fields on an expanding spacetime as well as issues in the quantization of gravity itself. This session had three parts, one of which was in a joint session with quantum aspects of black holes (D1) and other quantum aspects (D3). The first block of talks was related to quantum aspects of field theories on a classical spacetime (with possible back-reaction), while the second block dealt in several ways with quantizations of gravity itself. The two talks in the combined session discussed issues in quantum theory on de Sitter space and will therefore be included here in the summary of the first block. For each talk, a reference is given for further details
Two-point functions in (loop) quantum cosmology
Energy Technology Data Exchange (ETDEWEB)
Calcagni, Gianluca; Oriti, Daniele [Max-Planck-Institute for Gravitational Physics (Albert Einstein Institute), Am Muehlenberg 1, D-14476 Golm (Germany); Gielen, Steffen [Max-Planck-Institute for Gravitational Physics (Albert Einstein Institute), Am Muehlenberg 1, D-14476 Golm (Germany); DAMTP, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA (United Kingdom)
2011-07-01
We discuss the path-integral formulation of quantum cosmology with a massless scalar field as a sum-over-histories of volume transitions, with particular but non-exclusive reference to loop quantum cosmology (LQC). Exploiting the analogy with the relativistic particle, we give a complete overview of the possible two-point functions, pointing out the choices involved in their definitions, deriving their vertex expansions and the composition laws they satisfy. We clarify the origin and relations of different quantities previously defined in the literature, in particular the tie between definitions using a group averaging procedure and those in a deparametrized framework. Finally, we draw some conclusions about the physics of a single quantum universe (where there exist superselection rules on positive- and negative-frequency sectors and different choices of inner product are physically equivalent) and multiverse field theories where the role of these sectors and the inner product are reinterpreted.
Two-point functions in (loop) quantum cosmology
Energy Technology Data Exchange (ETDEWEB)
Calcagni, Gianluca; Gielen, Steffen; Oriti, Daniele, E-mail: calcagni@aei.mpg.de, E-mail: gielen@aei.mpg.de, E-mail: doriti@aei.mpg.de [Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Muehlenberg 1, D-14476 Golm (Germany)
2011-06-21
The path-integral formulation of quantum cosmology with a massless scalar field as a sum-over-histories of volume transitions is discussed, with particular but non-exclusive reference to loop quantum cosmology. Exploiting the analogy with the relativistic particle, we give a complete overview of the possible two-point functions, pointing out the choices involved in their definitions, deriving their vertex expansions and the composition laws they satisfy. We clarify the origin and relations of different quantities previously defined in the literature, in particular the tie between definitions using a group averaging procedure and those in a deparametrized framework. Finally, we draw some conclusions about the physics of a single quantum universe (where there exist superselection rules on positive- and negative-frequency sectors and different choices of inner product are physically equivalent) and multiverse field theories where the role of these sectors and the inner product are reinterpreted.
Two-point functions in (loop) quantum cosmology
International Nuclear Information System (INIS)
Calcagni, Gianluca; Gielen, Steffen; Oriti, Daniele
2011-01-01
The path-integral formulation of quantum cosmology with a massless scalar field as a sum-over-histories of volume transitions is discussed, with particular but non-exclusive reference to loop quantum cosmology. Exploiting the analogy with the relativistic particle, we give a complete overview of the possible two-point functions, pointing out the choices involved in their definitions, deriving their vertex expansions and the composition laws they satisfy. We clarify the origin and relations of different quantities previously defined in the literature, in particular the tie between definitions using a group averaging procedure and those in a deparametrized framework. Finally, we draw some conclusions about the physics of a single quantum universe (where there exist superselection rules on positive- and negative-frequency sectors and different choices of inner product are physically equivalent) and multiverse field theories where the role of these sectors and the inner product are reinterpreted.
Measure problem in slow roll inflation and loop quantum cosmology
International Nuclear Information System (INIS)
Corichi, Alejandro; Karami, Asieh
2011-01-01
We consider the measure problem in standard slow-roll inflationary models from the perspective of loop quantum cosmology (LQC). Following recent results by Ashtekar and Sloan, we study the probability of having enough e-foldings and focus on its dependence on the quantum gravity scale, including the transition of the theory to the limit where general relativity (GR) is recovered. Contrary to the standard expectation, the probability of having enough inflation, that is close to 1 in LQC, grows and tends to 1 as one approaches the GR limit. We study the origin of the tension between these results with those by Gibbons and Turok, and offer an explanation that brings these apparent contradictory results into a coherent picture. As we show, the conflicting results stem from different choices of initial conditions for the computation of probability. The singularity-free scenario of loop quantum cosmology offers a natural choice of initial conditions, and suggests that enough inflation is generic.
Cosmological horizons and reconstruction of quantum field theories
International Nuclear Information System (INIS)
Dappiaggi, C.; Pinamonti, N.
2007-12-01
As a starting point for this manuscript, we remark how the cosmological horizon of a certain class of Friedmann-Robertson-Walker backgrounds shares some non trivial geometric properties with null infinity in an asymptotically flat spacetime. Such a feature is generalized to a larger class of expanding spacetimes M admitting a geodesically complete cosmological horizon J - common to all co-moving observers. This property is later exploited in order to recast, in a cosmological background, some recent results for a linear scalar quantum field theory in spacetimes asymptotically flat at null infinity. Under suitable hypotheses on M - valid for de Sitter spacetime and some other FRW spacetimes obtained by perturbing deSitter space - the algebra of observables for a Klein-Gordon field is mapped into a subalgebra of the algebra of observables W(J - ) constructed on the cosmological horizon. There is exactly one pure quasifree state λ on W(J - ) which fulfills a suitable energy positivity condition with respect to a generator related with the cosmological time displacements. Furthermore λ induces a preferred physically meaningful quantum state λ M for the quantum theory in the bulk. If M admits a timelike Killing generator preserving J - , then the associated self-adjoint generator in the GNS representation of λ M has positive spectrum (i.e. energy). Moreover λ M turns out to be invariant under every symmetry of the bulk metric which preserves the cosmological horizon. In the case of an expanding de Sitter spacetime, λ M coincides with the Euclidean (Bunch-Davies) vacuum state, hence being Hadamard in this case. Remarks on the validity of the Hadamard property for λ M in more general spacetimes are presented. (orig.)
Cosmological horizons and reconstruction of quantum field theories
Energy Technology Data Exchange (ETDEWEB)
Dappiaggi, C.; Pinamonti, N. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik]|[Trento Univ., Povo (Italy). Istituto Nazionale di Alta Matematica ' ' F. Severi' ' - GNFM; Moretti, V. [Trento Univ. (Italy). Dipt. di Matematica]|[Istituto Nazionale di Fisica Nucleare - Gruppo Collegato di Trento, Povo (Italy)
2007-12-15
As a starting point for this manuscript, we remark how the cosmological horizon of a certain class of Friedmann-Robertson-Walker backgrounds shares some non trivial geometric properties with null infinity in an asymptotically flat spacetime. Such a feature is generalized to a larger class of expanding spacetimes M admitting a geodesically complete cosmological horizon J{sup -} common to all co-moving observers. This property is later exploited in order to recast, in a cosmological background, some recent results for a linear scalar quantum field theory in spacetimes asymptotically flat at null infinity. Under suitable hypotheses on M - valid for de Sitter spacetime and some other FRW spacetimes obtained by perturbing deSitter space - the algebra of observables for a Klein-Gordon field is mapped into a subalgebra of the algebra of observables W(J{sup -}) constructed on the cosmological horizon. There is exactly one pure quasifree state {lambda} on W(J{sup -}) which fulfills a suitable energy positivity condition with respect to a generator related with the cosmological time displacements. Furthermore {lambda} induces a preferred physically meaningful quantum state {lambda}{sub M} for the quantum theory in the bulk. If M admits a timelike Killing generator preserving J{sup -}, then the associated self-adjoint generator in the GNS representation of {lambda}{sub M} has positive spectrum (i.e. energy). Moreover {lambda}{sub M} turns out to be invariant under every symmetry of the bulk metric which preserves the cosmological horizon. In the case of an expanding de Sitter spacetime, {lambda}{sub M} coincides with the Euclidean (Bunch-Davies) vacuum state, hence being Hadamard in this case. Remarks on the validity of the Hadamard property for {lambda}{sub M} in more general spacetimes are presented. (orig.)
Cosmological implications of modified gravity induced by quantum metric fluctuations
Energy Technology Data Exchange (ETDEWEB)
Liu, Xing [Sun Yat-Sen University, School of Physics, Guangzhou (China); Sun Yat-Sen University, Yat Sen School, Guangzhou (China); Harko, Tiberiu [Babes-Bolyai University, Department of Physics, Cluj-Napoca (Romania); University College London, Department of Mathematics, London (United Kingdom); Liang, Shi-Dong [Sun Yat-Sen University, School of Physics, Guangzhou (China); Sun Yat-Sen University, State Key Laboratory of Optoelectronic Material and Technology, Guangdong Province Key Laboratory of Display Material and Technology, School of Physics, Guangzhou (China)
2016-08-15
We investigate the cosmological implications of modified gravities induced by the quantum fluctuations of the gravitational metric. If the metric can be decomposed as the sum of the classical and of a fluctuating part, of quantum origin, then the corresponding Einstein quantum gravity generates at the classical level modified gravity models with a non-minimal coupling between geometry and matter. As a first step in our study, after assuming that the expectation value of the quantum correction can be generally expressed in terms of an arbitrary second order tensor constructed from the metric and from the thermodynamic quantities characterizing the matter content of the Universe, we derive the (classical) gravitational field equations in their general form. We analyze in detail the cosmological models obtained by assuming that the quantum correction tensor is given by the coupling of a scalar field and of a scalar function to the metric tensor, and by a term proportional to the matter energy-momentum tensor. For each considered model we obtain the gravitational field equations, and the generalized Friedmann equations for the case of a flat homogeneous and isotropic geometry. In some of these models the divergence of the matter energy-momentum tensor is non-zero, indicating a process of matter creation, which corresponds to an irreversible energy flow from the gravitational field to the matter fluid, and which is direct consequence of the non-minimal curvature-matter coupling. The cosmological evolution equations of these modified gravity models induced by the quantum fluctuations of the metric are investigated in detail by using both analytical and numerical methods, and it is shown that a large variety of cosmological models can be constructed, which, depending on the numerical values of the model parameters, can exhibit both accelerating and decelerating behaviors. (orig.)
Classical and quantum aspects of brane-world cosmology
International Nuclear Information System (INIS)
Cordero, Ruben; Rojas, Efrain
2011-01-01
We give a brief overview of several models in brane-world cosmology. In particular, we focus on the asymmetric DGP and Regge-Teiltelboim models. We present the associated equations of motion governing the dynamics of the brane and their corresponding Friedmann-like equations. In order to develop the quantum Regge-Teiltelboim type cosmology we construct its Ostrogradski Hamiltonian formalism which naturally leads to the corresponding Wheeler-DeWitt equation. In addition, we comment on possible generalizations for these models including second order derivative geometrical terms.
Value of the Cosmological Constant in Emergent Quantum Gravity
Energy Technology Data Exchange (ETDEWEB)
Hogan, Craig [Fermilab
2018-03-30
It is suggested that the exact value of the cosmological constant could be derived from first principles, based on entanglement of the Standard Model field vacuum with emergent holographic quantum geometry. For the observed value of the cosmological constant, geometrical information is shown to agree closely with the spatial information density of the QCD vacuum, estimated in a free-field approximation. The comparison is motivated by a model of exotic rotational fluctuations in the inertial frame that can be precisely tested in laboratory experiments. Cosmic acceleration in this model is always positive, but fluctuates with characteristic coherence length $\\approx 100$km and bandwidth $\\approx 3000$ Hz.
Quantum cosmology. The supersymmetric perspective. Vol. 1. Fundamentals
International Nuclear Information System (INIS)
Vargas Moniz, Paulo
2010-01-01
The two volumes that comprise Quantum Cosmology tackle the quantum description of the early universe from the perspective of supersymmetric models of elementary particle physics. The first volume is an accessible primer that covers the basics of the field, critically discussing ideas and concepts that comprise our current knowledge of supersymmetry and supergravity. After reviewing the fundamentals, it provides a thorough analysis of a first set of quantum cosmological models. The second volume is dedicated to more advanced topics. In it, the scope for analyzing quantum cosmological models within a supersymmetric framework is broadened. As much as possible, these two volumes treat what we know, what we think we know and what we think we do not know on an equal footing. Complete with problems and solutions for each chapter, the books are ideal for young, inquisitive minds eager to embark on in-depth research in this field. They provide readers with the tools they need to go on their own, pushing them to ask the right questions rather than seek definitive answers. (orig.)
Black-hole creation in quantum cosmology
Energy Technology Data Exchange (ETDEWEB)
Zhong Chao, Wu [Rome, Univ. `La Sapienza` (Italy). International Center for Relativistic Astrophysics]|[Specola Vaticana, Vatican City State (Vatican City State, Holy See)
1997-11-01
It is proven that the probability of a black hole created from the de Sitter space-time background, at the Wkb level, is the exponential of one quarter of the sum of the black hole and cosmological horizon areas, or the total entropy of the universe. This is true not only for the spherically symmetric cases of the Schwarzschild or Reissner-Nordstroem black holes, but also for the rotating cases of the Kerr black hole and the rotating charged case of the Newman black hole. The de Sitter metric is the most probable evolution at the Planckian era of the universe.
de Broglie-Bohm FRW universes in quantum string cosmology
International Nuclear Information System (INIS)
Marto, J.; Moniz, P. Vargas
2002-01-01
The purpose of this paper is to establish possible implications of the de Broglie-Bohm interpretation of quantum mechanics towards superstring cosmological dynamics. In this context, we investigate spatially flat FRW models retrieved from scalar-tensor theories of gravity with a cosmological constant present in the gravitational sector. These models are further characterized by the presence of different types of de Broglie-Bohm quantum potential terms. These are constructed from various classes of wave packets formed by superpositions of Bessel functions of different imaginary orders. As far as pre-big-bang scenarios are concerned, we find that quantum potentials yield varied types of an amplified influence of the singular classical boundary into the FRW early dynamics. Some consequences of the de Broglie-Bohm program towards pre-big-bang inflation and the graceful exit problem are then discussed. Other cosmological scenarios are also studied by means of modulation effects extracted from additional wave packets. We subsequently obtain a broader set of new solutions. Among the new solutions we find that they could still be related by duality properties, although a separation into pre- and post-big-bang classes is less clear. Some solutions show a cyclical behavior. Inflationary solutions can be identified and some of their dynamical features are subsequently analyzed. In particular, we discuss some of the differences between string inspired inflationary cosmologies with quantum potentials. The results suggest that de Broglie-Bohm quantum gravitational terms slow down inflation, constituting an effect similar to others previously described in the literature
Loop quantum cosmology with self-dual variables
Wilson-Ewing, Edward
2015-12-01
Using the complex-valued self-dual connection variables, the loop quantum cosmology of a closed Friedmann space-time coupled to a massless scalar field is studied. It is shown how the reality conditions can be imposed in the quantum theory by choosing a particular inner product for the kinematical Hilbert space. While holonomies of the self-dual Ashtekar connection are not well defined in the kinematical Hilbert space, it is possible to introduce a family of generalized holonomylike operators of which some are well defined; these operators in turn are used in the definition of the Hamiltonian constraint operator where the scalar field can be used as a relational clock. The resulting quantum theory is closely related, although not identical, to standard loop quantum cosmology constructed from the Ashtekar-Barbero variables with a real Immirzi parameter. Effective Friedmann equations are derived which provide a good approximation to the full quantum dynamics for sharply peaked states whose volume remains much larger than the Planck volume, and they show that for these states quantum gravity effects resolve the big-bang and big-crunch singularities and replace them by a nonsingular bounce. Finally, the loop quantization in self-dual variables of a flat Friedmann space-time is recovered in the limit of zero spatial curvature and is identical to the standard loop quantization in terms of the real-valued Ashtekar-Barbero variables.
Effective dynamics of the closed loop quantum cosmology
International Nuclear Information System (INIS)
Mielczarek, Jakub; Szydłowski, Marek; Hrycyna, Orest
2009-01-01
In this paper we study dynamics of the closed FRW model with holonomy corrections coming from loop quantum cosmology. We consider models with a scalar field and cosmological constant. In case of the models with cosmological constant and free scalar field, dynamics reduce to 2D system and analysis of solutions simplify. If only free scalar field is included then universe undergoes non-singular oscillations. For the model with cosmological constant, different behaviours are obtained depending on the value of Λ. If the value of Λ is sufficiently small, bouncing solutions with asymptotic de Sitter stages are obtained. However if the value of Λ exceeds critical value Λ c = 3 1/2 m Pl 2 /2πγ 3 ≅ 21m Pl 2 then solutions become oscillatory. Subsequently we study models with a massive scalar field. We find that this model possess generic inflationary attractors. In particular field, initially situated in the bottom of the potential, is driven up during the phase of quantum bounce. This subsequently leads to the phase of inflation. Finally we find that, comparing with the flat case, effects of curvature do not change qualitatively dynamics close to the phase of bounce. Possible effects of inverse volume corrections are also briefly discussed
arXiv Quantum coherence of cosmological perturbations
Giovannini, Massimo
2017-10-26
In this paper, the degrees of quantum coherence of cosmological perturbations of different spins are computed in the large-scale limit and compared with the standard results holding for a single mode of the electromagnetic field in an optical cavity. The degree of second-order coherence of curvature inhomogeneities (and, more generally, of the scalar modes of the geometry) reproduces faithfully the optical limit. For the vector and tensor fluctuations, the numerical values of the normalized degrees of second-order coherence in the zero time-delay limit are always larger than unity (which is the Poisson benchmark value) but differ from the corresponding expressions obtainable in the framework of the single-mode approximation. General lessons are drawn on the quantum coherence of large-scale cosmological fluctuations.
Effective state metamorphosis in semi-classical loop quantum cosmology
Energy Technology Data Exchange (ETDEWEB)
Singh, Parampreet [Institute for Gravitational Physics and Geometry, Pennsylvania State University, University Park, PA 16802 (United States)
2005-10-21
Modification to the behaviour of geometrical density at short scales is a key result of loop quantum cosmology, responsible for an interesting phenomenology in the very early universe. We demonstrate the way matter with arbitrary scale factor dependence in Hamiltonian incorporates this change in its effective dynamics in the loop-modified phase. For generic matter, the equation of state starts varying near a critical scale factor, becomes negative below it and violates the strong energy condition. This opens a new avenue to generalize various phenomenological applications in loop quantum cosmology. We show that different ways to define energy density may yield radically different results, especially for the case corresponding to classical dust. We also discuss implications for frequency dispersion induced by modification to geometric density at small scales.
Quantum cosmology with effects of a preferred reference frame
International Nuclear Information System (INIS)
Ghaffarnejad, Hossein
2010-01-01
Recently, we presented a gravity model by generalizing the Brans-Dicke theory which is suitable for studying the metric signature transition dynamics without using an imaginary time parameter. Adding a suitable scalar potential described in terms of the Brans-Dicke scalar field 'Φ-tilde, this alternative theory is used to study the Wheeler-DeWitt approach of quantum cosmology. We assumed that the universe is defined in a flat Robertson-Walker metric with Lorentzian signature. In that case, the Wheeler-DeWitt wavefunctional is obtained as two-dimensional quantum harmonic oscillator convergent polynomials for both of the choices of positive and negative values of the Brans-Dicke parameter. Here we choose a preferred reference frame with a time coordinate of 'γ' which relates to time of cosmological free falling observer 't' as 'dt= Φ-tilde(γ)dγ'.
Aspects of Nonlocality in Quantum Field Theory, Quantum Gravity and Cosmology
Barvinsky, A O
2015-01-01
This paper contains a collection of essays on nonlocal phenomena in quantum field theory, gravity and cosmology. Mechanisms of nonlocal contributions to the quantum effective action are discussed within the covariant perturbation expansion in field strengths and spacetime curvatures and the nonperturbative method based on the late time asymptotics of the heat kernel. Euclidean version of the Schwinger-Keldysh technique for quantum expectation values is presented as a special rule of obtaining the nonlocal effective equations of motion for the mean quantum field from the Euclidean effective action. This rule is applied to a new model of ghost free nonlocal cosmology which can generate the de Sitter stage of cosmological evolution at an arbitrary value of $\\varLambda$ -- a model of dark energy with its scale played by the dynamical variable that can be fixed by a kind of a scaling symmetry breaking mechanism. This model is shown to interpolate between the superhorizon phase of gravity theory mediated by a scala...
Relational motivation for conformal operator ordering in quantum cosmology
International Nuclear Information System (INIS)
Anderson, Edward
2010-01-01
Operator ordering in quantum cosmology is a major as-yet unsettled ambiguity with not only formal but also physical consequences. We determine the Lagrangian origin of the conformal invariance that underlies the conformal operator-ordering choice in quantum cosmology. This arises particularly naturally and simply from relationalist product-type actions (such as the Jacobi action for mechanics or Baierlein-Sharp-Wheeler-type actions for general relativity), for which all that is required is for the kinetic and potential factors to rescale in compensation to each other. These actions themselves mathematically sharply implement philosophical principles relevant to whole-universe modelling, so that the motivation for conformal operator ordering in quantum cosmology is thereby substantially strengthened. Relationalist product-type actions also give emergent times which amount to recovering Newtonian, proper and cosmic time in various contexts. The conformal scaling of these actions directly tells us how emergent time scales; if one follows suit with the Newtonian time or the lapse in the more commonly used difference-type Euler-Lagrange or Arnowitt-Deser-Misner-type actions, one sees how these too obey a more complicated conformal invariance. Moreover, our discovery of the conformal scaling of the emergent time permits relating how this simplifies equations of motion with how affine parametrization simplifies geodesics.
Approximating the physical inner product of loop quantum cosmology
International Nuclear Information System (INIS)
Bahr, Benjamin; Thiemann, Thomas
2007-01-01
In this paper, we investigate the possibility of approximating the physical inner product of constrained quantum theories. In particular, we calculate the physical inner product of a simple cosmological model in two ways: firstly, we compute it analytically via a trick; secondly, we use the complexifier coherent states to approximate the physical inner product defined by the master constraint of the system. We find that the approximation is able to recover the analytic solution of the problem, which consolidates hopes that coherent states will help to approximate solutions of more complicated theories, like loop quantum gravity
COVARIANT INTEGRAL QUANTIZATIONS AND THEIR APPLICATIONS TO QUANTUM COSMOLOGY
Directory of Open Access Journals (Sweden)
Jean-Pierre Gazeau
2016-06-01
Full Text Available We present a general formalism for giving a measure space paired with a separable Hilbert space a quantum version based on a normalized positive operator-valued measure. The latter are built from families of density operators labeled by points of the measure space. We especially focus on group representation and probabilistic aspects of these constructions. Simple phase space examples illustrate the procedure: plane (Weyl-Heisenberg symmetry, half-plane (affine symmetry. Interesting applications to quantum cosmology (“smooth bouncing” for Friedmann-Robertson-Walker metric are presented and those for Bianchi I and IX models are mentioned.
Cosmological implications of quantum entanglement in the multiverse
International Nuclear Information System (INIS)
Kanno, Sugumi
2015-01-01
We explore the cosmological implications of quantum entanglement between two causally disconnected universes in the multiverse. We first consider two causally separated de Sitter spaces with a state which is initially entangled. We derive the reduced density matrix of our universe and compute the spectrum of vacuum fluctuations. We then consider the same system with an initially non-entangled state. We find that due to quantum interference scale dependent modulations may enter the spectrum for the case of initially non-entangled state. This gives rise to the possibility that the existence of causally disconnected universes may be experimentally tested by analyzing correlators in detail.
Cosmological implications of quantum entanglement in the multiverse
Directory of Open Access Journals (Sweden)
Sugumi Kanno
2015-12-01
Full Text Available We explore the cosmological implications of quantum entanglement between two causally disconnected universes in the multiverse. We first consider two causally separated de Sitter spaces with a state which is initially entangled. We derive the reduced density matrix of our universe and compute the spectrum of vacuum fluctuations. We then consider the same system with an initially non-entangled state. We find that due to quantum interference scale dependent modulations may enter the spectrum for the case of initially non-entangled state. This gives rise to the possibility that the existence of causally disconnected universes may be experimentally tested by analyzing correlators in detail.
Cosmological implications of quantum entanglement in the multiverse
Energy Technology Data Exchange (ETDEWEB)
Kanno, Sugumi, E-mail: sugumi.kanno@ehu.es [Department of Theoretical Physics and History of Science, University of the Basque Country UPV/EHU, 48080 Bilbao (Spain); IKERBASQUE, Basque Foundation for Science, Maria Diaz de Haro 3, 48013 Bilbao (Spain)
2015-12-17
We explore the cosmological implications of quantum entanglement between two causally disconnected universes in the multiverse. We first consider two causally separated de Sitter spaces with a state which is initially entangled. We derive the reduced density matrix of our universe and compute the spectrum of vacuum fluctuations. We then consider the same system with an initially non-entangled state. We find that due to quantum interference scale dependent modulations may enter the spectrum for the case of initially non-entangled state. This gives rise to the possibility that the existence of causally disconnected universes may be experimentally tested by analyzing correlators in detail.
Cosmological implications of quantum entanglement in the multiverse
Kanno, Sugumi
2015-12-01
We explore the cosmological implications of quantum entanglement between two causally disconnected universes in the multiverse. We first consider two causally separated de Sitter spaces with a state which is initially entangled. We derive the reduced density matrix of our universe and compute the spectrum of vacuum fluctuations. We then consider the same system with an initially non-entangled state. We find that due to quantum interference scale dependent modulations may enter the spectrum for the case of initially non-entangled state. This gives rise to the possibility that the existence of causally disconnected universes may be experimentally tested by analyzing correlators in detail.
On a Continuum Limit for Loop Quantum Cosmology
International Nuclear Information System (INIS)
Corichi, Alejandro; Vukasinac, Tatjana; Zapata, Jose Antonio
2008-01-01
The use of non-regular representations of the Heisenberg-Weyl commutation relations has proved to be useful for studying conceptual and technical issues in quantum gravity. Of particular relevance is the study of Loop Quantum Cosmology (LQC), symmetry reduced theory that is related to Loop Quantum Gravity, and that is based on a non-regular, polymeric representation. Recently, a soluble model was used by Ashtekar, Corichi and Singh to study the relation between Loop Quantum Cosmology and the standard Wheeler-DeWitt theory and, in particular, the passage to the limit in which the auxiliary parameter (interpreted as ''quantum geometry discreetness'') is sent to zero in hope to get rid of this 'regulator' that dictates the LQC dynamics at each 'scale'. In this note we outline the first steps toward reformulating this question within the program developed by the authors for studying the continuum limit of polymeric theories, which was successfully applied to simple systems such as a Simple Harmonic Oscillator
Probing models of quantum decoherence in particle physics and cosmology
Energy Technology Data Exchange (ETDEWEB)
Mavromatos, Nikolaos E; Sarkar, Sarben [King' s College London, Department of Physics, Theoretical Physics, Strand London WC2R 2LS (United Kingdom)
2007-05-15
In this review we discuss the string theoretical motivations for induced decoherence and deviations from ordinary quantum-mechanical behaviour; this leads to intrinsic CPT violation in the context of an extended class of quantum-gravity models. We proceed to a description of precision tests of CPT symmetry and quantum mechanics using mainly neutral kaons and neutrinos. We emphasize the possibly unique role of neutral meson factories in providing tests of models where the quantum-mechanical CPT operator is not well-defined, leading to modifications of Einstein-Podolsky-Rosen particle correlators. Finally, we discuss experimental probes of decoherence in cosmology, including studies of dissipative relaxation models of dark energy in non-critical (non-equilibrium) string theory and the associated modifications of the Boltzmann equation for the evolution of species abundances.
Numerical analysis of the big bounce in loop quantum cosmology
International Nuclear Information System (INIS)
Laguna, Pablo
2007-01-01
Loop quantum cosmology (LQC) homogeneous models with a massless scalar field show that the big-bang singularity can be replaced by a big quantum bounce. To gain further insight on the nature of this bounce, we study the semidiscrete loop quantum gravity Hamiltonian constraint equation from the point of view of numerical analysis. For illustration purposes, we establish a numerical analogy between the quantum bounces and reflections in finite difference discretizations of wave equations triggered by the use of nonuniform grids or, equivalently, reflections found when solving numerically wave equations with varying coefficients. We show that the bounce is closely related to the method for the temporal update of the system and demonstrate that explicit time-updates in general yield bounces. Finally, we present an example of an implicit time-update devoid of bounces and show back-in-time, deterministic evolutions that reach and partially jump over the big-bang singularity
de Haro, Jaume; Amorós, Jaume
2018-03-01
We consider the Arnowitt-Deser-Misner formalism as a tool to build bouncing cosmologies. In this approach, the foliation of the spacetime has to be fixed in order to go beyond general relativity modifying the gravitational sector. Once a preferred slicing, which we choose based on the matter content of the Universe following the spirit of Weyl's postulate, has been fixed, f theories depending on the extrinsic and intrinsic curvature of the slicing are covariant for all the reference frames preserving the foliation; i.e., the constraint and dynamical equations have the same form for all these observers. Moreover, choosing multivalued f functions, bouncing backgrounds emerge in a natural way. In fact, the simplest is the one corresponding to holonomy corrected loop quantum cosmology. The final goal of this work is to provide the equations of perturbations which, unlike the full equations, become gauge invariant in this theory, and apply them to the so-called matter bounce scenario.
Understanding big bang in loop quantum cosmology: Recent advances
Energy Technology Data Exchange (ETDEWEB)
Singh, Parampreet [Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario N2L 2Y5 (Canada)], E-mail: psingh@perimeterinstitute.ca
2008-11-01
We discuss the way non-perturbative quantization of cosmological spacetimes in loop quantum cosmology provides insights on the physics of Planck scale and the resolution of big bang singularity. In recent years, rigorous examination of mathematical and physical aspects of the quantum theory, have singled out a consistent quantization which is physically viable and various early ideas have been shown to be inconsistent. These include 'physical effects' originating from modifications to inverse scale factors in the flat models. The singularity resolution is understood to originate from the non-local nature of curvature in the quantum theory and the underlying polymer representation. Based on insights from extensive numerical simulations, an exactly solvable model involving a small approximation at the quantum level can be developed. The model predicts occurrence of bounce for a dense subspace of the Hilbert space and a supremum for the value of energy density. It also provides answers to the growth of fluctuations, showing that semi-classicality is preserved to an amazing degree across the bounce.
Understanding big bang in loop quantum cosmology: Recent advances
Singh, Parampreet
2008-11-01
We discuss the way non-perturbative quantization of cosmological spacetimes in loop quantum cosmology provides insights on the physics of Planck scale and the resolution of big bang singularity. In recent years, rigorous examination of mathematical and physical aspects of the quantum theory, have singled out a consistent quantization which is physically viable and various early ideas have been shown to be inconsistent. These include 'physical effects' originating from modifications to inverse scale factors in the flat models. The singularity resolution is understood to originate from the non-local nature of curvature in the quantum theory and the underlying polymer representation. Based on insights from extensive numerical simulations, an exactly solvable model involving a small approximation at the quantum level can be developed. The model predicts occurrence of bounce for a dense subspace of the Hilbert space and a supremum for the value of energy density. It also provides answers to the growth of fluctuations, showing that semi-classicality is preserved to an amazing degree across the bounce.
Loop quantum cosmology of k=1 FRW models
International Nuclear Information System (INIS)
Ashtekar, Abhay; Pawlowski, Tomasz; Singh, Parampreet; Vandersloot, Kevin
2007-01-01
The closed, k=1, FRW model coupled to a massless scalar field is investigated in the framework of loop quantum cosmology using analytical and numerical methods. As in the k=0 case, the scalar field can be again used as emergent time to construct the physical Hilbert space and introduce Dirac observables. The resulting framework is then used to address a major challenge of quantum cosmology: resolving the big-bang singularity while retaining agreement with general relativity at large scales. It is shown that the framework fulfills this task. In particular, for states which are semiclassical at some late time, the big bang is replaced by a quantum bounce and a recollapse occurs at the value of the scale factor predicted by classical general relativity. Thus, the ''difficulties'' pointed out by Green and Unruh in the k=1 case do not arise in a more systematic treatment. As in k=0 models, quantum dynamics is deterministic across the deep Planck regime. However, because it also retains the classical recollapse, in contrast to the k=0 case one is now led to a cyclic model. Finally, we clarify some issues raised by Laguna's recent work addressed to computational physicists
Understanding big bang in loop quantum cosmology: Recent advances
International Nuclear Information System (INIS)
Singh, Parampreet
2008-01-01
We discuss the way non-perturbative quantization of cosmological spacetimes in loop quantum cosmology provides insights on the physics of Planck scale and the resolution of big bang singularity. In recent years, rigorous examination of mathematical and physical aspects of the quantum theory, have singled out a consistent quantization which is physically viable and various early ideas have been shown to be inconsistent. These include 'physical effects' originating from modifications to inverse scale factors in the flat models. The singularity resolution is understood to originate from the non-local nature of curvature in the quantum theory and the underlying polymer representation. Based on insights from extensive numerical simulations, an exactly solvable model involving a small approximation at the quantum level can be developed. The model predicts occurrence of bounce for a dense subspace of the Hilbert space and a supremum for the value of energy density. It also provides answers to the growth of fluctuations, showing that semi-classicality is preserved to an amazing degree across the bounce.
Quantum cosmology based on discrete Feynman paths
International Nuclear Information System (INIS)
Chew, Geoffrey F.
2002-01-01
Although the rules for interpreting local quantum theory imply discretization of process, Lorentz covariance is usually regarded as precluding time quantization. Nevertheless a time-discretized quantum representation of redshifting spatially-homogeneous universe may be based on discrete-step Feynman paths carrying causal Lorentz-invariant action--paths that not only propagate the wave function but provide a phenomenologically-promising elementary-particle Hilbert-space basis. In a model under development, local path steps are at Planck scale while, at a much larger ''wave-function scale'', global steps separate successive wave-functions. Wave-function spacetime is but a tiny fraction of path spacetime. Electromagnetic and gravitational actions are ''at a distance'' in Wheeler-Feynman sense while strong (color) and weak (isospin) actions, as well as action of particle motion, are ''local'' in a sense paralleling the action of local field theory. ''Nonmaterial'' path segments and ''trivial events'' collaborate to define energy and gravity. Photons coupled to conserved electric charge enjoy privileged model status among elementary fermions and vector bosons. Although real path parameters provide no immediate meaning for ''measurement'', the phase of the complex wave function allows significance for ''information'' accumulated through ''gentle'' electromagnetic events involving charged matter and ''soft'' photons. Through its soft-photon content the wave function is an ''information reservoir''
Black-hole horizons in modified spacetime structures arising from canonical quantum gravity
International Nuclear Information System (INIS)
Bojowald, Martin; Paily, George M; Reyes, Juan D; Tibrewala, Rakesh
2011-01-01
Several properties of canonical quantum gravity modify spacetime structures, sometimes to the degree that no effective line elements exist to describe the geometry. An analysis of solutions, for instance in the context of black holes, then requires new insights. In this paper, standard definitions of horizons in spherical symmetry are first reformulated canonically, and then evaluated for solutions of equations and constraints modified by inverse-triad corrections of loop quantum gravity. When possible, a spacetime analysis is performed which reveals a mass threshold for black holes and small changes to Hawking radiation. For more general conclusions, canonical perturbation theory is developed to second order to include back-reaction from matter. The results shed light on the questions of whether renormalization of Newton's constant or other modifications of horizon conditions should be taken into account in computations of black-hole entropy in loop quantum gravity.
Loop quantum cosmology: from pre-inflationary dynamics to observations
International Nuclear Information System (INIS)
Ashtekar, Abhay; Barrau, Aurélien
2015-01-01
The Planck collaboration has provided us rich information about the early Universe, and a host of new observational missions will soon shed further light on the ‘anomalies’ that appear to exist on the largest angular scales. From a quantum gravity perspective, it is natural to inquire if one can trace back the origin of such puzzling features to Planck scale physics. Loop quantum cosmology provides a promising avenue to explore this issue because of its natural resolution of the big bang singularity. Thanks to advances over the last decade, the theory has matured sufficiently to allow concrete calculations of the phenomenological consequences of its pre-inflationary dynamics. In this article we summarize the current status of the ensuing two-way dialog between quantum gravity and observations. (paper)
Non-minimally coupled varying constants quantum cosmologies
International Nuclear Information System (INIS)
Balcerzak, Adam
2015-01-01
We consider gravity theory with varying speed of light and varying gravitational constant. Both constants are represented by non-minimally coupled scalar fields. We examine the cosmological evolution in the near curvature singularity regime. We find that at the curvature singularity the speed of light goes to infinity while the gravitational constant vanishes. This corresponds to the Newton's Mechanics limit represented by one of the vertex of the Bronshtein-Zelmanov-Okun cube [1,2]. The cosmological evolution includes both the pre-big-bang and post-big-bang phases separated by the curvature singularity. We also investigate the quantum counterpart of the considered theory and find the probability of transition of the universe from the collapsing pre-big-bang phase to the expanding post-big-bang phase
Tunneling in quantum cosmology and holographic SYM theory
Ghoroku, Kazuo; Nakano, Yoshimasa; Tachibana, Motoi; Toyoda, Fumihiko
2018-03-01
We study the time evolution of the early Universe, which is developed by a cosmological constant Λ4 and supersymmetric Yang-Mills (SYM) fields in the Friedmann-Robertson-Walker space-time. The renormalized vacuum expectation value of the energy-momentum tensor of the SYM theory is obtained in a holographic way. It includes a radiation of the SYM field, parametrized as C . The evolution is controlled by this radiation C and the cosmological constant Λ4. For positive Λ4, an inflationary solution is obtained at late time. When C is added, the quantum mechanical situation at early time is fairly changed. Here we perform the early time analysis in terms of two different approaches, (i) the Wheeler-DeWitt equation and (ii) Lorentzian path integral with the Picard-Lefschetz method by introducing an effective action. The results of two methods are compared.
Canonical quantum theory of gravitational field with higher derivatives, 2
International Nuclear Information System (INIS)
Kawasaki, Shoichiro; Kimura, Tadahiko
1982-01-01
The asymptotic fields in a canonically quantized graviational field with higher derivatives are analyzed. A possible mechanism of the recovery of the physical S-matrix unitarity is discussed. The constraint nabla sub(μ)(B sup(μν) + (Beta /α)g sup(μν)B) = 0 due to the Bianchi identity on R sub(μν) is treated by Dirac's method. (author)
Canonical quantum theory of gravitational field with higher derivatives
International Nuclear Information System (INIS)
Kawasaki, Shoichiro; Kimura, Tadahiko; Kitago, Koichi.
1981-01-01
A renormalizable gravitational theory with higher derivatives is canonically quantized in the Landau gauge. Field equations and various equal-time commutation relations are explicitly given. The main results obtained in this work are 1) the equal-time commutation relations involving b sub(μ) exhibit the tensor-like behaviour and 2) the theory has the 16-dimensional Poincare-like superalgebra. These results are just the same as those discovered by Nakanishi in the Einstein case. (author)
Recollapsing quantum cosmologies and the question of entropy
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Bojowald, Martin; Tavakol, Reza
2008-01-01
Recollapsing homogeneous and isotropic models present one of the key ingredients for cyclic scenarios. This is considered here within a quantum cosmological framework in the presence of a free scalar field with, in turn, a negative cosmological constant and spatial curvature. Effective equations shed light on the quantum dynamics around a recollapsing phase and the evolution of state parameters such as fluctuations and correlations through such a turn around. In the models considered here, the squeezing of an initial state is found to be strictly monotonic in time during the expansion, turn around, and contraction phases. The presence of such monotonicity is of potential importance in relation to a long-standing debate concerning the (a)symmetry between the expanding and contracting phases in a recollapsing universe. Furthermore, together with recent analogous results concerning a bounce, one can extend this monotonicity throughout an entire cycle. This provides a strong motivation for employing the degree of squeezing as an alternative measure of (quantum) entropy. It may also serve as a new concept of emergent time described by a variable without classical analog. The evolution of the squeezing in emergent oscillating scenarios can in principle provide constraints on the viability of such models.
Loop quantum cosmology of Bianchi IX: effective dynamics
International Nuclear Information System (INIS)
Corichi, Alejandro; Montoya, Edison
2017-01-01
We study solutions to the effective equations for the Bianchi IX class of spacetimes within loop quantum cosmology (LQC). We consider Bianchi IX models whose matter content is a massless scalar field, by numerically solving the loop quantum cosmology effective equations, with and without inverse triad corrections. The solutions are classified using certain geometrically motivated classical observables. We show that both effective theories—with lapse N = V and N = 1—resolve the big bang singularity and reproduce the classical dynamics far from the bounce. Moreover, due to the positive spatial curvature, there is an infinite number of bounces and recollapses. We study the limit of large field momentum and show that both effective theories reproduce the same dynamics, thus recovering general relativity. We implement a procedure to identify amongst the Bianchi IX solutions, those that behave like k = 0,1 FLRW as well as Bianchi I, II, and VII 0 models. The effective solutions exhibit Bianchi I phases with Bianchi II transitions and also Bianchi VII 0 phases, which had not been studied before. We comment on the possible implications of these results for a quantum modification to the classical BKL behaviour. (paper)
Loop quantum cosmology of Bianchi IX: effective dynamics
Corichi, Alejandro; Montoya, Edison
2017-03-01
We study solutions to the effective equations for the Bianchi IX class of spacetimes within loop quantum cosmology (LQC). We consider Bianchi IX models whose matter content is a massless scalar field, by numerically solving the loop quantum cosmology effective equations, with and without inverse triad corrections. The solutions are classified using certain geometrically motivated classical observables. We show that both effective theories—with lapse N = V and N = 1—resolve the big bang singularity and reproduce the classical dynamics far from the bounce. Moreover, due to the positive spatial curvature, there is an infinite number of bounces and recollapses. We study the limit of large field momentum and show that both effective theories reproduce the same dynamics, thus recovering general relativity. We implement a procedure to identify amongst the Bianchi IX solutions, those that behave like k = 0,1 FLRW as well as Bianchi I, II, and VII0 models. The effective solutions exhibit Bianchi I phases with Bianchi II transitions and also Bianchi VII0 phases, which had not been studied before. We comment on the possible implications of these results for a quantum modification to the classical BKL behaviour.
Quantum scalar-metric cosmology with Chaplygin gas
International Nuclear Information System (INIS)
Majumder, Barun
2011-01-01
A spatially flat Friedmann-Robertson-Walker (FRW) cosmological model with generalized Chaplygin gas is studied in the context of scalar-metric formulation of cosmology. Schutz's mechanism for the perfect fluid is applied with generalized Chaplygin gas and the classical and quantum dynamics for this model is studied. It is found that the only surviving matter degree of freedom played the role of cosmic time. For the quantum mechanical description it is possible to find the wave packet which resulted from the linear superposition of the wave functions of the Schroedinger-Wheeler-DeWitt (SWD) equation, which is a consequence of the above formalism. The wave packets show two distinct dominant peaks and propagate in the direction of increasing scale factor. It may happen that our present universe originated from one of those peaks. The many-world and ontological interpretation of quantum mechanics is applied to investigate about the behavior of the scale factor and the scalar field (considered for this model). In both the cases the scale factor avoids singularity and a bouncing non-singular universe is found.
Quantum effects in the Gowdy T3 cosmology
International Nuclear Information System (INIS)
Berger, B.K.
1984-01-01
The Gowdy T 3 Cosmology is an exact solution to the vacuum Einstein equations interpreted to be a single polarization of gravitational waves propagating in an anisotropic, spatially inhomogeneous background. The classical behavior is reviewed and related to standard cosmological parameters. Canonical quantization of the dynamical degrees of freedom is reviewed. An adiabatic vacuum state is constructed. Adiabatic regularization if used to obtain non-divergent stress-energy tensor vacuum expectation values. Casimir energy terms due to T 3 imposed discrete modes are evaluated. The vacuum expectation values are analyzed in early and late time limits and evaluated numerically. The regularized expectation value is used as a source for the classical background spacetime in the spirit of semi-classical gravity. An entirely vacuum expectation value source term produces essentially the time reverse of the classical evolution. Classical stress-energy added to the source restores the classical behavior at lates times only. The combined system collapses from infinite to small but non-zero volume and reexpands. The classical singularity is replaced by a symmetric bounce
Holographic Bound in Quantum Field Energy Density and Cosmological Constant
Castorina, Paolo
2012-01-01
The cosmological constant problem is reanalyzed by imposing the limitation of the number of degrees of freedom (d.o.f.) due to entropy bounds directly in the calculation of the energy density of a field theory. It is shown that if a quantum field theory has to be consistent with gravity and holography, i.e. with an upper limit of storing information in a given area, the ultraviolet momentum cut-off is not the Planck mass, M_p, as naively expected, but M_p/N_U^(1/4) where N_U is the number of ...
Clifford Algebras and Spinorial Representation of Linear Canonical Transformations in Quantum Theory
International Nuclear Information System (INIS)
Raoelina Andriambololona; Ranaivoson, R.T.R.; Rakotoson, H.
2017-11-01
This work is a continuation of previous works that we have done concerning linear canonical transformations and a phase space representation of quantum theory. It is mainly focused on the description of an approach which permits to establish spinorial representation of linear canonical transformations. It begins with an introduction section in which the reason and context of the content are discussed. The introduction section is followed by a brief recall about Clifford algebra and spin group. The description of the approach is started with the presentation of an adequate parameterization of linear canonical transformations which permits to represent them with special pseudo-orthogonal transformations in an operators space. The establishment of the spinorial representation is deduced using relation between special pseudo-orthogonal groups and spin groups. The cases of one dimension quantum mechanics and general multidimensional theory are both studied. The case of linear canonical transformation related to Minkowski space is particularly studied and it is shown that Lorentz transformation may be considered as particular case of linear canonical transformation. Some results from the spinorial representation are also exploited to define operators which may be used to establish equations for fields if one considers the possibility of envisaging a field theory which admits as main symmetry group the group constituted by linear canonical transformations.
Quantum to classical transition in the Hořava-Lifshitz quantum cosmology
Bernardini, A. E.; Leal, P.; Bertolami, O.
2018-02-01
A quasi-Gaussian quantum superposition of Hořava-Lifshitz (HL) stationary states is built in order to describe the transition of the quantum cosmological problem to the related classical dynamics. The obtained HL phase-space superposed Wigner function and its associated Wigner currents describe the conditions for the matching between classical and quantum phase-space trajectories. The matching quantum superposition parameter is associated to the total energy of the classical trajectory which, at the same time, drives the engendered Wigner function to the classical stationary regime. Through the analysis of the Wigner flows, the quantum fluctuations that distort the classical regime can be quantified as a measure of (non)classicality. Finally, the modifications to the Wigner currents due to the inclusion of perturbative potentials are computed in the HL quantum cosmological context. In particular, the inclusion of a cosmological constant provides complementary information that allows for connecting the age of the Universe with the overall stiff matter density profile.
The canonical quantization of local scalar fields over quantum space-time
International Nuclear Information System (INIS)
Banai, M.
1983-05-01
Canonical quantization of a classical local field theory (CLFT) consisting of N real scalar fields is formulated in the Hilbert space over the sup(*)-algebra A of linear operators of L 2 (R 3 ). The canonical commutation relations (CCR) have an irreducible solution, unique up to A-unitary equivalence. The canonical equations as operator equations are equivalent to the classical (c) field equations. The interaction picture can be introduced in a well-defined manner. The main adventage of this treatment is that the corresponding S-matrix is free of divergences. The Feynman's graph technique is adaptable in a straightforward manner. This approach is a natural extension of the conventional canonical quantization method of quantum mechanics. (author)
Decoherence, discord, and the quantum master equation for cosmological perturbations
Hollowood, Timothy J.; McDonald, Jamie I.
2017-05-01
We examine environmental decoherence of cosmological perturbations in order to study the quantum-to-classical transition and the impact of noise on entanglement during inflation. Given an explicit interaction between the system and environment, we derive a quantum master equation for the reduced density matrix of perturbations, drawing parallels with quantum Brownian motion, where we see the emergence of fluctuation and dissipation terms. Although the master equation is not in Lindblad form, we see how typical solutions exhibit positivity on super-horizon scales, leading to a physically meaningful density matrix. This allows us to write down a Langevin equation with stochastic noise for the classical trajectories which emerge from the quantum system on super-horizon scales. In particular, we find that environmental decoherence increases in strength as modes exit the horizon, with the growth driven essentially by white noise coming from local contributions to environmental correlations. Finally, we use our master equation to quantify the strength of quantum correlations as captured by discord. We show that environmental interactions have a tendency to decrease the size of the discord and that these effects are determined by the relative strength of the expansion rate and interaction rate of the environment. We interpret this in terms of the competing effects of particle creation versus environmental fluctuations, which tend to increase and decrease the discord respectively.
Global effects of scalar matter production in quantum cosmology
International Nuclear Information System (INIS)
Barvinskij, A.O.; Ponomarev, V.N.
1978-01-01
Within the framework of the geometrodynamical approach global effects of the production of scalar matter filling the closed uniform Friedman Universe are considered. The physical situation is discussed, which corresponds to such a scale of space-time intervals and energies, at which the matter is essentially quantum and the quantized gravitational field is within the quasi-classical limits when its spatial inhomogeneities are small and only global quantum effects are considerable. The only dynamic variable of the gravitational field is the Friedman Universe radius. The main principles of the formalism of the canonical superspace quantization of gravitational and material fields are considered. The method shows the applicability limits of the field theory on the background of classical geometry and leads to the principally new types of interaction
Directory of Open Access Journals (Sweden)
Marcos Moshinsky
2008-07-01
Full Text Available For classical canonical transformations, one can, using the Wigner transformation, pass from their representation in Hilbert space to a kernel in phase space. In this paper it will be discussed how the time-dependence of the uncertainties of the corresponding time-dependent quantum problems can be incorporated into this formalism.
From Classical to Quantum: New Canonical Tools for the Dynamics of Gravity
Höhn, P.A.
2012-01-01
In a gravitational context, canonical methods offer an intuitive picture of the dynamics and simplify an identification of the degrees of freedom. Nevertheless, extracting dynamical information from background independent approaches to quantum gravity is a highly non-trivial challenge. In this
International Nuclear Information System (INIS)
Ji, Un Cig; Obata, Nobuaki
2010-01-01
The implementation problem for the canonical commutation relation is reduced to a system of differential equations for Fock space operators containing new type of derivatives. We solve these differential equations systematically by means of quantum white noise calculus, and obtain the solution to the implementation problem.
International Nuclear Information System (INIS)
Novikov, I.D.
1979-01-01
Progress made by this Commission over the period 1976-1978 is reviewed. Topics include the Hubble constant, deceleration parameter, large-scale distribution of matter in the universe, radio astronomy and cosmology, space astronomy and cosmology, formation of galaxies, physics near the cosmological singularity, and unconventional cosmological models. (C.F.)
A new quantum representation for canonical gravity and SU(2) Yang-Mills theory
International Nuclear Information System (INIS)
Loll, R.
1990-04-01
Starting from Rovelli-Smolin's infinite-dimensional graded Poisson-bracket algebra of loop variables, we propose a new way of constructing a corresponding quantum representation. After eliminating certain quadratic constraints, we 'integrate' an infinite-dimensional subalgebra of loop variables, using a formal group law expansion. With the help of techniques from the representation theory of semidirect-product groups, we find an exact quantum representation of the full classical Poisson-bracket algebra of loop variables, without any higher-order correction terms. This opens new ways of tackling the quantum dynamics for both canonical gravity and Yang-Mills theory. (orig.)
A new quantum representation for canonical gravity and SU(2) Yang-Mills theory
International Nuclear Information System (INIS)
Loll, R.
1991-01-01
Starting from Rovelli-Smolin's infinite-dimensional graded Poisson-bracket algebra of loop variables, we propose a new way of constructing a corresponding quantum representation. After eliminating certain quadratic constraints, we 'integrate' an infinite-dimensional subalgebra of loop variables, using a formal group law expansion. With the help of techniques from the representation theory of semidirect-product groups, we find an exact quantum representation of the full classical Poisson-bracket algebra of loop variables, without any higher-order correction terms. This opens new ways of tackling the quantum dynamics for both canonical gravity and Yang-Mills theory. (orig.)
Towards canonical quantum gravity for G1 geometries in 2+1 dimensions with a Λ-term
International Nuclear Information System (INIS)
Christodoulakis, T; Doulis, G; Terzis, Petros A; Melas, E; Grammenos, Th; Papadopoulos, G O; Spanou, A
2008-01-01
The canonical analysis and subsequent quantization of the (2+1)-dimensional action of pure gravity plus a cosmological constant term is considered, under the assumption of the existence of one spacelike Killing vector field. The proper imposition of the quantum analogues of two linear (momentum) constraints reduces an initial collection of state vectors, consisting of all smooth functionals of the components (and/or their derivatives) of the spatial metric, to particular scalar smooth functionals. The demand that the midi-superspace metric (inferred from the kinetic part of the quadratic (Hamiltonian) constraint) must define on the space of these states an induced metric whose components are given in terms of the same states, which is made possible through an appropriate re-normalization assumption, severely reduces the possible state vectors to three unique (up to general coordinate transformations) smooth scalar functionals. The quantum analogue of the Hamiltonian constraint produces a Wheeler-DeWitt equation based on this reduced manifold of states, which is completely integrated
Relating loop quantum cosmology to loop quantum gravity: symmetric sectors and embeddings
International Nuclear Information System (INIS)
Engle, J
2007-01-01
In this paper we address the meaning of states in loop quantum cosmology (LQC), in the context of loop quantum gravity. First, we introduce a rigorous formulation of an embedding proposed by Bojowald and Kastrup, of LQC states into loop quantum gravity. Then, using certain holomorphic representations, a new class of embeddings, called b-embeddings, are constructed, following the ideas of Engle (2006 Quantum field theory and its symmetry reduction Class. Quantum Gravity 23 2861-94). We exhibit a class of operators preserving each of these embeddings, and show their consistency with the LQC quantization. In the b-embedding case, the classical analogues of these operators separate points in phase space. Embedding at the gauge and diffeomorphism invariant level is discussed briefly in the conclusions
Quantum kinematics of spacetime. II. A model quantum cosmology with real clocks
International Nuclear Information System (INIS)
Hartle, J.B.
1988-01-01
Nonrelativistic model quantum cosmologies are studied in which the basic time variable is the position of a clock indicator and the time parameter of the Schroedinger equation is an unobservable label. Familiar Schroedinger-Heisenberg quantum mechanics emerges if the clock is ideal: arbitrarily accurate for arbitrarily long times. More realistically, however, the usual formulation emerges only as an approximation appropriate to states of this model universe in which part of the system functions approximately as an ideal clock. It is suggested that the quantum kinematics of spacetime theories such as general relativity may be analogous to those of this model. In particular it is suggested that our familiar notion of time in quantum mechanics is not an inevitable property of a general quantum framework but an approximate feature of specific initial conditions
Time in Quantum Cosmology of FRW f(R Theories
Directory of Open Access Journals (Sweden)
C. Ramírez
2018-01-01
Full Text Available The time problem is a problem of canonical quantum gravity that has long been known about; it is related to the relativistic invariance and the consequent absence of an explicit time variable in the quantum equations. This fact complicates the interpretation of the wave function of the universe. Following proposals to assign the clock function to a scalar field, we look at the scalar degree of freedom contained in f ( R theories. For this purpose we consider a quadratic f ( R theory in an equivalent formulation with a scalar field, with a FRW metric, and consider its Wheeler-DeWitt equation. The wave function is obtained numerically and is consistent with the interpretation of the scalar field as time by means of a conditional probability, from which an effective time-dependent wave function follows. The evolution the scale factor is obtained by its mean value, and the quantum fluctuations are consistent with the Heisenberg relations and a classical universe today.
The matter-ekpyrotic bounce scenario in Loop Quantum Cosmology
Energy Technology Data Exchange (ETDEWEB)
Haro, Jaume; Amorós, Jaume; Saló, Llibert Aresté, E-mail: jaime.haro@upc.edu, E-mail: jaume.amoros@upc.edu, E-mail: llibert.areste@estudiant.upc.edu [Departament de Matemàtica Aplicada, Universitat Politècnica de Catalunya, Diagonal 647, 08028 Barcelona (Spain)
2017-09-01
We will perform a detailed study of the matter-ekpyrotic bouncing scenario in Loop Quantum Cosmology using the methods of the dynamical systems theory. We will show that when the background is driven by a single scalar field, at very late times, in the contracting phase, all orbits depict a matter dominated Universe, which evolves to an ekpyrotic phase. After the bounce the Universe enters in the expanding phase, where the orbits leave the ekpyrotic regime going to a kination (also named deflationary) regime. Moreover, this scenario supports the production of heavy massive particles conformally coupled with gravity, which reheats the universe at temperatures compatible with the nucleosynthesis bounds and also the production of massless particles non-conformally coupled with gravity leading to very high reheating temperatures but ensuring the nucleosynthesis success. Dealing with cosmological perturbations, these background dynamics produce a nearly scale invariant power spectrum for the modes that leave the Hubble radius, in the contracting phase, when the Universe is quasi-matter dominated, whose spectral index and corresponding running is compatible with the recent experimental data obtained by PLANCK's team.
The matter-ekpyrotic bounce scenario in Loop Quantum Cosmology
Haro, Jaume; Amorós, Jaume; Aresté Saló, Llibert
2017-09-01
We will perform a detailed study of the matter-ekpyrotic bouncing scenario in Loop Quantum Cosmology using the methods of the dynamical systems theory. We will show that when the background is driven by a single scalar field, at very late times, in the contracting phase, all orbits depict a matter dominated Universe, which evolves to an ekpyrotic phase. After the bounce the Universe enters in the expanding phase, where the orbits leave the ekpyrotic regime going to a kination (also named deflationary) regime. Moreover, this scenario supports the production of heavy massive particles conformally coupled with gravity, which reheats the universe at temperatures compatible with the nucleosynthesis bounds and also the production of massless particles non-conformally coupled with gravity leading to very high reheating temperatures but ensuring the nucleosynthesis success. Dealing with cosmological perturbations, these background dynamics produce a nearly scale invariant power spectrum for the modes that leave the Hubble radius, in the contracting phase, when the Universe is quasi-matter dominated, whose spectral index and corresponding running is compatible with the recent experimental data obtained by PLANCK's team.
Cosmic recall and the scattering picture of loop quantum cosmology
International Nuclear Information System (INIS)
Kaminski, Wojciech; Pawlowski, Tomasz
2010-01-01
The global dynamics of a homogeneous Universe in loop quantum cosmology is viewed as a scattering process of its geometrodynamical equivalent. This picture is applied to build a flexible (easy to generalize) and not restricted just to exactly solvable models method of verifying the preservation of the semiclassicality through the bounce. The devised method is next applied to two simple examples: (i) the isotropic Friedmann-Robertson-Walker universe, and (ii) the isotropic sector of the Bianchi I model. For both of them we show that the dispersions in the logarithm of the volume ln(v) and scalar field momentum ln(p φ ) in the distant future and past are related via strong triangle inequalities. This implies, in particular, a strict preservation of the semiclassicality (in considered degrees of freedom) in both the cases (i) and (ii). Derived inequalities are general: valid for all the physical states within the considered models.
Covariant effective action for loop quantum cosmology from order reduction
International Nuclear Information System (INIS)
Sotiriou, Thomas P.
2009-01-01
Loop quantum cosmology (LQC) seems to be predicting modified effective Friedmann equations without extra degrees of freedom. A puzzle arises if one decides to seek for a covariant effective action which would lead to the given Friedmann equation: The Einstein-Hilbert action is the only action that leads to second order field equations and, hence, there exists no covariant action which, under metric variation, leads to a modified Friedmann equation without extra degrees of freedom. It is shown that, at least for isotropic models in LQC, this issue is naturally resolved and a covariant effective action can be found if one considers higher order theories of gravity but faithfully follows effective field theory techniques. However, our analysis also raises doubts on whether a covariant description without background structures can be found for anisotropic models.
From big crunch to big bang: A quantum string cosmology perspective
International Nuclear Information System (INIS)
Maharana, Jnanadeva
2002-01-01
The scenario that the Universe contracts towards a big crunch and then undergoes a transition to an expanding universe is envisaged in the quantum string cosmology approach. The Wheeler-DeWitt (WDW) equation is solved exactly for an exponential dilaton potential. An S-duality invariant cosmological effective action for type IIB theory is considered to derive classical solutions and solve WDW equations
Study of interacting fields in a canonical formalism in Heisenberg picture of quantum field theory
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RANAIVOSON, R.T.R.
2011-01-01
In this work, we have made a study on the canonical formalism of the quantum field theory. Our contribution has been the development of a study using the Heisenberg picture. We showed that this approach may be useful for the description of quantum dynamics of interacting fields in bounded states. Our approach is to start from the lagrangian density of a classical theory from which one deduce the classical evolution equations of the fields via Euler-Lagrange equation for fields and establish the expression of conserved quantities characterizing the dynamics using the Noether theorem. Passing to the canonical quantization, fields and quantities characterizing the dynamics become quantum operators and evolution equations become operatorial evolution equations in Heisenberg picture. Expressions of quantum observable are also deduced from the expressions of classical conserved quantities. After, we showed that using the properties of fields operators and quantum states vectors, one can deduce from the operatorial evolution equations, the evolution equations for the wave functions of fermions and the evolution equations of expectation values of boson fields. For the illustration, various studies were conducted: the case of electrodynamics, the case of a general gauge theory and the case of the Standard Model. [fr
Classical and quantum Big Brake cosmology for scalar field and tachyonic models
Energy Technology Data Exchange (ETDEWEB)
Kamenshchik, A. Yu. [Dipartimento di Fisica e Astronomia and INFN, Via Irnerio 46, 40126 Bologna (Italy) and L.D. Landau Institute for Theoretical Physics of the Russian Academy of Sciences, Kosygin str. 2, 119334 Moscow (Russian Federation); Manti, S. [Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa (Italy)
2013-02-21
We study a relation between the cosmological singularities in classical and quantum theory, comparing the classical and quantum dynamics in some models possessing the Big Brake singularity - the model based on a scalar field and two models based on a tachyon-pseudo-tachyon field . It is shown that the effect of quantum avoidance is absent for the soft singularities of the Big Brake type while it is present for the Big Bang and Big Crunch singularities. Thus, there is some kind of a classical - quantum correspondence, because soft singularities are traversable in classical cosmology, while the strong Big Bang and Big Crunch singularities are not traversable.
Classical and quantum Big Brake cosmology for scalar field and tachyonic models
International Nuclear Information System (INIS)
Kamenshchik, A. Yu.; Manti, S.
2013-01-01
We study a relation between the cosmological singularities in classical and quantum theory, comparing the classical and quantum dynamics in some models possessing the Big Brake singularity - the model based on a scalar field and two models based on a tachyon-pseudo-tachyon field . It is shown that the effect of quantum avoidance is absent for the soft singularities of the Big Brake type while it is present for the Big Bang and Big Crunch singularities. Thus, there is some kind of a classical - quantum correspondence, because soft singularities are traversable in classical cosmology, while the strong Big Bang and Big Crunch singularities are not traversable.
Some problems of quantum cosmology and dark matter physics
Wang, Jin
The quantum cosmology is studied of the string universe obtained by embedding the Robertson-Walker metric in the nonlinear sigma model. It was found that initially the universe exists in a series of metastable bound states with the scale factor taking discrete values. Then it tunnels through a barrier and comes out in an inflationary state. This tunneling (or evolution in imaginary time) also has the effect of heating up the matter field so that we have a condition of chaotic inflation. The asymptotic solutions agree with those obtained from the classical Einstein equations. Quantum cosmology was considered of a 4-D universe using the effective action of superstrings. Both Hartle-Hawking and Vilenkin boundary conditions were applied to the solution of Wheeler-DeWitt equation. Under certain conditions (fermions added) the universe was found to tunnel through to the Lorentzian regime from the Euclidean regime and time is dynamically generated. Chudnovsky and Vilenkin's idea was applied to possible existence of cosmic strings in the Sun. Stellar evolution with cosmic strings at solar age gives a radius and luminosity of the star which are in contradiction with observation. The astrophysical bound was studied on the change of gravitational constant with time. It was found that (G/G) less than 10-12yr-1 is the condition that has to be satisfied in order not to cause the conflict with observation. The effect was studied of axions on the steller evolution of a 10 solar mass star model. If the axion mass is larger than .1 ev the star's age is significantly different at late stages, compared to the star without axions. It is argued that if cosmions (or WIMPS) solve the solar neutrino problem, then they must also play an important role in the evolution of low mass star main sequence stars. If they do so, then a simple (long mean free path) model for the interaction of cosmions with baryons leads to changes in the structure of the nuclear-burning core which may in principle
International Nuclear Information System (INIS)
Contopoulos, G.; Kotsakis, D.
1987-01-01
An extensive first part on a wealth of observational results relevant to cosmology lays the foundation for the second and central part of the book; the chapters on general relativity, the various cosmological theories, and the early universe. The authors present in a complete and almost non-mathematical way the ideas and theoretical concepts of modern cosmology including the exciting impact of high-energy particle physics, e.g. in the concept of the ''inflationary universe''. The final part addresses the deeper implications of cosmology, the arrow of time, the universality of physical laws, inflation and causality, and the anthropic principle
Quantum Gowdy model within the new loop quantum cosmology improved dynamics
International Nuclear Information System (INIS)
Martin-Benito, M; Garay, L J; Mena Marugan, G A
2011-01-01
The linearly polarized Gowdy T 3 model can be regarded as compact Bianchi I cosmologies with inhomogeneous modes allowed to travel in one direction. We study a hybrid quantization of this model that combines the loop quantization of the Bianchi I background, adopting the improved dynamics scheme put forward by Ashtekar and Wilson-Ewing, with a Fock quantization for the inhomogeneities. The Hamiltonian constraint operator provides a resolution of the cosmological singularity and superselects separable sectors. We analyze the complicated structure of these sectors. In any of them the Hamiltonian constraint provides an evolution equation with respect to the volume of the associated Bianchi I universe, with a well posed initial value problem. This fact allows us to construct the Hilbert space of physical states and to show that we recover the standard quantum field theory for the inhomogeneities.
Quantum Analogues: From Phase Transitions to Black Holes and Cosmology
International Nuclear Information System (INIS)
Liberati, Stefano
2008-01-01
'And I cherish more than anything else the analogies, my most trustworthy masters. They know all the secrets of nature, and they ought to be least neglected in geometry.' These words of the great astronomer Johannes Kepler embody the philosophy behind the research recounted in this interesting book-a book composed of nine selected lectures (and a nice introduction by Bill Unruh) from the international workshop on 'Quantum Simulations via Analogues', which was held in the Max Planck Institute for the Physics of Complex Systems in Dresden during the summer of 2005. Analogue models of (and for) gravity have a long and distinguished history dating back to the earliest years of general relativity. However the last decade has seen a remarkable and steady development of analogue gravity models based on condensed matter systems, leading to some hundreds of published articles, numerous workshops, and several books. While the main driver for this booming field has definitely been the puzzling physics associated with quantum effects in black holes, more recently much attention has also been devoted to other interesting issues-such as cosmological particle production or the cosmological constant problem. Moreover, together with these new themes there has been a persistent interest in the possibility of simulating cosmic topological defects in the laboratory (although it should be said that momentum for this line of research has been somewhat weakened by the progressive decrease of interest in cosmological topological defects as an alternative to inflationary scenarios). All these aspects are faithfully accounted for in this book, which does a good job at presenting a vivid snapshot of many (if not quite all) of the most interesting lines of research in the field. All the articles have a self-consistent structure-which allows one to read them in arbitrary order and appreciate the full richness of each topic. However, when considered together I would say that they also provide a
Yanai, Takeshi; Kurashige, Yuki; Neuscamman, Eric; Chan, Garnet Kin-Lic
2010-01-14
We describe the joint application of the density matrix renormalization group and canonical transformation theory to multireference quantum chemistry. The density matrix renormalization group provides the ability to describe static correlation in large active spaces, while the canonical transformation theory provides a high-order description of the dynamic correlation effects. We demonstrate the joint theory in two benchmark systems designed to test the dynamic and static correlation capabilities of the methods, namely, (i) total correlation energies in long polyenes and (ii) the isomerization curve of the [Cu(2)O(2)](2+) core. The largest complete active spaces and atomic orbital basis sets treated by the joint DMRG-CT theory in these systems correspond to a (24e,24o) active space and 268 atomic orbitals in the polyenes and a (28e,32o) active space and 278 atomic orbitals in [Cu(2)O(2)](2+).
Brane classical and quantum cosmology from an effective action
International Nuclear Information System (INIS)
Seahra, Sanjeev S.; Sepangi, H.R.; Ponce de Leon, J.
2003-01-01
Motivated by the Randall-Sundrum braneworld scenario, we discuss the classical and quantum dynamics of a (d+1)-dimensional boundary wall between a pair of (d+2)-dimensional topological Schwarzschild-AdS black holes. We assume there are quite general--but not completely arbitrary--matter fields living on the boundary 'brane universe', and that its geometry is that of a Friedmann-Lemaitre-Robertson-Walker (FLRW) model. The effective action governing the model in the minisuperspace approximation is derived. We find that the presence of black hole horizons in the bulk gives rise to a complex action for certain classically allowed brane configurations, but that the imaginary contribution plays no role in the equations of motion. Classical and instanton brane trajectories are examined in general and for special cases, and we find a subset of configuration space that is not allowed at the classical or semiclassical level; this subset corresponds to spacelike branes carrying tachyonic matter. The Hamiltonization and Dirac quantization of the model is then performed for the general case; the latter involves the manipulation of the Hamiltonian constraint before it is transformed into an operator that annihilates physical state vectors. The ensuing covariant Wheeler-DeWitt equation is examined at the semiclassical level, and we consider the possible localization of the brane universe's wave function away from the cosmological singularity. This is easier to achieve for branes with low density and/or spherical spatial sections
Brane classical and quantum cosmology from an effective action
Seahra, Sanjeev S.; Sepangi, H. R.; Ponce de Leon, J.
2003-09-01
Motivated by the Randall-Sundrum braneworld scenario, we discuss the classical and quantum dynamics of a (d+1)-dimensional boundary wall between a pair of (d+2)-dimensional topological Schwarzschild-AdS black holes. We assume there are quite general—but not completely arbitrary—matter fields living on the boundary “brane universe,” and that its geometry is that of a Friedmann-Lemaître-Robertson-Walker (FLRW) model. The effective action governing the model in the minisuperspace approximation is derived. We find that the presence of black hole horizons in the bulk gives rise to a complex action for certain classically allowed brane configurations, but that the imaginary contribution plays no role in the equations of motion. Classical and instanton brane trajectories are examined in general and for special cases, and we find a subset of configuration space that is not allowed at the classical or semiclassical level; this subset corresponds to spacelike branes carrying tachyonic matter. The Hamiltonization and Dirac quantization of the model is then performed for the general case; the latter involves the manipulation of the Hamiltonian constraint before it is transformed into an operator that annihilates physical state vectors. The ensuing covariant Wheeler-DeWitt equation is examined at the semiclassical level, and we consider the possible localization of the brane universe’s wave function away from the cosmological singularity. This is easier to achieve for branes with low density and/or spherical spatial sections.
Condensates in quantum chromodynamics and the cosmological constant
Brodsky, Stanley J.; Shrock, Robert
2011-01-01
Casher and Susskind [Casher A, Susskind L (1974) Phys Rev 9:436–460] have noted that in the light-front description, spontaneous chiral symmetry breaking is a property of hadronic wavefunctions and not of the vacuum. Here we show from several physical perspectives that, because of color confinement, quark and gluon condensates in quantum chromodynamics (QCD) are associated with the internal dynamics of hadrons. We discuss condensates using condensed matter analogues, the Anti de Sitter/conformal field theory correspondence, and the Bethe–Salpeter–Dyson–Schwinger approach for bound states. Our analysis is in agreement with the Casher and Susskind model and the explicit demonstration of “in-hadron” condensates by Roberts and coworkers [Maris P, Roberts CD, Tandy PC (1998) Phys Lett B 420:267–273], using the Bethe–Salpeter–Dyson–Schwinger formalism for QCD-bound states. These results imply that QCD condensates give zero contribution to the cosmological constant, because all of the gravitational effects of the in-hadron condensates are already included in the normal contribution from hadron masses.
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V. S. Olkhovsky
2009-01-01
Full Text Available Recent developments are reviewed and some new results are presented in the study of time in quantum mechanics and quantum electrodynamics as an observable, canonically conjugate to energy. This paper deals with the maximal Hermitian (but nonself-adjoint operator for time which appears in nonrelativistic quantum mechanics and in quantum electrodynamics for systems with continuous energy spectra and also, briefly, with the four-momentum and four-position operators, for relativistic spin-zero particles. Two measures of averaging over time and connection between them are analyzed. The results of the study of time as a quantum observable in the cases of the discrete energy spectra are also presented, and in this case the quasi-self-adjoint time operator appears. Then, the general foundations of time analysis of quantum processes (collisions and decays are developed on the base of time operator with the proper measures of averaging over time. Finally, some applications of time analysis of quantum processes (concretely, tunneling phenomena and nuclear processes are reviewed.
Relating covariant and canonical approaches to triangulated models of quantum gravity
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Arnsdorf, Matthias
2002-01-01
In this paper we explore the relation between covariant and canonical approaches to quantum gravity and BF theory. We will focus on the dynamical triangulation and spin-foam models, which have in common that they can be defined in terms of sums over spacetime triangulations. Our aim is to show how we can recover these covariant models from a canonical framework by providing two regularizations of the projector onto the kernel of the Hamiltonian constraint. This link is important for the understanding of the dynamics of quantum gravity. In particular, we will see how in the simplest dynamical triangulation model we can recover the Hamiltonian constraint via our definition of the projector. Our discussion of spin-foam models will show how the elementary spin-network moves in loop quantum gravity, which were originally assumed to describe the Hamiltonian constraint action, are in fact related to the time-evolution generated by the constraint. We also show that the Immirzi parameter is important for the understanding of a continuum limit of the theory
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Gomberoff, Andres; Henneaux, Marc; Teitelboim, Claudio
2005-01-01
We study the decay of the cosmological constant in two spacetime dimensions through production of pairs. We show that the same nucleation process looks as quantum-mechanical tunneling (instanton) to one Killing observer and as thermal activation (thermalon) to another. Thus, we find another striking example of the deep interplay between gravity, thermodynamics and quantum mechanics which becomes apparent in presence of horizons
Higgs field and cosmological parameters in the fractal quantum system
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Abramov Valeriy
2017-01-01
Full Text Available For the fractal model of the Universe the relations of cosmological parameters and the Higgs field are established. Estimates of the critical density, the expansion and speed-up parameters of the Universe (the Hubble constant and the cosmological redshift; temperature and anisotropy of the cosmic microwave background radiation were performed.
García-Bellido, J
2015-01-01
In these lectures I review the present status of the so-called Standard Cosmological Model, based on the hot Big Bang Theory and the Inflationary Paradigm. I will make special emphasis on the recent developments in observational cosmology, mainly the acceleration of the universe, the precise measurements of the microwave background anisotropies, and the formation of structure like galaxies and clusters of galaxies from tiny primordial fluctuations generated during inflation.
Structure of multiphoton quantum optics. I. Canonical formalism and homodyne squeezed states
dell'Anno, Fabio; de Siena, Silvio; Illuminati, Fabrizio
2004-03-01
We introduce a formalism of nonlinear canonical transformations for general systems of multiphoton quantum optics. For single-mode systems the transformations depend on a tunable free parameter, the homodyne local-oscillator angle; for n -mode systems they depend on n heterodyne mixing angles. The canonical formalism realizes nontrivial mixing of pairs of conjugate quadratures of the electromagnetic field in terms of homodyne variables for single-mode systems, and in terms of heterodyne variables for multimode systems. In the first instance the transformations yield nonquadratic model Hamiltonians of degenerate multiphoton processes and define a class of non-Gaussian, nonclassical multiphoton states that exhibit properties of coherence and squeezing. We show that such homodyne multiphoton squeezed states are generated by unitary operators with a nonlinear time evolution that realizes the homodyne mixing of a pair of conjugate quadratures. Tuning of the local-oscillator angle allows us to vary at will the statistical properties of such states. We discuss the relevance of the formalism for the study of degenerate (up-)down-conversion processes. In a companion paper [ F. Dell’Anno, S. De Siena, and F. Illuminati, 69, 033813 (2004) ], we provide the extension of the nonlinear canonical formalism to multimode systems, we introduce the associated heterodyne multiphoton squeezed states, and we discuss their possible experimental realization.
Structure of multiphoton quantum optics. I. Canonical formalism and homodyne squeezed states
International Nuclear Information System (INIS)
Dell'Anno, Fabio; De Siena, Silvio; Illuminati, Fabrizio
2004-01-01
We introduce a formalism of nonlinear canonical transformations for general systems of multiphoton quantum optics. For single-mode systems the transformations depend on a tunable free parameter, the homodyne local-oscillator angle; for n-mode systems they depend on n heterodyne mixing angles. The canonical formalism realizes nontrivial mixing of pairs of conjugate quadratures of the electromagnetic field in terms of homodyne variables for single-mode systems, and in terms of heterodyne variables for multimode systems. In the first instance the transformations yield nonquadratic model Hamiltonians of degenerate multiphoton processes and define a class of non-Gaussian, nonclassical multiphoton states that exhibit properties of coherence and squeezing. We show that such homodyne multiphoton squeezed states are generated by unitary operators with a nonlinear time evolution that realizes the homodyne mixing of a pair of conjugate quadratures. Tuning of the local-oscillator angle allows us to vary at will the statistical properties of such states. We discuss the relevance of the formalism for the study of degenerate (up-)down-conversion processes. In a companion paper [F. Dell'Anno, S. De Siena, and F. Illuminati, 69, 033813 (2004)], we provide the extension of the nonlinear canonical formalism to multimode systems, we introduce the associated heterodyne multiphoton squeezed states, and we discuss their possible experimental realization
Teleparallel loop quantum cosmology in a system of intersecting branes
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Alireza Sepehri
2016-09-01
Full Text Available Recently, some authors have removed the big bang singularity in teleparallel Loop Quantum Cosmology (LQC and have shown that the universe may undergo a number of oscillations. We investigate the origin of this type of teleparallel theory in a system of intersecting branes in M-theory in which the angle between them changes with time. This system is constructed by two intersecting anti-D8-branes, one compacted D4-brane and a D3-brane. These branes are built by joining M0-branes which develop in decaying fundamental strings. The compacted D4-brane is located between two intersecting anti-D8 branes and glues to one of them. Our universe is located on the D3 brane which wraps around the D4 brane from one end and sticks to one of the anti-D8 branes from the other one. In this system, there are three types of fields, corresponding to compacted D4 branes, intersecting branes and D3-branes. These fields interact with each other and make the angle between branes oscillate. By decreasing this angle, the intersecting anti-D8 branes approach each other, the D4 brane rolls, the D3 brane wraps around the D4 brane, and the universe contracts. By separating the intersecting branes and increasing the angle, the D4 brane rolls in the opposite direction, the D3 brane separates from it and the expansion branch begins. Also, the interaction between branes in this system gives us the exact form of the relevant Lagrangian for teleparallel LQC.
Teleparallel loop quantum cosmology in a system of intersecting branes
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Sepehri, Alireza, E-mail: alireza.sepehri@uk.ac.ir [Faculty of Physics, Shahid Bahonar University, P.O. Box 76175, Kerman (Iran, Islamic Republic of); Research Institute for Astronomy and Astrophysics of Maragha (RIAAM), P.O. Box 55134-441, Maragha (Iran, Islamic Republic of); Pradhan, Anirudh, E-mail: pradhan.anirudh@gmail.com [Department of Mathematics, Institute of Applied Sciences and Humanities, GLA University, Mathura-281 406, Uttar Pradesh (India); Beesham, Aroonkumar, E-mail: beeshama@unizulu.ac.za [Department of Mathematical Sciences, University of Zululand, Kwa-Dlangezwa 3886 (South Africa); Haro, Jaume de, E-mail: jaime.haro@upc.edu [Departament de Matemàtiques, Universitat Politècnica de Catalunya, Diagonal 647, 08028 Barcelona (Spain)
2016-09-10
Recently, some authors have removed the big bang singularity in teleparallel Loop Quantum Cosmology (LQC) and have shown that the universe may undergo a number of oscillations. We investigate the origin of this type of teleparallel theory in a system of intersecting branes in M-theory in which the angle between them changes with time. This system is constructed by two intersecting anti-D8-branes, one compacted D4-brane and a D3-brane. These branes are built by joining M0-branes which develop in decaying fundamental strings. The compacted D4-brane is located between two intersecting anti-D8 branes and glues to one of them. Our universe is located on the D3 brane which wraps around the D4 brane from one end and sticks to one of the anti-D8 branes from the other one. In this system, there are three types of fields, corresponding to compacted D4 branes, intersecting branes and D3-branes. These fields interact with each other and make the angle between branes oscillate. By decreasing this angle, the intersecting anti-D8 branes approach each other, the D4 brane rolls, the D3 brane wraps around the D4 brane, and the universe contracts. By separating the intersecting branes and increasing the angle, the D4 brane rolls in the opposite direction, the D3 brane separates from it and the expansion branch begins. Also, the interaction between branes in this system gives us the exact form of the relevant Lagrangian for teleparallel LQC.
Quantum statistical model of nuclear multifragmentation in the canonical ensemble method
International Nuclear Information System (INIS)
Toneev, V.D.; Ploszajczak, M.; Parvant, A.S.; Toneev, V.D.; Parvant, A.S.
1999-01-01
A quantum statistical model of nuclear multifragmentation is proposed. The recurrence equation method used the canonical ensemble makes the model solvable and transparent to physical assumptions and allows to get results without involving the Monte Carlo technique. The model exhibits the first order phase transition. Quantum statistics effects are clearly seen on the microscopic level of occupation numbers but are almost washed out for global thermodynamic variables and the averaged observables studied. In the latter case, the recurrence relations for multiplicity distributions of both intermediate-mass and all fragments are derived and the specific changes in the shape of multiplicity distributions in the narrow region of the transition temperature is stressed. The temperature domain favorable to search for the HBT effect is noted. (authors)
Quantum statistical model of nuclear multifragmentation in the canonical ensemble method
Energy Technology Data Exchange (ETDEWEB)
Toneev, V.D.; Ploszajczak, M. [Grand Accelerateur National d' Ions Lourds (GANIL), 14 - Caen (France); Parvant, A.S. [Institute of Applied Physics, Moldova Academy of Sciences, MD Moldova (Ukraine); Parvant, A.S. [Joint Institute for Nuclear Research, Bogoliubov Lab. of Theoretical Physics, Dubna (Russian Federation)
1999-07-01
A quantum statistical model of nuclear multifragmentation is proposed. The recurrence equation method used the canonical ensemble makes the model solvable and transparent to physical assumptions and allows to get results without involving the Monte Carlo technique. The model exhibits the first order phase transition. Quantum statistics effects are clearly seen on the microscopic level of occupation numbers but are almost washed out for global thermodynamic variables and the averaged observables studied. In the latter case, the recurrence relations for multiplicity distributions of both intermediate-mass and all fragments are derived and the specific changes in the shape of multiplicity distributions in the narrow region of the transition temperature is stressed. The temperature domain favorable to search for the HBT effect is noted. (authors)
Space-Time Uncertainty and Cosmology: a Proposed Quantum Model of the Universe [ 245Kb
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Tosto S.
2013-10-01
Full Text Available The paper introduces a cosmological model of the quantum universe. The aim of the model is (i to identify the possible mechanism that governs the matter/antimatter ratio existing in the universe and concurrently to propose (ii a reasonable growth mechanism of the universe and (iii a possible explanation of the dark energy. The concept of timespace uncertainty, on which is based the present quantum approach, has been proven able to bridge quantum mechanics and relativity.
Zhu, Tao; Wang, Anzhong; Kirsten, Klaus; Cleaver, Gerald; Sheng, Qin
2018-02-01
Loop quantum cosmology provides a resolution of the classical big bang singularity in the deep Planck era. The evolution, prior to the usual slow-roll inflation, naturally generates excited states at the onset of the slow-roll inflation. It is expected that these quantum gravitational effects could leave its fingerprints on the primordial perturbation spectrum and non-Gaussianity, and lead to some observational evidences in the cosmic microwave background. While the impact of the quantum effects on the primordial perturbation spectrum has been already studied and constrained by current data, in this paper we continue to study such effects but now on the non-Gaussianity of the primordial curvature perturbations. We present detailed and analytical calculations of the non-Gaussianity and show explicitly that the corrections due to the quantum effects are at the same magnitude of the slow-roll parameters in the observable scales and thus are well within current observational constraints. Despite this, we show that the non-Gaussianity in the squeezed limit can be enhanced at superhorizon scales and it is these effects that can yield a large statistical anisotropy on the power spectrum through the Erickcek-Kamionkowski-Carroll mechanism.
Cosmology with a decaying vacuum energy parametrization derived from quantum mechanics
International Nuclear Information System (INIS)
Szydłowski, M; Stachowski, A; Urbanowski, K
2015-01-01
Within the quantum mechanical treatment of the decay problem one finds that at late times tthe survival probability of an unstable state cannot have the form of an exponentially decreasing function of time t but it has an inverse power-like form. This is a general property of unstable states following from basic principles of quantum theory. The consequence of this property is that in the case of false vacuum states the cosmological constant becomes dependent on time: Λ — Λ bare ≡ Λ(t) — Λ bare ∼ 1/t 2 . We construct the cosmological model with decaying vacuum energy density and matter for solving the cosmological constant problem and the coincidence problem. We show the equivalence of the proposed decaying false vacuum cosmology with the Λ(t) cosmologies (the Λ(t)CDM models). The cosmological implications of the model of decaying vacuum energy (dark energy) are discussed. We constrain the parameters of the model with decaying vacuum using astronomical data. For this aim we use the observation of distant supernovae of type Ia, measurements of H(z), BAO, CMB and others. The model analyzed is in good agreement with observation data and explain a small value of the cosmological constant today. (paper)
Elizaga Navascués, Beatriz; Martín de Blas, Daniel; Mena Marugán, Guillermo A.
2018-02-01
Loop quantum cosmology has recently been applied in order to extend the analysis of primordial perturbations to the Planck era and discuss the possible effects of quantum geometry on the cosmic microwave background. Two approaches to loop quantum cosmology with admissible ultraviolet behavior leading to predictions that are compatible with observations are the so-called hybrid and dressed metric approaches. In spite of their similarities and relations, we show in this work that the effective equations that they provide for the evolution of the tensor and scalar perturbations are somewhat different. When backreaction is neglected, the discrepancy appears only in the time-dependent mass term of the corresponding field equations. We explain the origin of this difference, arising from the distinct quantization procedures. Besides, given the privileged role that the big bounce plays in loop quantum cosmology, e.g. as a natural instant of time to set initial conditions for the perturbations, we also analyze the positivity of the time-dependent mass when this bounce occurs. We prove that the mass of the tensor perturbations is positive in the hybrid approach when the kinetic contribution to the energy density of the inflaton dominates over its potential, as well as for a considerably large sector of backgrounds around that situation, while this mass is always nonpositive in the dressed metric approach. Similar results are demonstrated for the scalar perturbations in a sector of background solutions that includes the kinetically dominated ones; namely, the mass then is positive for the hybrid approach, whereas it typically becomes negative in the dressed metric case. More precisely, this last statement is strictly valid when the potential is quadratic for values of the inflaton mass that are phenomenologically favored.
Vittorio, Nicola
2018-01-01
Modern cosmology has changed significantly over the years, from the discovery to the precision measurement era. The data now available provide a wealth of information, mostly consistent with a model where dark matter and dark energy are in a rough proportion of 3:7. The time is right for a fresh new textbook which captures the state-of-the art in cosmology. Written by one of the world's leading cosmologists, this brand new, thoroughly class-tested textbook provides graduate and undergraduate students with coverage of the very latest developments and experimental results in the field. Prof. Nicola Vittorio shows what is meant by precision cosmology, from both theoretical and observational perspectives.
Final Scientific/Technical Report-Quantum Field Theories for Cosmology
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Nicolis, Alberto [Columbia Univ., New York, NY (United States). Physics Dept.
2018-03-10
The research funded by this award spanned a wide range of subjects in theoretical cosmology and in field theory. In the first part, the PI and his collaborators applied effective field theory techniques to the study of macroscopic media and of cosmological perturbations. Such an approach—now standard in particle physics—is quite unconventional for theoretical cosmology. They addressed several concrete questions where this formalism proved valuable, both within and outside the cosmological context, concerning for instance macroscopic physical phenomena for fluids, superfluids, and solids, and their relationship to the dynamics of cosmological perturbations. A particularly successful outcome of this line of research has been the development of “solid inflation”: a cosmological model for primordial inflation where the expansion of the universe is driven by an exotic solid substance. In the second part, the PI and his collaborators investigated more fundamental questions and ideas, for the present universe as well as for the very early one, using quantum field theory as a guide. The questions addressed include: Is the present cosmic acceleration due to a new, ‘dark’ form of energy, or are we instead observing a breakdown of Einstein’s general relativity at cosmological distances? Is the cosmic acceleration accelerating? Is the Big Bang unavoidable? Related to this, is early inflation the only sensible cure for the shortcomings of the standard Big Bang model, and the only possible source for the observed scale-invariant cosmological perturbations?
Emergence of the product of constant curvature spaces in loop quantum cosmology
International Nuclear Information System (INIS)
Dadhich, Naresh; Joe, Anton; Singh, Parampreet
2015-01-01
The loop quantum dynamics of Kantowski–Sachs spacetime and the interior of higher genus black hole spacetimes with a cosmological constant has some peculiar features not shared by various other spacetimes in loop quantum cosmology. As in the other cases, though the quantum geometric effects resolve the physical singularity and result in a non-singular bounce, after the bounce a spacetime with small spacetime curvature does not emerge in either the subsequent backward or the forward evolution. Rather, in the asymptotic limit the spacetime manifold is a product of two constant curvature spaces. Interestingly, though the spacetime curvature of these asymptotic spacetimes is very high, their effective metric is a solution to Einstein’s field equations. Analysis of the components of the Ricci tensor shows that after the singularity resolution, the Kantowski–Sachs spacetime leads to an effective metric which can be interpreted as the ‘charged’ Nariai, while the higher genus black hole interior can similarly be interpreted as an anti Bertotti–Robinson spacetime with a cosmological constant. These spacetimes are ‘charged’ in the sense that the energy–momentum tensor that satisfies Einstein’s field equations is formally the same as the one for the uniform electromagnetic field, albeit it has a purely quantum geometric origin. The asymptotic spacetimes also have an emergent cosmological constant which is different in magnitude, and sometimes even its sign, from the cosmological constant in the Kantowski–Sachs and the interior of higher genus black hole metrics. With a fine tuning of the latter cosmological constant, we show that ‘uncharged’ Nariai, and anti Bertotti–Robinson spacetimes with a vanishing emergent cosmological constant can also be obtained. (paper)
A Langevin Canonical Approach to the Study of Quantum Stochastic Resonance in Chiral Molecules
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Germán Rojas-Lorenzo
2016-09-01
Full Text Available A Langevin canonical framework for a chiral two-level system coupled to a bath of harmonic oscillators is used within a coupling scheme different from the well-known spin-boson model to study the quantum stochastic resonance for chiral molecules. This process refers to the amplification of the response to an external periodic signal at a certain value of the noise strength, being a cooperative effect of friction, noise, and periodic driving occurring in a bistable system. Furthermore, from this stochastic dynamics within the Markovian regime and Ohmic friction, the competing process between tunneling and the parity violating energy difference present in this type of chiral systems plays a fundamental role. This mechanism is finally proposed to observe the so-far elusive parity-violating energy difference in chiral molecules.
Cosmological perturbations of quantum-mechanical origin and anisotropy of the microwave background
Grishchuk, L. P.
1993-01-01
Cosmological perturbations generated quantum mechanically (as a particular case, during inflation) possess statistical properties of squeezed quantum states. The power spectra of the perturbations are modulated and the angular distribution of the produced temperature fluctuations of the cosmic microwave background radiation is quite specific. An exact formula is derived for the angular correlation function of the temperature fluctuations caused by squeezed gravitational waves. The predicted angular pattern can, in principle, be revealed by observations like those by the Cosmic Background Explorer.
Quantum Stephani exact cosmological solutions and the selection of time variable
International Nuclear Information System (INIS)
Pedram, P; Jalalzadeh, S; Gousheh, S S
2007-01-01
We study a perfect fluid Stephani quantum cosmological model. In the present work, the Schutz's variational formalism which recovers the notion of time is applied. This gives rise to a Wheeler-DeWitt equation for the scale factor. We use the eigenfunctions in order to construct wave packets for each case. We study the time-dependent behavior of the expectation value of the scale factor, using many-worlds and de Broglie-Bohm interpretations of quantum mechanics
Sparaciari, Carlo; Paris, Matteo G. A.
2013-01-01
We address measurement schemes where certain observables Xk are chosen at random within a set of nondegenerate isospectral observables and then measured on repeated preparations of a physical system. Each observable has a probability zk to be measured, with ∑kzk=1, and the statistics of this generalized measurement is described by a positive operator-valued measure. This kind of scheme is referred to as quantum roulettes, since each observable Xk is chosen at random, e.g., according to the fluctuating value of an external parameter. Here we focus on quantum roulettes for qubits involving the measurements of Pauli matrices, and we explicitly evaluate their canonical Naimark extensions, i.e., their implementation as indirect measurements involving an interaction scheme with a probe system. We thus provide a concrete model to realize the roulette without destroying the signal state, which can be measured again after the measurement or can be transmitted. Finally, we apply our results to the description of Stern-Gerlach-like experiments on a two-level system.
Physics on all scales. Scalar-tensor theories of quantum gravity in particle physics and cosmology
Energy Technology Data Exchange (ETDEWEB)
Henz, Tobias
2016-05-10
In this thesis, we investigate dilaton quantum gravity using a functional renormalization group approach. We derive and discuss flow equations both in the background field approximation and using a vertex expansion as well as solve the fixed point equations globally to show how realistic gravity, connecting ultraviolet and infrared physics, can be realized on a pure fixed point trajectory by virtue of spontaneous breaking of scale invariance. The emerging physical system features a dynamically generated moving Planck scale resembling the Newton coupling as well as slow roll inflation with an exponentially decreasing effective cosmological constant that vanishes completely in the infrared. The moving Planck scale might make quantum gravity experimentally accessible at a different energy scale than previously believed. We therefore not only provide further evidence for the existence of a consistent quantum theory of gravity based on general relativity, but also offer potential solutions towards the hierarchy and cosmological constant problems, thereby opening up exciting opportunities for further research.
Quantization ambiguities and bounds on geometric scalars in anisotropic loop quantum cosmology
International Nuclear Information System (INIS)
Singh, Parampreet; Wilson-Ewing, Edward
2014-01-01
We study quantization ambiguities in loop quantum cosmology that arise for space-times with non-zero spatial curvature and anisotropies. Motivated by lessons from different possible loop quantizations of the closed Friedmann–Lemaître–Robertson–Walker cosmology, we find that using open holonomies of the extrinsic curvature, which due to gauge-fixing can be treated as a connection, leads to the same quantum geometry effects that are found in spatially flat cosmologies. More specifically, in contrast to the quantization based on open holonomies of the Ashtekar–Barbero connection, the expansion and shear scalars in the effective theories of the Bianchi type II and Bianchi type IX models have upper bounds, and these are in exact agreement with the bounds found in the effective theories of the Friedmann–Lemaître–Robertson–Walker and Bianchi type I models in loop quantum cosmology. We also comment on some ambiguities present in the definition of inverse triad operators and their role. (paper)
Quantization ambiguities and bounds on geometric scalars in anisotropic loop quantum cosmology
Singh, Parampreet; Wilson-Ewing, Edward
2014-02-01
We study quantization ambiguities in loop quantum cosmology that arise for space-times with non-zero spatial curvature and anisotropies. Motivated by lessons from different possible loop quantizations of the closed Friedmann-Lemaître-Robertson-Walker cosmology, we find that using open holonomies of the extrinsic curvature, which due to gauge-fixing can be treated as a connection, leads to the same quantum geometry effects that are found in spatially flat cosmologies. More specifically, in contrast to the quantization based on open holonomies of the Ashtekar-Barbero connection, the expansion and shear scalars in the effective theories of the Bianchi type II and Bianchi type IX models have upper bounds, and these are in exact agreement with the bounds found in the effective theories of the Friedmann-Lemaître-Robertson-Walker and Bianchi type I models in loop quantum cosmology. We also comment on some ambiguities present in the definition of inverse triad operators and their role.
Anomaly-free perturbations with inverse-volume and holonomy corrections in loop quantum cosmology
International Nuclear Information System (INIS)
Cailleteau, Thomas; Linsefors, Linda; Barrau, Aurelien
2014-01-01
This paper addresses the issue of the closure of the algebra of constraints for generic (cosmological) perturbations when taking into account simultaneously the two main corrections of effective loop quantum cosmology, namely the holonomy and the inverse-volume terms. Previous works on either the holonomy or the inverse-volume case are reviewed and generalized. In the inverse-volume case, we point out new possibilities. An anomaly-free solution including both corrections is found for perturbations, and the corresponding equations of motion are derived. (paper)
Classical and quantum evolution of cosmological perturbations in different spacetime backgrounds
International Nuclear Information System (INIS)
Anini, Y.
1991-06-01
In this paper I discuss the evolution of cosmological perturbations on different cosmological backgrounds. Conformal transformations will be used to transform the equations of motion for perturbations which have time dependent coefficients into the equation of motion of a simple harmonic oscillator with constant frequency. In this way we may work out an exact solution for the equations of motion of the perturbations. By using the regularity boundary condition we pick up one particular solution for each mode. And from these regular solutions we evaluate the quantum state for each perturbation mode. (author). 4 refs
Non-singular bounce scenarios in loop quantum cosmology and the effective field description
International Nuclear Information System (INIS)
Cai, Yi-Fu; Wilson-Ewing, Edward
2014-01-01
A non-singular bouncing cosmology is generically obtained in loop quantum cosmology due to non-perturbative quantum gravity effects. A similar picture can be achieved in standard general relativity in the presence of a scalar field with a non-standard kinetic term such that at high energy densities the field evolves into a ghost condensate and causes a non-singular bounce. During the bouncing phase, the perturbations can be stabilized by introducing a Horndeski operator. Taking the matter content to be a dust field and an ekpyrotic scalar field, we compare the dynamics in loop quantum cosmology and in a non-singular bouncing effective field model with a non-standard kinetic term at both the background and perturbative levels. We find that these two settings share many important properties, including the result that they both generate scale-invariant scalar perturbations. This shows that some quantum gravity effects of the very early universe may be mimicked by effective field models
Classical and quantum dynamics of a perfect fluid scalar-metric cosmology
International Nuclear Information System (INIS)
Vakili, Babak
2010-01-01
We study the classical and quantum models of a Friedmann-Robertson-Walker (FRW) cosmology, coupled to a perfect fluid, in the context of the scalar-metric gravity. Using the Schutz' representation for the perfect fluid, we show that, under a particular gauge choice, it may lead to the identification of a time parameter for the corresponding dynamical system. It is shown that the evolution of the universe based on the classical cosmology represents a late time power law expansion coming from a big-bang singularity in which the scale factor goes to zero while the scalar field blows up. Moreover, this formalism gives rise to a Schroedinger-Wheeler-DeWitt (SWD) equation for the quantum-mechanical description of the model under consideration, the eigenfunctions of which can be used to construct the wave function of the universe. We use the resulting wave function in order to investigate the possibility of the avoidance of classical singularities due to quantum effects by means of the many-worlds and ontological interpretation of quantum cosmology.
Lectures on General Relativity, Cosmology and Quantum Black Holes
Ydri, Badis
2017-07-01
This book is a rigorous text for students in physics and mathematics requiring an introduction to the implications and interpretation of general relativity in areas of cosmology. Readers of this text will be well prepared to follow the theoretical developments in the field and undertake research projects as part of an MSc or PhD programme. This ebook contains interactive Q&A technology, allowing the reader to interact with the text and reveal answers to selected exercises posed by the author within the book. This feature may not function in all formats and on reading devices.
Pre-big bang cosmology and quantum fluctuations
International Nuclear Information System (INIS)
Ghosh, A.; Pollifrone, G.; Veneziano, G.
2000-01-01
The quantum fluctuations of a homogeneous, isotropic, open pre-big bang model are discussed. By solving exactly the equations for tensor and scalar perturbations we find that particle production is negligible during the perturbative Pre-Big Bang phase
Directory of Open Access Journals (Sweden)
Serra Arslancan
2017-06-01
Full Text Available Interest in understanding the photophysics and photochemistry of thiated nucleobases has been awakened because of their possible involvement in primordial RNA or their potential use as photosensitizers in medicinal chemistry. The interpretation of the photodynamics of these systems, conditioned by their intricate potential energy surfaces, requires the powerful interplay between experimental measurements and state of the art molecular simulations. In this review, we provide an overview on the photophysics of natural nucleobases’ thioanalogs, which covers the last 30 years and both experimental and computational contributions. For all the canonical nucleobase’s thioanalogs, we have compiled the main steady state absorption and emission features and their interpretation in terms of theoretical calculations. Then, we revise the main topographical features, including stationary points and interstate crossings, of their potential energy surfaces based on quantum mechanical calculations and we conclude, by combining the outcome of different spectroscopic techniques and molecular dynamics simulations, with the mechanism by which these nucleobase analogs populate their triplet excited states, which are at the origin of their photosensitizing properties.
The quantum cosmological wavefunction at very early times for a quadratic gravity theory
International Nuclear Information System (INIS)
Davis, Simon
2003-01-01
The quantum cosmological wavefunction for a quadratic gravity theory derived from the heterotic string effective action is obtained near the inflationary epoch and during the initial Planck era. Neglecting derivatives with respect to the scalar field, the wavefunction would satisfy a third-order differential equation near the inflationary epoch which has a solution that is singular in the scale factor limit a(t) → 0. When scalar field derivatives are included, a sixth-order differential equation is obtained for the wavefunction and the solution by Mellin transform is regular in the a → 0 limit. It follows that inclusion of the scalar field in the quadratic gravity action is necessary for consistency of the quantum cosmology of the theory at very early times
Quantum cosmological origin of large scale structures of the universe
International Nuclear Information System (INIS)
Anini, Y.
1989-07-01
In this paper, the initial quantum state of matter perturbations about de Sitter minisuperspace model is found. For a large class of boundary conditions (bcs), including those of Hartle-Hawking and Vilenkin, the resulting quantum state is the de Sitter invariant vacuum. This result is found to depend only on the regularity requirement at the euclidean origin of spacetime which is common to all reasonable (bcs). The initial value of the density perturbations implied by these quantum fluctuations are found and evaluated at the initial horizon crossing. The perturbations are found to have an almost scale independent spectrum, and an amplitude which depends on the scale at which inflation took place. The amplitude would have the right value if the scale of inflation is H ≤ 10 15 Gev. (author). 9 refs
The Bianchi IX model in loop quantum cosmology
International Nuclear Information System (INIS)
Bojowald, Martin; Date, Ghanashyam; Hossain, Golam Mortuza
2004-01-01
The Bianchi IX model has been used often to investigate the structure close to singularities of general relativity. Its classical chaos is expected to have, via the BKL scenario, implications even for the approach to general inhomogeneous singularities. Thus, it is a popular model to test consequences of modifications to general relativity suggested by quantum theories of gravity. This paper presents a detailed proof that modifications coming from loop quantum gravity lead to a non-chaotic effective behaviour. The way this is realized, independently of quantization ambiguities, suggests a new look at initial and final singularities
Quantum fields in cosmological space-times: a soluble example
International Nuclear Information System (INIS)
Costa, I.; Novello, M.; Svaiter, N.F.; Deruelle, N.
1988-01-01
The Klein-Gordon equation for a massive real scalar field in the Novello-Salim Eternal Universe, i.e., non singular spatial homogeneous and isotropic cosmological background which is tangent to Milne universes in the distant past and future (and hence asymptotically flat) and evolves between these two geometries via a phase of contraction to a point of maximum curvature followed by expansion is solved. This allows a computation of the Bogolyubov coefficients of the scalar field, usually interpreted as the rate of creation of matter by the time varying gravitational field, either when the vacuum is defined at the moment of maximum curvature (the false Big-Bang) or at the far beginning of the cosmic evolution. This new exact solution is compared to the results obtained when the geometry is that of the Milne universe. (author) [pt
Analysing Hessence Intermediate and Logamediate Universe in Loop Quantum Cosmological Background
Mandal, Jyotirmay Das; Debnath, Ujjal
2017-06-01
We have discussed here Hessence inflation in Loop Quantum Cosmological background. In this work, we have emphasized on late times, taking into account various slow-roll conditions. This model has been constructed taking intermediate and logamediate scale factors. In both cases the forms of hessence field, potential, number of e-folds, slow-roll parameters are manipulated by taking the dissipative co-efficient Γ =Γ0, where Γ0 > 0 is a constant, in accordance with second law of thermodynamics.
The quantum cosmology of Einstein-Yang-Mills theory in Eight-dimensions
International Nuclear Information System (INIS)
Su Bing; Li Xinzhou
1991-01-01
The quantum cosmology of Einstein-Yang-Mills has been studied. The Hartle-Hawking's proposal for the boundary conditions of the universe is extended to Eight-dimensional Einstein-Yong-Mills theory. A miniuperspace wave function is calculated in the classical limit corresponding to a superposition of classical solutions in which four of the dimensions remain small while the other four behave like an inflationary universe
Evolution of Primordial Black Holes in Loop Quantum Cosmology D ...
Indian Academy of Sciences (India)
on initial mass fraction of presently evaporating PBHs are much greater ... that the black holes emit thermal radiation due to quantum effects (Hawking 1975). .... Here one can notice that the scale factor in LQC varies at a slower rate than .... where aH ∼ is the black body constant and TBH ∼ is the Hawking temperature = 1.
Quantum cosmology in Ashtekar variables with non-minimally ...
Indian Academy of Sciences (India)
tum effects or the conditions for the classical limit. In this paper we try to address these .... 8. +12e2x. =nH. (17). Since n is a Lagrange multiplier, we have the constraint H. 0. Hence in Dirac quan- ..... pected as in this case the quantum potential term has non-zero effect and consequently gives rise to a deviation from classical ...
Born in an infinite universe: A cosmological interpretation of quantum mechanics
International Nuclear Information System (INIS)
Aguirre, Anthony; Tegmark, Max
2011-01-01
We study the quantum measurement problem in the context of an infinite, statistically uniform space, as could be generated by eternal inflation. It has recently been argued that when identical copies of a quantum measurement system exist, the standard projection operators and Born rule method for calculating probabilities must be supplemented by estimates of relative frequencies of observers. We argue that an infinite space actually renders the Born rule redundant, by physically realizing all outcomes of a quantum measurement in different regions, with relative frequencies given by the square of the wave-function amplitudes. Our formal argument hinges on properties of what we term the quantum confusion operator, which projects onto the Hilbert subspace where the Born rule fails, and we comment on its relation to the oft-discussed quantum frequency operator. This analysis unifies the classical and quantum levels of parallel universes that have been discussed in the literature, and has implications for several issues in quantum measurement theory. Replacing the standard hypothetical ensemble of measurements repeated ad infinitum by a concrete decohered spatial collection of experiments carried out in different distant regions of space provides a natural context for a statistical interpretation of quantum mechanics. It also shows how, even for a single measurement, probabilities may be interpreted as relative frequencies in unitary (Everettian) quantum mechanics. We also argue that after discarding a zero-norm part of the wave function, the remainder consists of a superposition of indistinguishable terms, so that arguably 'collapse' of the wave function is irrelevant, and the ''many worlds'' of Everett's interpretation are unified into one. Finally, the analysis suggests a 'cosmological interpretation' of quantum theory in which the wave function describes the actual spatial collection of identical quantum systems, and quantum uncertainty is attributable to the
Effects of the quantum vacuum in particle physics and cosmology
Energy Technology Data Exchange (ETDEWEB)
Smirnov, Juri
2014-11-26
In this work we investigate numerous effects of virtual particles on processes relevant for particle physics and cosmology. A central question is, whether radiative spontaneous electroweak symmetry breaking can be combined with neutrino mass generation, we find that the answer is affirmative. We discuss the implication of the RSSB on the neutrino mass phenomenology and low-energy observables. Furthermore, by comparing the models to experimental data we find that several anomalies in the present observations favour particular scenarios over the pure Standard Model hypothesis. We are able to show, that the presence of sterile neutrinos with active-sterile mixing of order 10{sup -3} and masses in the TeV range leads to a reduced invisible decay width of the Z-boson and can bring the NuTeV observations in agreement with theoretical expectations. The models we discuss naturally incorporate long lived particles which can serve as dark matter candidates and we investigate this phenomenologically. We find that the combination of the requirements leads to interesting constraints on the model and parameter space. We find that loop induced electromagnetic moments for the neutral dark matter candidates, lead to interactions with charged particles. We use this and derive new constraints from existing XENON100 and LUX data. In addition we study how vacuum effects can backreact on a given geometry in electromagnetism and semiclassical gravity. We find that in the case of gravity the conformal set up plays a special role and indicate several ideas for further investigation of this topic.
Cosmology from quantum potential in brane–anti-brane system
Directory of Open Access Journals (Sweden)
Alireza Sepehri
2015-09-01
Full Text Available Recently, some authors removed the big-bang singularity and predicted an infinite age of our universe. In this paper, we show that the same result can be obtained in string theory and M-theory; however, the shape of universe changes in different epochs. In our mechanism, first, N fundamental string decay to N D0–anti-D0-brane. Then, D0-branes join each other, grow and form a six-dimensional brane–antibrane system. This system is unstable, broken and at present the form of four-dimensional universes, one anti-universe in addition to one wormhole are produced. Thus, there isn't any big-bang in cosmology and the universe is a fundamental string at the beginning. Also, the total age of universe contains two parts, one is related to initial age and the other corresponds to the present age of universe (ttot=tinitial+tpresent. On the other hand, the initial age of universe includes two parts, the age of fundamental string and the time of transition (tinitial=ttransition+tf-string. We observe that only in the case of (tf-string→∞, the scale factor of universe is zero and as a result, the total age of universe is infinity.
Impact of quantum entanglement on spectrum of cosmological fluctuations
Energy Technology Data Exchange (ETDEWEB)
Kanno, Sugumi, E-mail: sugumi.kanno@uct.ac.za [Laboratory for Quantum Gravity and Strings and Astrophysics, Cosmology and Gravity Center, Department of Mathematics and Applied Mathematics, University of Cape Town, Private Bag, Rondebosch 7701 (South Africa)
2014-07-01
We investigate the effect of entanglement between two causally separated open charts in de Sitter space on the spectrum of vacuum fluctuations. We consider a free massive scalar field, and construct the reduced density matrix by tracing out the vacuum state for one of the open charts, as recently derived by Maldacena and Pimentel. We formulate the mean-square vacuum fluctuations by using the reduced density matrix and show that the scale invariant spectrum of massless scalar field is realized on small scales. On the other hand, we find that the quantum entanglement affects the shape of the spectrum on large scales comparable to or greater than the curvature radius.
An unconventional canonical quantization of local scalar fields over quantum space-time
International Nuclear Information System (INIS)
Banai, M.
1985-12-01
An unconventional extension of the canonical quantization method is presented for a classical local field theory. The proposed canonical commutation relations have a solution in the A-valued Hilbert space where A is the algebra of the bounded operators of the Hilbert space Lsup(2) (IRsup(3)). The canonical equations as operator equations are equivalent formally with the classical field equations, and are well defined for interacting systems, too. This model of quantized field lacks some of the difficulties of the conventional approach. Examples satisfying the asymptotic condition provide examples for Haag-Kastler's axioms, however, they satisfy Wightman's axioms only partially. (author)
International Nuclear Information System (INIS)
Halliwell, J. J.
2009-01-01
In the quantization of simple cosmological models (minisuperspace models) described by the Wheeler-DeWitt equation, an important step is the construction, from the wave function, of a probability distribution answering various questions of physical interest, such as the probability of the system entering a given region of configuration space at any stage in its entire history. A standard but heuristic procedure is to use the flux of (components of) the wave function in a WKB approximation. This gives sensible semiclassical results but lacks an underlying operator formalism. In this paper, we address the issue of constructing probability distributions linked to the Wheeler-DeWitt equation using the decoherent histories approach to quantum theory. The key step is the construction of class operators characterizing questions of physical interest. Taking advantage of a recent decoherent histories analysis of the arrival time problem in nonrelativistic quantum mechanics, we show that the appropriate class operators in quantum cosmology are readily constructed using a complex potential. The class operator for not entering a region of configuration space is given by the S matrix for scattering off a complex potential localized in that region. We thus derive the class operators for entering one or more regions in configuration space. The class operators commute with the Hamiltonian, have a sensible classical limit, and are closely related to an intersection number operator. The definitions of class operators given here handle the key case in which the underlying classical system has multiple crossings of the boundaries of the regions of interest. We show that oscillatory WKB solutions to the Wheeler-DeWitt equation give approximate decoherence of histories, as do superpositions of WKB solutions, as long as the regions of configuration space are sufficiently large. The corresponding probabilities coincide, in a semiclassical approximation, with standard heuristic procedures
International Nuclear Information System (INIS)
Mishchenko, Yuriy
2004-01-01
MISHCHENKO, YURIY. Applications of Canonical Transformations and Nontrivial Vacuum Solutions to flavor mixing and critical phenomena in Quantum Field Theory. (Under the direction of Chueng-Ryong Ji.) In this dissertation we consider two recent applications of Bogoliubov Transformation to the phenomenology of quantum mixing and the theory of critical phenomena. In recent years quantum mixing got in the focus of the searches for New Physics due to its unparalleled sensitivity to SM parameters and indications of neutrino mixing. It was recently suggested that Bogoliubov Transformation may be important in proper definition of the flavor states that otherwise results in problems in perturbative treatment. As first part of this dissertation we investigate this conjecture and develop a complete formulation of such a mixing field theory involving introduction of general formalism, analysis of space-time conversion and phenomenological implications. As second part of this dissertati
Energy Technology Data Exchange (ETDEWEB)
Mishchenko, Yuriy [North Carolina State Univ., Raleigh, NC (United States)
2004-12-01
MISHCHENKO, YURIY. Applications of Canonical Transformations and Nontrivial Vacuum Solutions to flavor mixing and critical phenomena in Quantum Field Theory. (Under the direction of Chueng-Ryong Ji.) In this dissertation we consider two recent applications of Bogoliubov Transformation to the phenomenology of quantum mixing and the theory of critical phenomena. In recent years quantum mixing got in the focus of the searches for New Physics due to its unparalleled sensitivity to SM parameters and indications of neutrino mixing. It was recently suggested that Bogoliubov Transformation may be important in proper definition of the flavor states that otherwise results in problems in perturbative treatment. As first part of this dissertation we investigate this conjecture and develop a complete formulation of such a mixing field theory involving introduction of general formalism, analysis of space-time conversion and phenomenological implications. As second part of this dissertati
FRW cosmological model inside an isolated Schwarzschild black hole
Ortiz, C.; Rosales, J. J.; Socorro, J.; Tkach, V. I.
2004-01-01
Using the canonical quantum theory of spherically symmetric pure gravitational systems, we present a direct correspondence between the Friedmann-Robertson-Walker (FRW) cosmological model in the interior of a Schwarzschild black hole and the nth energy eigenstate of a linear harmonic oscillator. Such type of universe has a quantized mass of the order of the Planck mass and harmonic oscillator wave functions
Cosmological perturbations from quantum fluctuations to large scale structure
International Nuclear Information System (INIS)
Bardeen, J.M.
1988-01-01
Classical perturbation theory is developed from the 3 + 1 form of the Einstein equations. A somewhat unusual form of the perturbation equations in the synchronous gauge is recommended for carrying out computations, but interpretation is based on certain hypersurface-invariant combinations of the variables. The formalism is used to analyze the origin of density perturbations from quantum fluctuations during inflation, with particular emphasis on dealing with 'double inflation' and deviations from the Zel'dovich spectrum. The evolution of the density perturbation to the present gives the final density perturbation power spectrum, whose relationship to observed large scale structure is discussed in the context of simple cold-dark-matter biasing schemes. 86 refs
Quantum FRW cosmological solutions in the presence of Chaplygin gas and perfect fluid
International Nuclear Information System (INIS)
Pedram, P.; Jalalzadeh, S.
2008-01-01
We present a Friedmann-Robertson-Walker quantum cosmological model in the presence of Chaplygin gas and perfect fluid for early and late time epochs. In this work, we consider perfect fluid as an effective potential and apply Schutz's variational formalism to the Chaplygin gas which recovers the notion of time. These give rise to Schroedinger-Wheeler-DeWitt equation for the scale factor. We use the eigenfunctions in order to construct wave packets and study the time dependent behavior of the expectation value of the scale factor using the many-worlds interpretation of quantum mechanics. We show that contrary to the classical case, the expectation value of the scale factor avoids singularity at quantum level. Moreover, this model predicts that the expansion of Universe is accelerating for the late times
Phenomenological dynamics of loop quantum cosmology in Kantowski-Sachs spacetime
International Nuclear Information System (INIS)
Chiou, D.-W.
2008-01-01
The fundamental theory and the semiclassical description of loop quantum cosmology (LQC) have been studied in the Friedmann-Robertson-Walker and Bianchi I models. As an extension to include both anisotropy and intrinsic curvature, this paper investigates the cosmological model of Kantowski-Sachs spacetime with a free massless scalar field at the level of phenomenological dynamics with the LQC discreteness corrections. The LQC corrections are implemented in two different improved quantization schemes. In both schemes, the big bang and big crunch singularities of the classical solution are resolved and replaced by the big bounces when the area or volume scale factor approaches the critical values in the Planck regime measured by the reference of the scalar field momentum. Symmetries of scaling are also noted and suggest that the fundamental spatial scale (area gap) may give rise to a temporal scale. The bouncing scenarios are in an analogous fashion of the Bianchi I model, naturally extending the observations obtained previously.
Propagator with positive cosmological constant in the 3D Euclidean quantum gravity toy model
International Nuclear Information System (INIS)
Bunting, William E; Rovelli, Carlo
2014-01-01
We study the propagator on a single tetrahedron in a three-dimensional toy model of quantum gravity with positive cosmological constant. The cosmological constant is included in the model via q-deformation of the spatial symmetry algebra, that is, we use the Turaev–Viro amplitude. The expected repulsive effect of dark energy is recovered in numerical and analytic calculations of the propagator at large scales comparable to the infrared cutoff. However, due to the simplicity of the model, we do not obtain the exact Newton limit of the propagator. This is a first step toward the similar calculation in the full 3+1 dimensional theory with larger numbers of simplicies. (paper)
Dynamical study of DBI-essence in loop quantum cosmology and brane world
Energy Technology Data Exchange (ETDEWEB)
Bhadra, Jhumpa; Debnath, Ujjal [Bengal Engineering and Science University, Department of Mathematics, Howrah (India)
2012-08-15
We have studied homogeneous isotropic FRW model having dynamical dark energy DBI-essence with scalar field. Existence of cosmological scaling solutions restricts the Lagrangian of the scalar field {phi}. Choosing p=Xg(Xe{sup {lambda}{phi}}), where X=-g {sup {mu}{nu}}{partial_derivative}{sub {mu}}{phi}{partial_derivative}{sub {nu}}{phi}/2 with g any function of Xe{sup {lambda}{phi}} and defining some suitable transformations, we have constructed the dynamical system in different models of gravity: (i) Loop Quantum Cosmology (LQC), (ii) DGP brane world and (iii) RS II brane world. We have investigated stability of this dynamical system around the critical point for three gravity models and investigated the scalar-field dominated attractor solution in support of accelerated universe. The roles of the physical parameters have also been shown graphically during the accelerating phase of the universe. (orig.)
Dynamical study of DBI-essence in loop quantum cosmology and brane world
International Nuclear Information System (INIS)
Bhadra, Jhumpa; Debnath, Ujjal
2012-01-01
We have studied homogeneous isotropic FRW model having dynamical dark energy DBI-essence with scalar field. Existence of cosmological scaling solutions restricts the Lagrangian of the scalar field φ. Choosing p=Xg(Xe λφ ), where X=-g μν ∂ μ φ∂ ν φ/2 with g any function of Xe λφ and defining some suitable transformations, we have constructed the dynamical system in different models of gravity: (i) Loop Quantum Cosmology (LQC), (ii) DGP brane world and (iii) RS II brane world. We have investigated stability of this dynamical system around the critical point for three gravity models and investigated the scalar-field dominated attractor solution in support of accelerated universe. The roles of the physical parameters have also been shown graphically during the accelerating phase of the universe. (orig.)
A Non-Polynomial Gravity Formulation for Loop Quantum Cosmology Bounce
Directory of Open Access Journals (Sweden)
Stefano Chinaglia
2017-09-01
Full Text Available Recently the so-called mimetic gravity approach has been used to obtain corrections to the Friedmann equation of General Relativity similar to the ones present in loop quantum cosmology. In this paper, we propose an alternative way to derive this modified Friedmann equation via the so-called non-polynomial gravity approach, which consists of adding geometric non-polynomial higher derivative terms to Hilbert–Einstein action, which are nonetheless polynomials and lead to a second-order differential equation in Friedmann–Lemaître–Robertson–Walker space-times. Our explicit action turns out to be a realization of the Helling proposal of effective action with an infinite number of terms. The model is also investigated in the presence of a non-vanishing cosmological constant, and a new exact bounce solution is found and studied.
Dark matter as the Bose-Einstein condensation in loop quantum cosmology
International Nuclear Information System (INIS)
Atazadeh, K.; Mousavi, M.; Darabi, F.
2016-01-01
We consider the FLRW universe in a loop quantum cosmological model filled with radiation, baryonic matter (with negligible pressure), dark energy, and dark matter. The dark matter sector is supposed to be of Bose-Einstein condensate type. The Bose-Einstein condensation process in a cosmological context by supposing it as an approximate first-order phase transition, has already been studied in the literature. Here, we study the evolution of the physical quantities related to the early universe description such as the energy density, temperature, and scale factor of the universe, before, during, and after the condensation process. We also consider in detail the evolution era of the universe in a mixed normal-condensate dark matter phase. The behavior and time evolution of the condensate dark matter fraction is also analyzed. (orig.)
International Nuclear Information System (INIS)
Tarasov, V.E.
1994-07-01
Sedov variational principle, which is the generalization of the least actional principle for the dissipative processes is used to generalize the canonical quantization and von Neumann equation for dissipative systems (particles and strings). (author). 66 refs, 1 fig
Scalar-metric quantum cosmology with Chaplygin gas and perfect fluid
Energy Technology Data Exchange (ETDEWEB)
Ghosh, Saumya; Panigrahi, Prasanta K. [Indian Institute of Science Education and Research Kolkata, Nadia, West Bengal (India); Gangopadhyay, Sunandan [Indian Institute of Science Education and Research Kolkata, Nadia, West Bengal (India); S.N. Bose National Centre for Basic Sciences, Kolkata (India)
2018-01-15
In this paper we consider the flat FRW cosmology with a scalar field coupled with the metric along with generalized Chaplygin gas and perfect fluid comprising the matter sector. We use the Schutz's formalism to deal with the generalized Chaplygin gas sector. The full theory is then quantized canonically using the Wheeler-DeWitt Hamiltonian formalism. We then solve the WD equation with appropriate boundary conditions. Then by defining a proper completeness relation for the self-adjointness of the WD equation we arrive at the wave packet for the universe. It is observed that the peak in the probability density gets affected due to both fluids in the matter sector, namely, the Chaplygin gas and perfect fluid. (orig.)
Geometric perspective on singularity resolution and uniqueness in loop quantum cosmology
International Nuclear Information System (INIS)
Corichi, Alejandro; Singh, Parampreet
2009-01-01
We reexamine the issue of singularity resolution in homogeneous loop quantum cosmology from the perspective of geometrical entities such as expansion rate and the shear scalar. These quantities are very reliable measures of the properties of spacetime and can be defined not only at the classical and effective level, but also at an operator level in the quantum theory. From their behavior in the effective constraint surface and in the effective loop quantum spacetime, we show that one can severely restrict the ambiguities in regularization of the quantum constraint and rule out unphysical choices. We analyze this in the flat isotropic model and the Bianchi-I spacetimes. In the former case we show that the expansion rate is absolutely bounded only for the so-called improved quantization, a result which synergizes with uniqueness of this quantization as proved earlier. Surprisingly, for the Bianchi-I spacetime, we show that out of the available choices, the expansion rate and shear are bounded for only one regularization of the quantum constraint. It turns out that only for this choice, the theory exhibits quantum gravity corrections at a unique scale, and is physically viable.
Barvinsky, A O
2007-08-17
The density matrix of the Universe for the microcanonical ensemble in quantum cosmology describes an equipartition in the physical phase space of the theory (sum over everything), but in terms of the observable spacetime geometry this ensemble is peaked about the set of recently obtained cosmological instantons limited to a bounded range of the cosmological constant. This suggests the mechanism of constraining the landscape of string vacua and a possible solution to the dark energy problem in the form of the quasiequilibrium decay of the microcanonical state of the Universe.
International Nuclear Information System (INIS)
Mandal, Jyotirmay Das; Debnath, Ujjal
2016-01-01
We have studied the tachyon intermediate and logamediate warm inflation in loop quantum cosmological background by taking the dissipative co-efficient Γ = Γ 0 (where Γ 0 is a constant) in “intermediate” inflation and Γ = V(ϕ), (where V(ϕ) is the potential of tachyonic field) in “logamediate” inflation. We have assumed slow-roll condition to construct scalar field ϕ, potential V, N-folds, etc. Various slow-roll parameters have also been obtained. We have analyzed the stability of this model through graphical representations. (paper)
Quantum correlations of ideal Bose and Fermi gases in the canonical ensemble
International Nuclear Information System (INIS)
Tsutsui, Kazumasa; Kita, Takafumi
2016-01-01
We derive an expression for the reduced density matrices of ideal Bose and Fermi gases in the canonical ensemble, which corresponds to the Bloch-De Dominicis (or Wick's) theorem in the grand canonical ensemble for normal-ordered products of operators. Using this expression, we study one- and two-body correlations of homogeneous ideal gases with N particles. The pair distribution function g (2) (r) of fermions clearly exhibits antibunching with g (2) (0) = 0 due to the Pauli exclusion principle at all temperatures, whereas that of normal bosons shows bunching with g (2) (0) ≈ 2, corresponding to the Hanbury Brown-Twiss effect. For bosons below the Bose-Einstein condensation temperature T 0 , an off-diagonal long-range order develops in the one-particle density matrix to reach g (1) (r) = 1 at T = 0, and the pair correlation starts to decrease towards g (2) (r) ≈ 1 at T = 0. The results for N → ∞ are seen to converge to those of the grand canonical ensemble obtained by assuming the average <ψ(r)> of the field operator ψ(r) below T 0 . This fact justifies the introduction of the 'anomalous' average <ψ(r)> ≠ 0 below T 0 in the grand canonical ensemble as a mathematical means of removing unphysical particle-number fluctuations to reproduce the canonical results in the thermodynamic limit. (author)
Towards N = 2 SUSY homogeneous quantum cosmology; Einstein-Yang-Mills systems
International Nuclear Information System (INIS)
Donets, E.E.; Tentyukov, M.N.; Tsulaya, M.M.
1998-01-01
The application of N = 2 supersymmetric Quantum Mechanics for the quantization of homogeneous systems coupled with gravity is discussed. Starting with the superfield formulation of N = 2 SUSY sigma-model, Hermitian self-adjoint expressions for quantum Hamiltonians and Lagrangians for any signature of a sigma-model metric are obtained. This approach is then applied to coupled SU (2) Einstein-Yang-Mills (EYM) systems in axially-symmetric Bianchi - I,II,VIII, IX, Kantowski-Sachs and closed Friedmann-Robertson-Walker cosmological models. It is shown that all these models admit the embedding into N = 2 SUSY sigma-model with the explicit expressions for superpotentials, being direct sums of gravitational and Yang-Mills (YM) parts. In addition, YM parts of superpotentials exactly coincide with the corresponding Chern-Simons terms. The spontaneous SUSY breaking, caused by YM instantons in EYM systems is discussed in a number of examples
Refined tropical curve counts and canonical bases for quantum cluster algebras
DEFF Research Database (Denmark)
Mandel, Travis
We express the (quantizations of the) Gross-Hacking-Keel-Kontsevich canonical bases for cluster algebras in terms of certain (Block-Göttsche) weighted counts of tropical curves. In the process, we obtain via scattering diagram techniques a new invariance result for these Block-Göttsche counts....
International Nuclear Information System (INIS)
Zanzi, Andrea
2010-01-01
The chameleonic behavior of the string theory dilaton is suggested. Some of the possible consequences of the chameleonic string dilaton are analyzed in detail. In particular, (1) we suggest a new stringy solution to the cosmological constant problem and (2) we point out the nonequivalence of different conformal frames at the quantum level. In order to obtain these results, we start taking into account the (strong coupling) string loop expansion in the string frame (S-frame), therefore the so-called form factors are present in the effective action. The correct dark energy scale is recovered in the Einstein frame (E-frame) without unnatural fine-tunings and this result is robust against all quantum corrections, granted that we assume a proper structure of the S-frame form factors in the strong coupling regime. At this stage, the possibility still exists that a certain amount of fine-tuning may be required to satisfy some phenomenological constraints. Moreover in the E-frame, in our proposal, all the interactions are switched off on cosmological length scales (i.e., the theory is IR-free), while higher derivative gravitational terms might be present locally (on short distances) and it remains to be seen whether these facts clash with phenomenology. A detailed phenomenological analysis is definitely necessary to clarify these points.
Gravity and the quantum pedagogical essays on cosmology, astrophysics, and quantum gravity
Engineer, Sunu
2017-01-01
This book provides a compilation of in-depth articles and reviews on key topics within gravitation, cosmology and related issues. It is a celebratory volume dedicated to Prof. Thanu Padmanabhan ("Paddy"), the renowned relativist and cosmologist from IUCAA, India, on the occasion of his 60th birthday. The authors, many of them leaders of their fields, are all colleagues, collaborators and former students of Paddy, who have worked with him over a research career spanning more than four decades. Paddy is a scientist of diverse interests, who attaches great importance to teaching. With this in mind, the aim of this compilation is to provide an accessible pedagogic introduction to, and overview of, various important topics in cosmology, gravitation and astrophysics. As such it will be an invaluable resource for scientists, graduate students and also advanced undergraduates seeking to broaden their horizons.
Loop quantum cosmology of the k=1 FRW: A tale of two bounces
International Nuclear Information System (INIS)
Corichi, Alejandro; Karami, Asieh
2011-01-01
We consider the k=1 Friedman-Robertson-Walker (FRW) model within loop quantum cosmology, paying special attention to the existence of an ambiguity in the quantization process. In spatially nonflat anisotropic models such as Bianchi II and IX, the standard method of defining the curvature through closed holonomies is not admissible. Instead, one has to implement the quantum constraints by approximating the connection via open holonomies. In the case of flat k=0 FRW and Bianchi I models, these two quantization methods coincide, but in the case of the closed k=1 FRW model they might yield different quantum theories. In this manuscript we explore these two quantizations and the different effective descriptions they provide of the bouncing cyclic universe. In particular, as we show in detail, the most dramatic difference is that in the theory defined by the new quantization method, there is not one, but two different bounces through which the cyclic universe alternates. We show that for a 'large' universe, these two bounces are very similar and, therefore, practically indistinguishable, approaching the dynamics of the 'curvature-based' quantum theory.
International Nuclear Information System (INIS)
Christodoulakis, T; Doulis, G; Terzis, Petros A; Melas, E; Grammenos, Th; Papadopoulos, G O; Spanou, A
2010-01-01
The canonical decomposition of all 3+1 geometries admitting two-dimensional space-like surfaces is exhibited as a generalization of a previous work. A proposal, consisting of a specific renormalization Assumption and an accompanying Requirement, which has been put forward in the 2+1 case is now generalized to 3+1 dimensions. This enables the canonical quantization of these geometries through a generalization of Kuchar's quantization scheme in the case of infinite degrees of freedom. The resulting Wheeler-DeWitt equation is based on a renormalized manifold parameterized by three smooth scalar functionals. The entire space of solutions to this equation is analytically given, a fact that is entirely new to the present case. This is made possible through the exploitation of the residual freedom in the choice of the third functional, which is left by the imposition of the Requirement, and is proven to correspond to a general coordinate transformation in the renormalized manifold.
Quantum Mechanics from Newton's Second Law and the Canonical Commutation Relation [X,P]=i
Palenik, Mark C.
2014-01-01
Despite the fact that it has been known since the time of Heisenberg that quantum operators obey a quantum version of Newton's laws, students are often told that derivations of quantum mechanics must necessarily follow from the Hamiltonian or Lagrangian formulations of mechanics. Here, we first derive the existing Heisenberg equations of motion from Newton's laws and the uncertainty principle using only the equations $F=\\frac{dP}{dt}$, $P=m\\frac{dV}{dt}$, and $\\left[X,P\\right]=i$. Then, a new...
Off-shell dark matter: A cosmological relic of quantum gravity
Saravani, Mehdi; Afshordi, Niayesh
2017-02-01
We study a novel proposal for the origin of cosmological cold dark matter (CDM) which is rooted in the quantum nature of spacetime. In this model, off-shell modes of quantum fields can exist in asymptotic states as a result of spacetime nonlocality (expected in generic theories of quantum gravity) and play the role of CDM, which we dub off-shell dark matter (O f DM ). However, their rate of production is suppressed by the scale of nonlocality (e.g. Planck length). As a result, we show that O f DM is only produced in the first moments of big bang, and then effectively decouples (except through its gravitational interactions). We examine the observational predictions of this model: In the context of cosmic inflation, we show that this proposal relates the reheating temperature to the inflaton mass, which narrows down the uncertainty in the number of e -foldings of specific inflationary scenarios. We also demonstrate that O f DM is indeed cold, and discuss potentially observable signatures on small scale matter power spectrum.
Mass quantization in quantum and susy cosmological models with matter content
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Ortiz, C; Socorro, J; Tkach, V I; Torres, J; Rosales, J
2005-01-01
We present the study of the quantum closed Friedmann-Robertson-Walker (FRW) cosmological model with a matter content given by a perfect fluid with barotropic state equation p = γρ The Wheeler-DeWitt equation is viewed as the Schroedinger equation for the linear harmonic oscillator with energy E. Such type of Universe has quantized masses of the order of the Planck mass and harmonic oscillator wave functions. Then, we consider the n = 2 supersymmetric superfield approach for the same model and obtain a normalizable wave function (at zero energy) of the universe. Besides, the mass parameter spectrum is found in the Schroedinger picture, being similar to those obtained by other methods, using a black hole system
Simulating quantum effects of cosmological expansion using a static ion trap
Menicucci, Nicolas C.; Olson, S. Jay; Milburn, Gerard J.
2010-09-01
We propose a new experimental test bed that uses ions in the collective ground state of a static trap to study the analogue of quantum-field effects in cosmological spacetimes, including the Gibbons-Hawking effect for a single detector in de Sitter spacetime, as well as the possibility of modeling inflationary structure formation and the entanglement signature of de Sitter spacetime. To date, proposals for using trapped ions in analogue gravity experiments have simulated the effect of gravity on the field modes by directly manipulating the ions' motion. In contrast, by associating laboratory time with conformal time in the simulated universe, we can encode the full effect of curvature in the modulation of the laser used to couple the ions' vibrational motion and electronic states. This model simplifies the experimental requirements for modeling the analogue of an expanding universe using trapped ions, and it enlarges the validity of the ion-trap analogy to a wide range of interesting cases.
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Weinberg, S.
1989-01-01
Cosmological constant problem is discussed. History of the problem is briefly considered. Five different approaches to solution of the problem are described: supersymmetry, supergravity, superstring; anthropic approach; mechamism of lagrangian alignment; modification of gravitation theory and quantum cosmology. It is noted that approach, based on quantum cosmology is the most promising one
Lorentzian condition in holographic cosmology
International Nuclear Information System (INIS)
Hertog, Thomas; Monten, Ruben; Vreys, Yannick
2017-01-01
We derive a sufficient set of conditions on the Euclidean boundary theory in dS/CFT for it to predict classical, Lorentzian bulk evolution at large spatial volumes. Our derivation makes use of a canonical transformation to express the bulk wave function at large volume in terms of the sources of the dual partition function. This enables a sharper formulation of dS/CFT. The conditions under which the boundary theory predicts classical bulk evolution are stronger than the criteria usually employed in quantum cosmology. We illustrate this in a homogeneous isotropic minisuperspace model of gravity coupled to a scalar field in which we identify the ensemble of classical histories explicitly.
No rescue for the no boundary proposal: Pointers to the future of quantum cosmology
Feldbrugge, Job; Lehners, Jean-Luc; Turok, Neil
2018-01-01
In recent work [J. Feldbrugge et al. Phys. Rev. D 95, 103508 (2017)., 10.1103/PhysRevD.95.103508 and J. Feldbrugge et al. Phys. Rev. Lett. 119, 171301 (2017)., 10.1103/PhysRevLett.119.171301], we introduced Picard-Lefschetz theory as a tool for defining the Lorentzian path integral for quantum gravity in a systematic semiclassical expansion. This formulation avoids several pitfalls occurring in the Euclidean approach. Our method provides, in particular, a more precise formulation of the Hartle-Hawking no boundary proposal, as a sum over real Lorentzian four-geometries interpolating between an initial three-geometry of zero size, i.e., a point, and a final three-geometry. With this definition, we calculated the no boundary amplitude for a closed universe with a cosmological constant, assuming cosmological symmetry for the background and including linear perturbations. We found the opposite semiclassical exponent to that obtained by Hartle and Hawking for the creation of a de Sitter spacetime "from nothing." Furthermore, we found the linearized perturbations to be governed by an inverse Gaussian distribution, meaning they are unsuppressed and out of control. Recently, Diaz Dorronsoro et al. [Phys. Rev. D 96, 043505 (2017), 10.1103/PhysRevD.96.043505] followed our methods but attempted to rescue the no boundary proposal by integrating the lapse over a different, intrinsically complex contour. Here, we show that, in addition to the desired Hartle-Hawking saddle point contribution, their contour yields extra, nonperturbative corrections which again render the perturbations unsuppressed. We prove there is no choice of complex contour for the lapse which avoids this problem. We extend our discussion to include backreaction in the leading semiclassical approximation, fully nonlinearly for the lowest tensor harmonic and to second order for all higher modes. Implications for quantum de Sitter spacetime and for cosmic inflation are briefly discussed.
Odintsov, S. D.; Oikonomou, V. K.; Saridakis, Emmanuel N.
2015-12-01
We investigate the realization of two bouncing paradigms, namely of the superbounce and the loop quantum cosmological ekpyrosis, in the framework of various modified gravities. In particular, we focus on the F(R) , F(G) and F(T) gravities, and we reconstruct their specific subclasses which lead to such universe evolutions. These subclasses constitute from power laws, polynomials, or hypergeometric ansatzes, which can be approximated by power laws. The qualitative similarity of the different effective gravities which realize the above two bouncing cosmologies, indicates that a universality might be lying behind the bounce. Finally, performing a linear perturbation analysis, we show that the obtained solutions are conditionally or fully stable.
Energy Technology Data Exchange (ETDEWEB)
Jalalzadeh, S.; Rostami, T. [Shahid Beheshti University, Department of Physics, Tehran (Iran, Islamic Republic of); Moniz, P.V. [Centro de Matematica e Aplicacoes-UBI, Covilha (Portugal); Universidade da Beira Interior, Departamento de Fisica, Covilha (Portugal)
2015-01-01
A framework associating quantum cosmological boundary conditions to minisuperspace hidden symmetries has been introduced in Jalalzadeh and Moniz (Phys Rev D 89:083504, 2014). The scope of the application was, notwithstanding the novelty, restrictive because it lacked a discussion involving realistic matter fields. Therefore, in the present letter, we extend the framework scope to encompass elements from a scalar-tensor theory in the presence of a cosmological constant. More precisely, it is shown that hidden minisuperspace symmetries present in a pre-big bang model suggest a process from which boundary conditions can be selected. (orig.)
Quantum mechanics from Newton's second law and the canonical commutation relation [X, P] = i
International Nuclear Information System (INIS)
Palenik, Mark C
2014-01-01
Despite the fact that it has been known since the time of Heisenberg that quantum operators obey a quantum version of Newton's laws, students are often told that derivations of quantum mechanics must necessarily follow from the Hamiltonian or Lagrangian formulations of mechanics. Here, we first derive the existing Heisenberg equations of motion from Newton's laws and the uncertainty principle using only the equations F=((dP)/(dt)), P=m((dV)/(dt)), and [X, P] = i. Then, a new expression for the propagator is derived that makes a connection between time evolution in quantum mechanics and the motion of a classical particle under Newton's laws. The propagator is solved for three cases where an exact solution is possible: (1) the free particle; (2) the harmonic oscillator; and (3) a constant force, or linear potential in the standard interpretation. We then show that for a general for a general force F(X), by Taylor expanding X(t) in time, we can use this methodology to reproduce the Feynman path integral formula for the propagator. Such a picture may be useful for students as they make the transition from classical to quantum mechanics and help solidify the equivalence of the Hamiltonian, Lagrangian, and Newtonian pictures of physics in their minds. (paper)
Quantum vacuum energy in Taub-NUT (Newman-Unti-Tamburino)-type cosmologies
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Hiscock, W.A.; Konkowski, D.A.
1982-01-01
The effects of vacuum polarization on the mildest possible sort of cosmological singularity, the Taub-NUT (Newman-Unti-Tamburino)-type singularities, are studied. Unlike stronger sorts of singularities where physical quantities (e.g., curvature, energy density) diverge, in these universes the only barrier is a pathological topology. Quantum effects, known to be important in regions of large spacetime curvature, are found to also be important in these universes, where the curvature may be arbitrarily small or even zero. The vacuum expectation value of the stress-energy tensor for a conformal scalar field is calculated on a flat archetype of the Taub-NUT-type universes, the Misner universe (flat Kasner spacetime with S 1 x R 3 topology). The vacuum stress energy diverges at the singularity and on its associated Cauchy horizons. This divergence, together with the ''fixed'' nature of the spacetime's topology, suggests that these boundaries will be replaced by curvature singularities in a better approximation to full quantum gravity
Quantum cosmology of a Bianchi III LRS geometry coupled to a source free electromagnetic field
Karagiorgos, A.; Pailas, T.; Dimakis, N.; Terzis, Petros A.; Christodoulakis, T.
2018-03-01
We consider a Bianchi type III axisymmetric geometry in the presence of an electromagnetic field. A first result at the classical level is that the symmetry of the geometry need not be applied on the electromagnetic tensor Fμν the algebraic restrictions, implied by the Einstein field equations to the stress energy tensor Tμν, suffice to reduce the general Fμν to the appropriate form. The classical solution thus found contains a time dependent electric and a constant magnetic charge. The solution is also reachable from the corresponding mini-superspace action, which is strikingly similar to the Reissner-Nordstr{öm one. This points to a connection between the black hole geometry and the cosmological solution here found, which is the analog of the known correlation between the Schwarzschild and the Kantowski-Sachs metrics. The configuration space is drastically modified by the presence of the magnetic charge from a 3D flat to a 3D pp wave geometry. We map the emerging linear and quadratic classical integrals of motion, to quantum observables. Along with the Wheeler-DeWitt equation these observables provide unique, up to constants, wave functions. The employment of a Bohmian interpretation of these quantum states results in deterministic (semi-classical) geometries most of which are singularity free.
A quantum retrograde canon: complete population inversion in n 2-state systems
Padan, Alon; Suchowski, Haim
2018-04-01
We present a novel approach for analytically reducing a family of time-dependent multi-state quantum control problems to two-state systems. The presented method translates between {SU}(2)× {SU}(2) related n 2-state systems and two-state systems, such that the former undergo complete population inversion (CPI) if and only if the latter reach specific states. For even n, the method translates any two-state CPI scheme to a family of CPI schemes in n 2-state systems. In particular, facilitating CPI in a four-state system via real time-dependent nearest-neighbors couplings is reduced to facilitating CPI in a two-level system. Furthermore, we show that the method can be used for operator control, and provide conditions for producing several universal gates for quantum computation as an example. In addition, we indicate a basis for utilizing the method in optimal control problems.
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Castagnino, Mario [Instituto de Astronomia y Fisica del Espacio, Casilla de Correo 67, Sucursal 28, 1428 Buenos Aires (Argentina); Catren, Gabriel [Instituto de Astronomia y Fisica del Espacio, Casilla de Correo 67, Sucursal 28, 1428 Buenos Aires (Argentina); Ferraro, Rafael [Instituto de Astronomia y Fisica del Espacio, Casilla de Correo 67, Sucursal 28, 1428 Buenos Aires (Argentina)
2002-09-21
This paper addresses the quantization of minisuperspace cosmological models by studying a possible solution to the problem of time and time asymmetries in quantum cosmology. Since general relativity does not have a privileged time variable of Newtonian type, it is necessary, in order to have a dynamical evolution, to select a physical clock. This choice yields, in the proposed approach, to the breaking of the so-called clock-reversal invariance of the theory which is clearly distinguished from the well-known motion-reversal invariance of both classical and quantum mechanics. In light of this new perspective, the problem of imposing proper boundary conditions on the space of solutions of the Wheeler-DeWitt equation is reformulated. The symmetry-breaking formalism of previous papers is analyzed and a clarification of it is proposed in order to satisfy the requirements of the new interpretation.
International Nuclear Information System (INIS)
Castagnino, Mario; Catren, Gabriel; Ferraro, Rafael
2002-01-01
This paper addresses the quantization of minisuperspace cosmological models by studying a possible solution to the problem of time and time asymmetries in quantum cosmology. Since general relativity does not have a privileged time variable of Newtonian type, it is necessary, in order to have a dynamical evolution, to select a physical clock. This choice yields, in the proposed approach, to the breaking of the so-called clock-reversal invariance of the theory which is clearly distinguished from the well-known motion-reversal invariance of both classical and quantum mechanics. In light of this new perspective, the problem of imposing proper boundary conditions on the space of solutions of the Wheeler-DeWitt equation is reformulated. The symmetry-breaking formalism of previous papers is analyzed and a clarification of it is proposed in order to satisfy the requirements of the new interpretation
International Nuclear Information System (INIS)
Zeldovich, Ya.
1984-01-01
The knowledge is summed up of contemporary cosmology on the universe and its development resulting from a great number of highly sensitive observations and the application of contemporary physical theories to the entire universe. The questions are assessed of mass density in the universe, the structure and origin of the universe, its baryon asymmetry and the quantum explanation of the origin of the universe. Physical problems are presented which should be resolved for the future development of cosmology. (Ha)
Jorgensen, Palle E T
1987-01-01
Historically, operator theory and representation theory both originated with the advent of quantum mechanics. The interplay between the subjects has been and still is active in a variety of areas.This volume focuses on representations of the universal enveloping algebra, covariant representations in general, and infinite-dimensional Lie algebras in particular. It also provides new applications of recent results on integrability of finite-dimensional Lie algebras. As a central theme, it is shown that a number of recent developments in operator algebras may be handled in a particularly e
BOOK REVIEW: Quantum Analogues: From Phase Transitions to Black Holes and Cosmology
Liberati, Stefano
2008-09-01
'And I cherish more than anything else the analogies, my most trustworthy masters. They know all the secrets of nature, and they ought to be least neglected in geometry.' These words of the great astronomer Johannes Kepler embody the philosophy behind the research recounted in this interesting book—a book composed of nine selected lectures (and a nice introduction by Bill Unruh) from the international workshop on 'Quantum Simulations via Analogues', which was held in the Max Planck Institute for the Physics of Complex Systems in Dresden during the summer of 2005. Analogue models of (and for) gravity have a long and distinguished history dating back to the earliest years of general relativity. However the last decade has seen a remarkable and steady development of analogue gravity models based on condensed matter systems, leading to some hundreds of published articles, numerous workshops, and several books. While the main driver for this booming field has definitely been the puzzling physics associated with quantum effects in black holes, more recently much attention has also been devoted to other interesting issues—such as cosmological particle production or the cosmological constant problem. Moreover, together with these new themes there has been a persistent interest in the possibility of simulating cosmic topological defects in the laboratory (although it should be said that momentum for this line of research has been somewhat weakened by the progressive decrease of interest in cosmological topological defects as an alternative to inflationary scenarios). All these aspects are faithfully accounted for in this book, which does a good job at presenting a vivid snapshot of many (if not quite all) of the most interesting lines of research in the field. All the articles have a self-consistent structure—which allows one to read them in arbitrary order and appreciate the full richness of each topic. However, when considered together I would say that they also
Exactly solvable models of two-dimensional dilaton cosmology with quantum backreaction
International Nuclear Information System (INIS)
Zaslavskii, O B
2003-01-01
We consider a general approach to exactly solvable 2D dilaton cosmology with one-loop backreaction from conformal fields taken into account. It includes as particular cases previous models discussed in the literature. We list different types of solutions and investigate their properties for simple models, typical for string theory. We find a rather rich class of everywhere-regular solutions, which exist practically in every type of analysed solution. They exhibit different kinds of asymptotic behaviour in the past and future, including inflation, superinflation, deflation, power expansion or contraction. In particular, for some models the dS spacetime with a time-dependent dilaton field is the exact solution of the field equations. For some kinds of solution the weak-energy condition is violated independently of a specific model. We also find the solutions with a singularity which is situated in an infinite past (or future), so at any finite moment of a comoving time the universe is singularity-free. It is pointed out that for some models the spacetime may be everywhere regular even in spite of infinitely large quantum backreaction in an infinite past
Liu, Jian; Miller, William H
2011-03-14
We show the exact expression of the quantum mechanical time correlation function in the phase space formulation of quantum mechanics. The trajectory-based dynamics that conserves the quantum canonical distribution-equilibrium Liouville dynamics (ELD) proposed in Paper I is then used to approximately evaluate the exact expression. It gives exact thermal correlation functions (of even nonlinear operators, i.e., nonlinear functions of position or momentum operators) in the classical, high temperature, and harmonic limits. Various methods have been presented for the implementation of ELD. Numerical tests of the ELD approach in the Wigner or Husimi phase space have been made for a harmonic oscillator and two strongly anharmonic model problems, for each potential autocorrelation functions of both linear and nonlinear operators have been calculated. It suggests ELD can be a potentially useful approach for describing quantum effects for complex systems in condense phase.
Dimakis, N.; Terzis, Petros A.; Zampeli, Adamantia; Christodoulakis, T.
2016-09-01
The high degree of symmetry renders the dynamics of cosmological as well as some black hole spacetimes describable by a system of finite degrees of freedom. These systems are generally known as minisuperspace models. One of their important key features is the invariance of the corresponding reduced actions under reparametrizations of the independent variable, a fact that can be seen as the remnant of the general covariance of the full theory. In the case of a system of n degrees of freedom, described by a Lagrangian quadratic in velocities, one can use the lapse by either gauge fixing it or letting it be defined by the constraint and subsequently substitute into the rest of the equations. In the first case, the system of the second-order equations of motion is solvable for all n accelerations and the constraint becomes a restriction among constants of integration. In the second case, the system can be solved for only n -1 accelerations and the "gauge" freedom is transferred to the choice of one of the scalar degrees of freedom. In this paper, we take the second path and express all n -1 scalar degrees of freedom in terms of the remaining one, say q . By considering these n -1 degrees of freedom as arbitrary but given functions of q , we manage to extract a two-dimensional pure gauge system consisting of the lapse N and the arbitrary q : in a way, we decouple the reparametrization invariance from the rest of the equations of motion, which are thus describing the "true" dynamics. The solution of the corresponding quantum two-dimensional system is used for the definition of a generalized probability for every configuration fi(q ), be it classical or not. The main result is that, interestingly enough, this probability attains its extrema on the classical solution of the initial n -dimensional system.
Rosen, Steven M
2017-12-01
This paper carries forward the author's contribution to PBMP's previous special issue on Integral Biomathics (Rosen 2015). In the earlier paper, the crisis in contemporary theoretical physics was described and it was demonstrated that the problem can be addressed effectively only by shifting the foundations of physics from objectivist Cartesian philosophy to phenomenological philosophy. To that end, a phenomenological string theory was proposed based on qualitative topology and hypercomplex numbers. The current presentation takes this further by delving into the ancient Chinese origin of phenomenological string theory. First, we discover a deep connection between the Klein bottle, which is crucial to the theory, and the Ho-t'u, an old Chinese number archetype central to Taoist cosmology. The two structures are seen to mirror each other in expressing the curious psychophysical (phenomenological) action pattern at the heart of microphysics. But tackling the question of quantum gravity requires that a whole family of topological dimensions be brought into play. What we find in engaging with these structures is a closely related family of Taoist forebears that, in concert with their successors, provide a blueprint for cosmic evolution. Whereas conventional string theory accounts for the generation of nature's fundamental forces via a notion of symmetry breaking that is essentially static and thus unable to explain cosmogony successfully, phenomenological/Taoist string theory is guided by the dialectical interplay between symmetry and asymmetry inherent in the principle of synsymmetry. This dynamic concept of cosmic change is elaborated on in the three concluding sections of the paper. Here, a detailed analysis of cosmogony is offered, first in terms of the theory of dimensional development and its Taoist (yin-yang) counterpart, then in terms of the evolution of the elemental force particles through cycles of expansion and contraction in a spiraling universe. The paper
Chamcham, Khalil; Silk, Joseph; Barrow, John D.; Saunders, Simon
2017-04-01
Part I. Issues in the Philosophy of Cosmology: 1. Cosmology, cosmologia and the testing of cosmological theories George F. R. Ellis; 2. Black holes, cosmology and the passage of time: three problems at the limits of science Bernard Carr; 3. Moving boundaries? - comments on the relationship between philosophy and cosmology Claus Beisbart; 4. On the question why there exists something rather than nothing Roderich Tumulka; Part II. Structures in the Universe and the Structure of Modern Cosmology: 5. Some generalities about generality John D. Barrow; 6. Emergent structures of effective field theories Jean-Philippe Uzan; 7. Cosmological structure formation Joel R. Primack; 8. Formation of galaxies Joseph Silk; Part III. Foundations of Cosmology: Gravity and the Quantum: 9. The observer strikes back James Hartle and Thomas Hertog; 10. Testing inflation Chris Smeenk; 11. Why Boltzmann brains do not fluctuate into existence from the de Sitter vacuum Kimberly K. Boddy, Sean M. Carroll and Jason Pollack; 12. Holographic inflation revised Tom Banks; 13. Progress and gravity: overcoming divisions between general relativity and particle physics and between physics and HPS J. Brian Pitts; Part IV. Quantum Foundations and Quantum Gravity: 14. Is time's arrow perspectival? Carlo Rovelli; 15. Relational quantum cosmology Francesca Vidotto; 16. Cosmological ontology and epistemology Don N. Page; 17. Quantum origin of cosmological structure and dynamical reduction theories Daniel Sudarsky; 18. Towards a novel approach to semi-classical gravity Ward Struyve; Part V. Methodological and Philosophical Issues: 19. Limits of time in cosmology Svend E. Rugh and Henrik Zinkernagel; 20. Self-locating priors and cosmological measures Cian Dorr and Frank Arntzenius; 21. On probability and cosmology: inference beyond data? Martin Sahlén; 22. Testing the multiverse: Bayes, fine-tuning and typicality Luke A. Barnes; 23. A new perspective on Einstein's philosophy of cosmology Cormac O
Canonical quantization of general relativity in discrete space-times.
Gambini, Rodolfo; Pullin, Jorge
2003-01-17
It has long been recognized that lattice gauge theory formulations, when applied to general relativity, conflict with the invariance of the theory under diffeomorphisms. We analyze discrete lattice general relativity and develop a canonical formalism that allows one to treat constrained theories in Lorentzian signature space-times. The presence of the lattice introduces a "dynamical gauge" fixing that makes the quantization of the theories conceptually clear, albeit computationally involved. The problem of a consistent algebra of constraints is automatically solved in our approach. The approach works successfully in other field theories as well, including topological theories. A simple cosmological application exhibits quantum elimination of the singularity at the big bang.
Particle physics and cosmology
International Nuclear Information System (INIS)
Turner, M.S.; Schramm, D.N.
1985-01-01
During the past year, the research of the members of our group has spanned virtually all the topics at the interface of cosmology and particle physics: inflationary Universe scenarios, astrophysical and cosmological constraints on particle properties, ultra-high energy cosmic ray physics, quantum field theory in curved space-time, cosmology with extra dimensions, superstring cosmology, neutrino astronomy with large, underground detectors, and the formation of structure in the Universe
International Nuclear Information System (INIS)
Singh, Parampreet; Soni, S K
2016-01-01
The problem of obtaining canonical Hamiltonian structures from the equations of motion, without any knowledge of the action, is studied in the context of the spatially flat Friedmann, ‘Robertson’, and Walker models. Modifications to the Raychaudhuri equation are implemented independently as quadratic and cubic terms of energy density without introducing additional degrees of freedom. Depending on their sign, modifications make gravity repulsive above a curvature scale for matter satisfying strong energy conditions, or more attractive than in the classical theory. The canonical structure of the modified theories is determined by demanding that the total Hamiltonian be a linear combination of gravity and matter Hamiltonians. In the quadratic repulsive case, the modified canonical phase space of gravity is a polymerized phase space with canonical momentum as inverse a trigonometric function of the Hubble rate; the canonical Hamiltonian can be identified with the effective Hamiltonian in loop quantum cosmology. The repulsive cubic modification results in a ‘generalized polymerized’ canonical phase space. Both the repulsive modifications are found to yield singularity avoidance. In contrast, the quadratic and cubic attractive modifications result in a canonical phase space in which canonical momentum is nontrigonometric and singularities persist. Our results hint at connections between the repulsive/attractive nature of modifications to gravity arising from the gravitational sector and polymerized/non polymerized gravitational phase space. (paper)
International Nuclear Information System (INIS)
Martín-Benito, Mercedes; Martín-de Blas, Daniel; Marugán, Guillermo A Mena
2014-01-01
We develop approximation methods in the hybrid quantization of the Gowdy model with linear polarization and a massless scalar field, for the case of three-torus spatial topology. The loop quantization of the homogeneous gravitational sector of the Gowdy model (according to the improved dynamics prescription) and the presence of inhomogeneities lead to a very complicated Hamiltonian constraint. Therefore, the extraction of physical results calls for the introduction of well justified approximations. We first show how to approximate the homogeneous part of the Hamiltonian constraint, corresponding to Bianchi I geometries, as if it described a Friedmann–Robertson–Walker (FRW) model corrected with anisotropies. This approximation is valid in the sector of high energies of the FRW geometry (concerning its contribution to the constraint) and for anisotropy profiles that are sufficiently smooth. In addition, for certain families of states related to regimes of physical interest, with negligible quantum effects of the anisotropies and small inhomogeneities, one can approximate the Hamiltonian constraint of the inhomogeneous system by that of an FRW geometry with a relatively simple matter content, and then obtain its solutions. (paper)
Unitary evolution and uniqueness of the Fock quantization in flat cosmologies
International Nuclear Information System (INIS)
Marugán, G A Mena; Błas, D Martín-de; Gomar, L Castelló
2013-01-01
We study the Fock quantization of scalar fields with a time dependent mass in cosmological scenarios with flat compact spatial sections. This framework describes physically interesting situations like, e.g., cosmological perturbations in flat Friedmann-Robertson-Walker spacetimes, generally including a suitable scaling of them by a background function. We prove that the requirements of vacuum invariance under the spatial isometries and of a unitary quantum dynamics select (a) a unique canonical pair of field variables among all those related by time dependent canonical transformations which scale the field configurations, and (b) a unique Fock representation for the canonical commutation relations of this pair of variables. The proof is generalizable to any compact spatial topology in three or less dimensions, though we focus on the case of the three-torus owing to the especially relevant implications.
Rajantie, Arttu
2018-03-06
The discovery of the Higgs boson in 2012 and other results from the Large Hadron Collider have confirmed the standard model of particle physics as the correct theory of elementary particles and their interactions up to energies of several TeV. Remarkably, the theory may even remain valid all the way to the Planck scale of quantum gravity, and therefore it provides a solid theoretical basis for describing the early Universe. Furthermore, the Higgs field itself has unique properties that may have allowed it to play a central role in the evolution of the Universe, from inflation to cosmological phase transitions and the origin of both baryonic and dark matter, and possibly to determine its ultimate fate through the electroweak vacuum instability. These connections between particle physics and cosmology have given rise to a new and growing field of Higgs cosmology, which promises to shed new light on some of the most puzzling questions about the Universe as new data from particle physics experiments and cosmological observations become available.This article is part of the Theo Murphy meeting issue 'Higgs cosmology'. © 2018 The Author(s).
Rajantie, Arttu
2018-01-01
The discovery of the Higgs boson in 2012 and other results from the Large Hadron Collider have confirmed the standard model of particle physics as the correct theory of elementary particles and their interactions up to energies of several TeV. Remarkably, the theory may even remain valid all the way to the Planck scale of quantum gravity, and therefore it provides a solid theoretical basis for describing the early Universe. Furthermore, the Higgs field itself has unique properties that may have allowed it to play a central role in the evolution of the Universe, from inflation to cosmological phase transitions and the origin of both baryonic and dark matter, and possibly to determine its ultimate fate through the electroweak vacuum instability. These connections between particle physics and cosmology have given rise to a new and growing field of Higgs cosmology, which promises to shed new light on some of the most puzzling questions about the Universe as new data from particle physics experiments and cosmological observations become available. This article is part of the Theo Murphy meeting issue `Higgs cosmology'.
Polymer quantum mechanics and its continuum limit
International Nuclear Information System (INIS)
Corichi, Alejandro; Vukasinac, Tatjana; Zapata, Jose A.
2007-01-01
A rather nonstandard quantum representation of the canonical commutation relations of quantum mechanics systems, known as the polymer representation, has gained some attention in recent years, due to its possible relation with Planck scale physics. In particular, this approach has been followed in a symmetric sector of loop quantum gravity known as loop quantum cosmology. Here we explore different aspects of the relation between the ordinary Schroedinger theory and the polymer description. The paper has two parts. In the first one, we derive the polymer quantum mechanics starting from the ordinary Schroedinger theory and show that the polymer description arises as an appropriate limit. In the second part we consider the continuum limit of this theory, namely, the reverse process in which one starts from the discrete theory and tries to recover back the ordinary Schroedinger quantum mechanics. We consider several examples of interest, including the harmonic oscillator, the free particle, and a simple cosmological model
International Nuclear Information System (INIS)
Melas, Evangelos
2011-01-01
The 3+1 (canonical) decomposition of all geometries admitting two-dimensional space-like surfaces is exhibited as a generalization of a previous work. A proposal, consisting of a specific re-normalization Assumption and an accompanying Requirement, which has been put forward in the 2+1 case is now generalized to 3+1 dimensions. This enables the canonical quantization of these geometries through a generalization of Kuchar's quantization scheme in the case of infinite degrees of freedom. The resulting Wheeler-deWitt equation is based on a re-normalized manifold parameterized by three smooth scalar functionals. The entire space of solutions to this equation is analytically given, a fact that is entirely new to the present case. This is made possible by exploiting the freedom left by the imposition of the Requirement and contained in the third functional.
The dark sector from interacting canonical and non-canonical scalar fields
International Nuclear Information System (INIS)
De Souza, Rudinei C; Kremer, Gilberto M
2010-01-01
In this work general models with interactions between two canonical scalar fields and between one non-canonical (tachyon type) and one canonical scalar field are investigated. The potentials and couplings to the gravity are selected through the Noether symmetry approach. These general models are employed to describe interactions between dark energy and dark matter, with the fields being constrained by the astronomical data. The cosmological solutions of some cases are compared with the observed evolution of the late Universe.
International Nuclear Information System (INIS)
Senjanovic, G.; Virginia Polytechnic Inst. and State Univ., Blacksburg
1984-07-01
Extended supersymmetry, Kaluza-Klein theory and family unification all suggest the existence of mirror fermions, with same quantum numbers but opposite helicities from ordinary fermions. The laboratory and especially cosmological implications of such particles are reviewed and summarized. (author)
de Martini, Francesco
The nature of the scalar field responsible for the cosmological inflation is found to be rooted in the most fundamental concept of the Weyl’s differential geometry: the parallel displacement of vectors in curved spacetime. Within this novel geometrical scenario, the standard electroweak theory of leptons based on the SU(2)L⊗U(1)Y as well as on the conformal groups of spacetime Weyl’s transformations is analyzed within the framework of a general-relativistic, conformally-covariant scalar-tensor theory that includes the electromagnetic and the Yang-Mills fields. A Higgs mechanism within a spontaneous symmetry breaking process is identified and this offers formal connections between some relevant properties of the elementary particles and the dark energy content of the Universe. An “effective cosmological potential”: Veff is expressed in terms of the dark energy potential: |VΛ| via the “mass reduction parameter”: |ζ|≡|Veff||VΛ|, a general property of the Universe. The mass of the Higgs boson, which is considered a “free parameter” by the standard electroweak theory, by our theory is found to be proportional to the mass MU≡|Veff| which contributes to the measured Cosmological Constant, i.e. the measured content of vacuum-energy in the Universe. The nonintegrable application of the Weyl’s geometry leads to a Proca equation accounting for the dynamics of a ϕρ-particle, a vector-meson proposed as an optimum candidate for Dark Matter. The peculiar mathematical structure of Veff offers a clue towards a very general resolution in 4-D of a most intriguing puzzle of modern quantum field theory, the “cosmological constant paradox”(here referred to as: “Λ-paradox”). Indeed, our “universal” theory offers a resolution of the “Λ-paradox” for all exponential inflationary potentials: VΛ(ϕ)∝e‑nϕ, and for all linear superpositions of these potentials, where n belongs to the mathematical set of the “real numbers”. An explicit
Kato, Rodrigo B; Silva, Frederico T; Pappa, Gisele L; Belchior, Jadson C
2015-01-28
We report the use of genetic algorithms (GA) as a method to refine force field parameters in order to determine RNA energy. Quantum-mechanical (QM) calculations are carried out for the isolated canonical ribonucleosides (adenosine, guanosine, cytidine and uridine) that are taken as reference data. In this particular study, the dihedral and electrostatic energies are reparametrized in order to test the proposed approach, i.e., GA coupled with QM calculations. Overall, RMSE comparison with recent published results for ribonucleosides energies shows an improvement, on average, of 50%. Finally, the new reparametrized potential energy function is used to determine the spatial structure of RNA (PDB code ) that was not taken into account in the parametrization process. This structure was improved about 82% comparable with previously published results.
Energy Technology Data Exchange (ETDEWEB)
Pinto-Neto, N.; Santini, E. Sergio. E-mail: nelsonpn@lafex.cbpf.br; santini@lafex.cbpf.br
2000-12-01
We consider quantum geometrodynamics and parametrized quantum field theories in the frame-work of the Bohm-de Broglie interpretation. In the first case, and following the lines of our previous work, where a Hamiltonian formalism for the bohmian trajectories was constructed, we show the consistency of the theory for any quantum potential, completing the scenarios for canonical quantum cosmology presented there. In the latter case, we prove the consistency of scalar field theory in Minkowski spacetime for any quantum potential, and we show, using this alternative Hamiltonian method, a concrete example already known in the literature where Lorentz invariance of individual events is broken. (author)
Distinguished quantum states in a class of cosmological spacetimes and their Hadamard property
Energy Technology Data Exchange (ETDEWEB)
Dappiaggi, Claudio; Pinamonti, Nicola [Hamburg Univ. (Germany). II. Inst. fuer Theoretische Physik; Moretti, Valter [Trento Univ. (Italy). Dipt. di Matematica; Ist. Nazionale di Alta Matematica, Unita locale di Trento (Italy); Ist. Nazionale di Fisica, Povo (Italy)
2008-12-15
In a recent paper, we proved that a large class of spacetimes, not necessarily homogeneous or isotropic and relevant at a cosmological level, possesses a preferred codimension one submanifold, i.e., the past cosmological horizon, on which it is possible to encode the information of a scalar field theory living in the bulk. Such bulk-to-boundary reconstruction procedure entails the identification of a preferred quasifree algebraic state for the bulk theory, enjoying remarkable properties concerning invariance under isometries (if any) of the bulk and energy positivity, and reducing to well-known vacua in standard situations. In this paper, specialising to open FRW models, we extend previously obtained results and we prove that the preferred state is of Hadamard form, hence the backreaction on the metric is finite and the state can be used as a starting point for renormalisation procedures. That state could play a distinguished role in the discussion of the evolution of scalar fluctuations of the metric, an analysis often performed in the development of any model describing the dynamic of an early Universe which undergoes an inflationary phase of rapid expansion in the past. (orig.)
Distinguished quantum states in a class of cosmological spacetimes and their Hadamard property
International Nuclear Information System (INIS)
Dappiaggi, Claudio; Pinamonti, Nicola
2008-12-01
In a recent paper, we proved that a large class of spacetimes, not necessarily homogeneous or isotropic and relevant at a cosmological level, possesses a preferred codimension one submanifold, i.e., the past cosmological horizon, on which it is possible to encode the information of a scalar field theory living in the bulk. Such bulk-to-boundary reconstruction procedure entails the identification of a preferred quasifree algebraic state for the bulk theory, enjoying remarkable properties concerning invariance under isometries (if any) of the bulk and energy positivity, and reducing to well-known vacua in standard situations. In this paper, specialising to open FRW models, we extend previously obtained results and we prove that the preferred state is of Hadamard form, hence the backreaction on the metric is finite and the state can be used as a starting point for renormalisation procedures. That state could play a distinguished role in the discussion of the evolution of scalar fluctuations of the metric, an analysis often performed in the development of any model describing the dynamic of an early Universe which undergoes an inflationary phase of rapid expansion in the past. (orig.)
Classical universe emerging from quantum cosmology without horizon and flatness problems
Energy Technology Data Exchange (ETDEWEB)
Fathi, M.; Jalalzadeh, S. [Shahid Beheshti University, Department of Physics, Tehran (Iran, Islamic Republic of); Moniz, P.V. [Centro de Matematica e Aplicacoes-UBI, Covilha (Portugal); Universidade da Beira Interior, Departmento de Fisica, Covilha (Portugal)
2016-10-15
We apply the complex de Broglie-Bohm formulation of quantum mechanics in Chou and Wyatt (Phys Rev A 76: 012115, 2007), Gozzi (Phys Lett B 165: 351, 1985), Bhalla et al. (Am J Phys 65: 1187, 1997) to a spatially closed homogeneous and isotropic early universe whose matter contents are radiation and dust perfect fluids. We then show that an expanding classical universe can emerge from an oscillating (with complex scale factor) quantum universe without singularity. Furthermore, the universe obtained in this process has no horizon or flatness problems. (orig.)
Directory of Open Access Journals (Sweden)
Boris A. Arbuzov
2017-11-01
Full Text Available Wouldbe consequences of the existence of effective interactions in quantum gravitation theory are considered. In the framework of the approach, the example of a running gravitational coupling is presented, corresponding to an adequate description of effects, which nowadays are usually prescribed to dark matter and dark energy.
Taming the cosmological constant in 2D causal quantum gravity with topology change
Loll, R.; Westra, W.; Zohren, S.
2005-01-01
As shown in previous work, there is a well-defined nonperturbative gravitational path integral including an explicit sum over topologies in the setting of Causal Dy- namical Triangulations in two dimensions. In this paper we derive a complete ana- lytical solution of the quantum continuum
Quantum Oscillations Can Prevent the Big Bang Singularity in an Einstein-Dirac Cosmology
Finster, Felix; Hainzl, Christian
2010-01-01
We consider a spatially homogeneous and isotropic system of Dirac particles coupled to classical gravity. The dust and radiation dominated closed Friedmann-Robertson-Walker space-times are recovered as limiting cases. We find a mechanism where quantum oscillations of the Dirac wave functions can prevent the formation of the big bang or big crunch singularity. Thus before the big crunch, the collapse of the universe is stopped by quantum effects and reversed to an expansion, so that the universe opens up entering a new era of classical behavior. Numerical examples of such space-times are given, and the dependence on various parameters is discussed. Generically, one has a collapse after a finite number of cycles. By fine-tuning the parameters we construct an example of a space-time which satisfies the dominant energy condition and is time-periodic, thus running through an infinite number of contraction and expansion cycles.
Zhang, Zhijun; Liu, Xinzijian; Chen, Zifei; Zheng, Haifeng; Yan, Kangyu; Liu, Jian
2017-07-01
We show a unified second-order scheme for constructing simple, robust, and accurate algorithms for typical thermostats for configurational sampling for the canonical ensemble. When Langevin dynamics is used, the scheme leads to the BAOAB algorithm that has been recently investigated. We show that the scheme is also useful for other types of thermostats, such as the Andersen thermostat and Nosé-Hoover chain, regardless of whether the thermostat is deterministic or stochastic. In addition to analytical analysis, two 1-dimensional models and three typical real molecular systems that range from the gas phase, clusters, to the condensed phase are used in numerical examples for demonstration. Accuracy may be increased by an order of magnitude for estimating coordinate-dependent properties in molecular dynamics (when the same time interval is used), irrespective of which type of thermostat is applied. The scheme is especially useful for path integral molecular dynamics because it consistently improves the efficiency for evaluating all thermodynamic properties for any type of thermostat.
Non-Vacuum Initial States for Cosmological Perturbations of Quantum-Mechanical Origin
Martín, J; Sakellariadou, M; Martin, Jerome; Riazuelo, Alain; Sakellariadou, Mairi
2000-01-01
In the context of inflation, non-vacuum initial states for cosmological perturbations that possess a built in scale are studied. It is demonstrated that this assumption leads to a falsifiable class of models. The question of whether they lead to conflicts with the available observations is addressed. For this purpose, the power spectrum of the Bardeen potential operator is calculated and compared with the CMBR anisotropies measurements and the redshift surveys of galaxies and clusters of galaxies. Generic predictions of the model are: a high first acoustic peak, the presence of a bump in the matter power spectrum and non-Gaussian statistics. The details are controlled by the number of quanta in the non-vacuum initial state. Comparisons with observations show that there exists a window for the free parameters such that good agreement between the data and the theoretical predictions is possible. However, in the case where the initial state is a state with a fixed number of quanta, it is shown that this number c...
Projective relativity, cosmology and gravitation
International Nuclear Information System (INIS)
Arcidiacono, G.
1986-01-01
This book describes the latest applications of projective geometry to cosmology and gravitation. The contents of the book are; the Poincare group and Special Relativity, the thermodynamics and electromagnetism, general relativity, gravitation and cosmology, group theory and models of universe, the special projective relativity, the Fantappie group and Big-Bang cosmology, a new cosmological projective mechanics, the plasma physics and cosmology, the projective magnetohydrodynamics field, projective relativity and waves propagation, the generalizations of the gravitational field, the general projective relativity, the projective gravitational field, the De Sitter Universe and quantum physics, the conformal relativity and Newton gravitation
Open problems in string cosmology
International Nuclear Information System (INIS)
Toumbas, N.
2010-01-01
Some of the open problems in string cosmology are highlighted within the context of the recently constructed thermal and quantum superstring cosmological solutions. Emphasis is given on the high temperature cosmological regime, where it is argued that thermal string vacua in the presence of gravito-magnetic fluxes can be used to bypass the Hagedorn instabilities of string gas cosmology. This article is based on a talk given at the workshop on ''Cosmology and Strings'', Corfu, September 6-13, 2009. (Abstract Copyright [2010], Wiley Periodicals, Inc.)
Analogue cosmological particle creation: Quantum correlations in expanding Bose-Einstein condensates
International Nuclear Information System (INIS)
Prain, Angus; Liberati, Stefano; Fagnocchi, Serena
2010-01-01
We investigate the structure of quantum correlations in an expanding Bose-Einstein condensate (BEC) through the analogue gravity framework. We consider both a 3+1 isotropically expanding BEC as well as the experimentally relevant case of an elongated, effectively 1+1 dimensional, expanding condensate. In this case we include the effects of inhomogeneities in the condensate, a feature rarely included in the analogue gravity literature. In both cases we link the BEC expansion to a simple model for an expanding spacetime and then study the correlation structure numerically and analytically (in suitable approximations). We also discuss the expected strength of such correlation patterns and experimentally feasible BEC systems in which these effects might be detected in the near future.
Physical states in the canonical tensor model from the perspective of random tensor networks
Energy Technology Data Exchange (ETDEWEB)
Narain, Gaurav [The Institute for Fundamental Study “The Tah Poe Academia Institute”,Naresuan University, Phitsanulok 65000 (Thailand); Sasakura, Naoki [Yukawa Institute for Theoretical Physics,Kyoto University, Kyoto 606-8502 (Japan); Sato, Yuki [National Institute for Theoretical Physics,School of Physics and Centre for Theoretical Physics,University of the Witwartersrand, WITS 2050 (South Africa)
2015-01-07
Tensor models, generalization of matrix models, are studied aiming for quantum gravity in dimensions larger than two. Among them, the canonical tensor model is formulated as a totally constrained system with first-class constraints, the algebra of which resembles the Dirac algebra of general relativity. When quantized, the physical states are defined to be vanished by the quantized constraints. In explicit representations, the constraint equations are a set of partial differential equations for the physical wave-functions, which do not seem straightforward to be solved due to their non-linear character. In this paper, after providing some explicit solutions for N=2,3, we show that certain scale-free integration of partition functions of statistical systems on random networks (or random tensor networks more generally) provides a series of solutions for general N. Then, by generalizing this form, we also obtain various solutions for general N. Moreover, we show that the solutions for the cases with a cosmological constant can be obtained from those with no cosmological constant for increased N. This would imply the interesting possibility that a cosmological constant can always be absorbed into the dynamics and is not an input parameter in the canonical tensor model. We also observe the possibility of symmetry enhancement in N=3, and comment on an extension of Airy function related to the solutions.
Highlights in gravitation and cosmology
International Nuclear Information System (INIS)
Iyer, B.R.; Kembhavi, Ajit; Narlikar, J.V.; Vishveshwara, C.V.
1988-01-01
This book assesses research into gravitation and cosmology by examining the subject from various viewpoints: the classical and quantum pictures, along with the cosmological and astrophysical applications. There are 35 articles by experts of international standing. Each defines the state of the art and contains a concise summary of our present knowledge of a facet of gravitational physics. These edited papers are based on those first given at an international conference held in Goa, India at the end of 1987. The following broad areas are covered: classical relativity, quantum gravity, cosmology, black holes, compact objects, gravitational radiation and gravity experiments. In this volume there are also summaries of discussions on the following special topics: exact solutions of cosmological equations, mathematical aspects of general relativity, the early universe, and quantum gravity. For research workers in cosmology and gravitation this reference book provides a broad view of present achievements and current problems. (author)
International Nuclear Information System (INIS)
Wainwright, J.
1990-01-01
The workshop on mathematical cosmology was devoted to four topics of current interest. This report contains a brief discussion of the historical background of each topic and a concise summary of the content of each talk. The topics were; the observational cosmology program, the cosmological perturbation program, isotropic singularities, and the evolution of Bianchi cosmologies. (author)
International Nuclear Information System (INIS)
Raychaudhuri, A.K.
1979-01-01
The subject is covered in chapters, entitled; introduction; Newtonian gravitation and cosmology; general relativity and relativistic cosmology; analysis of observational data; relativistic models not obeying the cosmological principle; microwave radiation background; thermal history of the universe and nucleosynthesis; singularity of cosmological models; gravitational constant as a field variable; cosmological models based on Einstein-Cartan theory; cosmological singularity in two recent theories; fate of perturbations of isotropic universes; formation of galaxies; baryon symmetric cosmology; assorted topics (including extragalactic radio sources; Mach principle). (U.K.)
International Nuclear Information System (INIS)
Turner, Michael S.
1999-01-01
For two decades the hot big-bang model as been referred to as the standard cosmology - and for good reason. For just as long cosmologists have known that there are fundamental questions that are not answered by the standard cosmology and point to a grander theory. The best candidate for that grander theory is inflation + cold dark matter. It holds that the Universe is flat, that slowly moving elementary particles left over from the earliest moments provide the cosmic infrastructure, and that the primeval density inhomogeneities that seed all the structure arose from quantum fluctuations. There is now prima facie evidence that supports two basic tenets of this paradigm. An avalanche of high-quality cosmological observations will soon make this case stronger or will break it. Key questions remain to be answered; foremost among them are: identification and detection of the cold dark matter particles and elucidation of the dark-energy component. These are exciting times in cosmology!
Gravitation and cosmology with York time
Roser, Philipp
Despite decades of inquiry an adequate theory of 'quantum gravity' has remained elusive, in part due to the absence of data that would guide the search and in part due to technical difficulties, prominently among them the 'problem of time'. The problem is a result of the attempt to quantise a classical theory with temporal reparameterisation and refoliation invariance such as general relativity. One way forward is therefore the breaking of this invariance via the identification of a preferred foliation of spacetime into parameterised spatial slices. In this thesis we argue that a foliation into slices of constant extrinsic curvature, parameterised by 'York time', is a viable contender. We argue that the role of York time in the initial-value problem of general relativity as well as a number of the parameter's other properties make it the most promising candidate for a physically preferred notion of time. A Hamiltonian theory describing gravity in the York-time picture may be derived from general relativity by 'Hamiltonian reduction', a procedure that eliminates certain degrees of freedom -- specifically the local scale and its rate of change -- in favour of an explicit time parameter and a functional expression for the associated Hamiltonian. In full generality this procedure is impossible to carry out since the equation that determines the Hamiltonian cannot be solved using known methods. However, it is possible to derive explicit Hamiltonian functions for cosmological scenarios (where matter and geometry is treated as spatially homogeneous). Using a perturbative expansion of the unsolvable equation enables us to derive a quantisable Hamiltonian for cosmological perturbations on such a homogeneous background. We analyse the (classical) theories derived in this manner and look at the York-time description of a number of cosmological processes. We then proceed to apply the canonical quantisation procedure to these systems and analyse the resulting quantum theories
McFadden, P.; Skenderis, K.
2010-01-01
We propose a holographic description of four-dimensional single-scalar inflationary universes, and show how cosmological observables, such as the primordial power spectrum, are encoded in the correlation functions of a three-dimensional quantum field theory (QFT). The holographic description
International Nuclear Information System (INIS)
Landsberg, P.T.; Evans, D.A.
1977-01-01
The subject is dealt with in chapters, entitled: cosmology -some fundamentals; Newtonian gravitation - some fundamentals; the cosmological differential equation - the particle model and the continuum model; some simple Friedmann models; the classification of the Friedmann models; the steady-state model; universe with pressure; optical effects of the expansion according to various theories of light; optical observations and cosmological models. (U.K.)
Observable cosmology and cosmological models
International Nuclear Information System (INIS)
Kardashev, N.S.; Lukash, V.N.; Novikov, I.D.
1987-01-01
Modern state of observation cosmology is briefly discussed. Among other things, a problem, related to Hibble constant and slowdown constant determining is considered. Within ''pancake'' theory hot (neutrino) cosmological model explains well the large-scale structure of the Universe, but does not explain the galaxy formation. A cold cosmological model explains well light object formation, but contradicts data on large-scale structure
Zhang Yuan Zhong
2002-01-01
This book is one of a series in the areas of high-energy physics, cosmology and gravitation published by the Institute of Physics. It includes courses given at a doctoral school on 'Relativistic Cosmology: Theory and Observation' held in Spring 2000 at the Centre for Scientific Culture 'Alessandro Volta', Italy, sponsored by SIGRAV-Societa Italiana di Relativita e Gravitazione (Italian Society of Relativity and Gravitation) and the University of Insubria. This book collects 15 review reports given by a number of outstanding scientists. They touch upon the main aspects of modern cosmology from observational matters to theoretical models, such as cosmological models, the early universe, dark matter and dark energy, modern observational cosmology, cosmic microwave background, gravitational lensing, and numerical simulations in cosmology. In particular, the introduction to the basics of cosmology includes the basic equations, covariant and tetrad descriptions, Friedmann models, observation and horizons, etc. The ...
Silk, Joseph; Barrow, John D; Saunders, Simon
2017-01-01
Following a long-term international collaboration between leaders in cosmology and the philosophy of science, this volume addresses foundational questions at the limit of science across these disciplines, questions raised by observational and theoretical progress in modern cosmology. Space missions have mapped the Universe up to its early instants, opening up questions on what came before the Big Bang, the nature of space and time, and the quantum origin of the Universe. As the foundational volume of an emerging academic discipline, experts from relevant fields lay out the fundamental problems of contemporary cosmology and explore the routes toward finding possible solutions. Written for graduates and researchers in physics and philosophy, particular efforts are made to inform academics from other fields, as well as the educated public, who wish to understand our modern vision of the Universe, related philosophical questions, and the significant impacts on scientific methodology.
Jones, Bernard J. T.
2017-04-01
Preface; Notation and conventions; Part I. 100 Years of Cosmology: 1. Emerging cosmology; 2. The cosmic expansion; 3. The cosmic microwave background; 4. Recent cosmology; Part II. Newtonian Cosmology: 5. Newtonian cosmology; 6. Dark energy cosmological models; 7. The early universe; 8. The inhomogeneous universe; 9. The inflationary universe; Part III. Relativistic Cosmology: 10. Minkowski space; 11. The energy momentum tensor; 12. General relativity; 13. Space-time geometry and calculus; 14. The Einstein field equations; 15. Solutions of the Einstein equations; 16. The Robertson-Walker solution; 17. Congruences, curvature and Raychaudhuri; 18. Observing and measuring the universe; Part IV. The Physics of Matter and Radiation: 19. Physics of the CMB radiation; 20. Recombination of the primeval plasma; 21. CMB polarisation; 22. CMB anisotropy; Part V. Precision Tools for Precision Cosmology: 23. Likelihood; 24. Frequentist hypothesis testing; 25. Statistical inference: Bayesian; 26. CMB data processing; 27. Parametrising the universe; 28. Precision cosmology; 29. Epilogue; Appendix A. SI, CGS and Planck units; Appendix B. Magnitudes and distances; Appendix C. Representing vectors and tensors; Appendix D. The electromagnetic field; Appendix E. Statistical distributions; Appendix F. Functions on a sphere; Appendix G. Acknowledgements; References; Index.
Cosmological horizons, quintessence and string theory
International Nuclear Information System (INIS)
Kaloper, Nemanja
2003-01-01
String theory is presently the best candidate for a quantum theory of gravity unified with other forces. It is natural to hope that applications of string theory to cosmology may shed new light on the cosmological conundra, such as singularities, initial conditions, cosmological constant problem and the origin of inflation. Before we can apply string theory to cosmology, there are important conceptual and practical problems which must be addressed. We have reviewed here some of these problems, related to how one defines string theory in a cosmological setting. (author)
The cosmological perturbation theory in loop cosmology with holonomy corrections
International Nuclear Information System (INIS)
Wu, Jian-Pin; Ling, Yi
2010-01-01
In this paper we investigate the scalar mode of first-order metric perturbations over spatially flat FRW spacetime when the holonomy correction is taken into account in the semi-classical framework of loop quantum cosmology. By means of the Hamiltonian derivation, the cosmological perturbation equations is obtained in longitudinal gauge. It turns out that in the presence of metric perturbation the holonomy effects influence both background and perturbations, and contribute the non-trivial terms S h1 and S h2 in the cosmological perturbation equations
Covariant canonical quantization of fields and Bohmian mechanics
International Nuclear Information System (INIS)
Nikolic, H.
2005-01-01
We propose a manifestly covariant canonical method of field quantization based on the classical De Donder-Weyl covariant canonical formulation of field theory. Owing to covariance, the space and time arguments of fields are treated on an equal footing. To achieve both covariance and consistency with standard non-covariant canonical quantization of fields in Minkowski spacetime, it is necessary to adopt a covariant Bohmian formulation of quantum field theory. A preferred foliation of spacetime emerges dynamically owing to a purely quantum effect. The application to a simple time-reparametrization invariant system and quantum gravity is discussed and compared with the conventional non-covariant Wheeler-DeWitt approach. (orig.)
Ostrogradski approach for the Regge-Teitelboim type cosmology
International Nuclear Information System (INIS)
Cordero, Ruben; Molgado, Alberto; Rojas, Efrain
2009-01-01
We present an alternative geometric inspired derivation of the quantum cosmology arising from a brane universe in the context of geodetic gravity. We set up the Regge-Teitelboim model to describe our universe, and we recover its original dynamics by thinking of such field theory as a second-order derivative theory. We refer to an Ostrogradski Hamiltonian formalism to prepare the system to its quantization. Our analysis highlights the second-order derivative nature of the RT model and the inherited geometrical aspect of the theory. A canonical transformation brings us to the internal physical geometry of the theory and induces its quantization straightforwardly. By using the Dirac canonical quantization method our approach comprises the management of both first- and second-class constraints where the counting of degrees of freedom follows accordingly. At the quantum level our Wheeler-De Witt equation agrees with previous results recently found. On these lines, we also comment upon the compatibility of our approach with the Hamiltonian approach proposed by Davidson and coworkers.
Sanders, RH; Papantonopoulos, E
2005-01-01
I discuss the classical cosmological tests, i.e., angular size-redshift, flux-redshift, and galaxy number counts, in the light of the cosmology prescribed by the interpretation of the CMB anisotropies. The discussion is somewhat of a primer for physicists, with emphasis upon the possible systematic
International Nuclear Information System (INIS)
Effenberger, R.
1974-09-01
The author summarizes some of the many questions and answers which have been raised over the years regarding the nature of matter, the origin of its forms and the associated concept of cosmology including the formation of the universe, our place in it and its course of evolution. An examination of the development of the classical concept of matter and its subsequent transformations within the space-time fields of relativity and quantum theory is also presented
International Nuclear Information System (INIS)
Markov, M.A.; West, P.C.
1984-01-01
This book discusses the state of the art of quantum gravity, quantum effects in cosmology, quantum black-hole physics, recent developments in supergravity, and quantum gauge theories. Topics considered include the problems of general relativity, pregeometry, complete cosmological theories, quantum fluctuations in cosmology and galaxy formation, a new inflationary universe scenario, grand unified phase transitions and the early Universe, the generalized second law of thermodynamics, vacuum polarization near black holes, the relativity of vacuum, black hole evaporations and their cosmological consequences, currents in supersymmetric theories, the Kaluza-Klein theories, gauge algebra and quantization, and twistor theory. This volume constitutes the proceedings of the Second Seminar on Quantum Gravity held in Moscow in 1981
Three dimensional canonical transformations
International Nuclear Information System (INIS)
Tegmen, A.
2010-01-01
A generic construction of canonical transformations is given in three-dimensional phase spaces on which Nambu bracket is imposed. First, the canonical transformations are defined as based on cannonade transformations. Second, it is shown that determination of the generating functions and the transformation itself for given generating function is possible by solving correspondent Pfaffian differential equations. Generating functions of type are introduced and all of them are listed. Infinitesimal canonical transformations are also discussed as the complementary subject. Finally, it is shown that decomposition of canonical transformations is also possible in three-dimensional phase spaces as in the usual two-dimensional ones.
Probing the small distance structure of canonical
t Hooft, G.
2010-01-01
In canonical quantum gravity, the formal functional integral includes an integration over the local conformal factor, and we propose to perform the functional integral over this factor before doing any of the other functional integrals. By construction, the resulting effective theory would be
Uniqueness of the Fock quantization of scalar fields in spatially flat cosmological spacetimes
Energy Technology Data Exchange (ETDEWEB)
Gomar, Laura Castelló [Facultad de Ciencias Físicas, Universidad Complutense de Madrid, Ciudad Universitaria, 28040 Madrid (Spain); Cortez, Jerónimo [Departamento de Física, Facultad de Ciencias, Universidad Nacional Autónoma de México, Mexico D.F. 04510 (Mexico); Blas, Daniel Martín-de; Marugán, Guillermo A. Mena [Instituto de Estructura de la Materia, CSIC, Serrano 121, 28006 Madrid (Spain); Velhinho, José M., E-mail: laucaste@estumail.ucm.es, E-mail: jacq@ciencias.unam.mx, E-mail: daniel.martin@iem.cfmac.csic.es, E-mail: jvelhi@ubi.pt [Departamento de Física, Faculdade de Ciências, Universidade da Beira Interior, R. Marquês D' Ávila e Bolama, 6201-001 Covilhã (Portugal)
2012-11-01
We study the Fock quantization of scalar fields in (generically) time dependent scenarios, focusing on the case in which the field propagation occurs in –either a background or effective– spacetime with spatial sections of flat compact topology. The discussion finds important applications in cosmology, like e.g. in the description of test Klein-Gordon fields and scalar perturbations in Friedmann-Robertson-Walker spacetime in the observationally favored flat case. Two types of ambiguities in the quantization are analyzed. First, the infinite ambiguity existing in the choice of a Fock representation for the canonical commutation relations, understandable as the freedom in the choice of inequivalent vacua for a given field. Besides, in cosmological situations, it is customary to scale the fields by time dependent functions, which absorb part of the evolution arising from the spacetime, which is treated classically. This leads to an additional ambiguity, this time in the choice of a canonical pair of field variables. We show that both types of ambiguities are removed by the requirements of (a) invariance of the vacuum under the symmetries of the three-torus, and (b) unitary implementation of the dynamics in the quantum theory. In this way, one arrives at a unique class of unitarily equivalent Fock quantizations for the system. This result provides considerable robustness to the quantum predictions and renders meaningful the confrontation with observation.
International Nuclear Information System (INIS)
Husain, Viqar
2008-01-01
There has been a flurry of books on quantum gravity in the past few years. The first edition of Kiefer's book appeared in 2004, about the same time as Carlo Rovelli's book with the same title. This was soon followed by Thomas Thiemann's 'Modern Canonical Quantum General Relativity'. Although the main focus of each of these books is non-perturbative and non-string approaches to the quantization of general relativity, they are quite orthogonal in temperament, style, subject matter and mathematical detail. Rovelli and Thiemann focus primarily on loop quantum gravity (LQG), whereas Kiefer attempts a broader introduction and review of the subject that includes chapters on string theory and decoherence. Kiefer's second edition attempts an even wider and somewhat ambitious sweep with 'new sections on asymptotic safety, dynamical triangulation, primordial black holes, the information-loss problem, loop quantum cosmology, and other topics'. The presentation of these current topics is necessarily brief given the size of the book, but effective in encapsulating the main ideas in some cases. For instance the few pages devoted to loop quantum cosmology describe how the mini-superspace reduction of the quantum Hamiltonian constraint of LQG becomes a difference equation, whereas the discussion of 'dynamical triangulations', an approach to defining a discretized Lorentzian path integral for quantum gravity, is less detailed. The first few chapters of the book provide, in a roughly historical sequence, the covariant and canonical metric variable approach to the subject developed in the 1960s and 70s. The problem(s) of time in quantum gravity are nicely summarized in the chapter on quantum geometrodynamics, followed by a detailed and effective introduction of the WKB approach and the semi-classical approximation. These topics form the traditional core of the subject. The next three chapters cover LQG, quantization of black holes, and quantum cosmology. Of these the chapter on LQG is
Graviton fluctuations erase the cosmological constant
Wetterich, C.
2017-10-01
Graviton fluctuations induce strong non-perturbative infrared renormalization effects for the cosmological constant. The functional renormalization flow drives a positive cosmological constant towards zero, solving the cosmological constant problem without the need to tune parameters. We propose a simple computation of the graviton contribution to the flow of the effective potential for scalar fields. Within variable gravity, with effective Planck mass proportional to the scalar field, we find that the potential increases asymptotically at most quadratically with the scalar field. The solutions of the derived cosmological equations lead to an asymptotically vanishing cosmological "constant" in the infinite future, providing for dynamical dark energy in the present cosmological epoch. Beyond a solution of the cosmological constant problem, our simplified computation also entails a sizeable positive graviton-induced anomalous dimension for the quartic Higgs coupling in the ultraviolet regime, substantiating the successful prediction of the Higgs boson mass within the asymptotic safety scenario for quantum gravity.
International Nuclear Information System (INIS)
Leibundgut, B.
2005-01-01
Supernovae have developed into a versatile tool for cosmology. Their impact on the cosmological model has been profound and led to the discovery of the accelerated expansion. The current status of the cosmological model as perceived through supernova observations will be presented. Supernovae are currently the only astrophysical objects that can measure the dynamics of the cosmic expansion during the past eight billion years. Ongoing experiments are trying to determine the characteristics of the accelerated expansion and give insight into what might be the physical explanation for the acceleration. (author)
International Nuclear Information System (INIS)
Berstein, J.
1984-01-01
These lectures offer a self-contained review of the role of neutrinos in cosmology. The first part deals with the question 'What is a neutrino.' and describes in a historical context the theoretical ideas and experimental discoveries related to the different types of neutrinos and their properties. The basic differences between the Dirac neutrino and the Majorana neutrino are pointed out and the evidence for different neutrino 'flavours', neutrino mass, and neutrino oscillations is discussed. The second part summarizes current views on cosmology, particularly as they are affected by recent theoretical and experimental advances in high-energy particle physics. Finally, the close relationship between neutrino physics and cosmology is brought out in more detail, to show how cosmological constraints can limit the various theoretical possibilities for neutrinos and, more particularly, how increasing knowledge of neutrino properties can contribute to our understanding of the origin, history, and future of the Universe. The level is that of the beginning graduate student. (orig.)
International Nuclear Information System (INIS)
Khalatnikov, I.M.; Belinskij, V.A.
1984-01-01
Application of the qualitative theory of dynamic systems to analysis of homogeneous cosmological models is described. Together with the well-known cases, requiring ideal liquid, the properties of cosmological evolution of matter with dissipative processes due to viscosity are considered. New cosmological effects occur, when viscosity terms being one and the same order with the rest terms in the equations of gravitation or even exceeding them. In these cases the description of the dissipative process by means of only two viscosity coefficients (volume and shift) may become inapplicable because all the rest decomposition terms of dissipative addition to the energy-momentum in velocity gradient can be large application of equations with hydrodynamic viscosty should be considered as a model of dissipative effects in cosmology
Lesgourgues, Julien; Miele, Gennaro; Pastor, Sergio
2013-01-01
The role that neutrinos have played in the evolution of the Universe is the focus of one of the most fascinating research areas that has stemmed from the interplay between cosmology, astrophysics and particle physics. In this self-contained book, the authors bring together all aspects of the role of neutrinos in cosmology, spanning from leptogenesis to primordial nucleosynthesis, their role in CMB and structure formation, to the problem of their direct detection. The book starts by guiding the reader through aspects of fundamental neutrino physics, such as the standard cosmological model and the statistical mechanics in the expanding Universe, before discussing the history of neutrinos in chronological order from the very early stages until today. This timely book will interest graduate students and researchers in astrophysics, cosmology and particle physics, who work with either a theoretical or experimental focus.
International Nuclear Information System (INIS)
Zeldovich, Y.B.
1983-01-01
This paper fives a general review of modern cosmology. The following subjects are discussed: hot big bang and periodization of the evolution; Hubble expansion; the structure of the universe (pancake theory); baryon asymmetry; inflatory universe. (Auth.)
Energy Technology Data Exchange (ETDEWEB)
Zhang Yuanzhong
2002-06-21
This book is one of a series in the areas of high-energy physics, cosmology and gravitation published by the Institute of Physics. It includes courses given at a doctoral school on 'Relativistic Cosmology: Theory and Observation' held in Spring 2000 at the Centre for Scientific Culture 'Alessandro Volta', Italy, sponsored by SIGRAV-Societa Italiana di Relativita e Gravitazione (Italian Society of Relativity and Gravitation) and the University of Insubria. This book collects 15 review reports given by a number of outstanding scientists. They touch upon the main aspects of modern cosmology from observational matters to theoretical models, such as cosmological models, the early universe, dark matter and dark energy, modern observational cosmology, cosmic microwave background, gravitational lensing, and numerical simulations in cosmology. In particular, the introduction to the basics of cosmology includes the basic equations, covariant and tetrad descriptions, Friedmann models, observation and horizons, etc. The chapters on the early universe involve inflationary theories, particle physics in the early universe, and the creation of matter in the universe. The chapters on dark matter (DM) deal with experimental evidence of DM, neutrino oscillations, DM candidates in supersymmetry models and supergravity, structure formation in the universe, dark-matter search with innovative techniques, and dark energy (cosmological constant), etc. The chapters about structure in the universe consist of the basis for structure formation, quantifying large-scale structure, cosmic background fluctuation, galaxy space distribution, and the clustering of galaxies. In the field of modern observational cosmology, galaxy surveys and cluster surveys are given. The chapter on gravitational lensing describes the lens basics and models, galactic microlensing and galaxy clusters as lenses. The last chapter, 'Numerical simulations in cosmology', deals with spatial and
CERN. Geneva
2007-01-01
The understanding of the Universe at the largest and smallest scales traditionally has been the subject of cosmology and particle physics, respectively. Studying the evolution of the Universe connects today's large scales with the tiny scales in the very early Universe and provides the link between the physics of particles and of the cosmos. This series of five lectures aims at a modern and critical presentation of the basic ideas, methods, models and observations in today's particle cosmology.
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Turner, Michael S
1999-03-01
For two decades the hot big-bang model as been referred to as the standard cosmology - and for good reason. For just as long cosmologists have known that there are fundamental questions that are not answered by the standard cosmology and point to a grander theory. The best candidate for that grander theory is inflation + cold dark matter. It holds that the Universe is flat, that slowly moving elementary particles left over from the earliest moments provide the cosmic infrastructure, and that the primeval density inhomogeneities that seed all the structure arose from quantum fluctuations. There is now prima facie evidence that supports two basic tenets of this paradigm. An avalanche of high-quality cosmological observations will soon make this case stronger or will break it. Key questions remain to be answered; foremost among them are: identification and detection of the cold dark matter particles and elucidation of the dark-energy component. These are exciting times in cosmology{exclamation_point}.
Hack, Thomas-Paul
2010-01-01
First, the present work is concerned with generalising constructions and results in quantum field theory on curved spacetimes from the well-known case of the Klein-Gordon field to Dirac fields. To this end, the enlarged algebra of observables of the Dirac field is constructed in the algebraic framework. This algebra contains normal-ordered Wick polynomials in particular, and an extended analysis of one of its elements, the stress-energy tensor, is performed. Based on detailed calculations of ...
Directory of Open Access Journals (Sweden)
Carlos García-Bedoya Maguiña
2011-05-01
Full Text Available Canon es un concepto clave en la historia literaria. En el presente artículo,se revisa la evolución histórica del canon literario peruano. Es solo con la llamada República Aristocrática, en las primeras décadas del siglo XX, que cabe hablar en el caso peruano de la formación de un auténtico canon nacional. El autor denomina a esta primera versión del canon literario peruano como canon oligárquico y destaca la importancia de la obra de Riva Agüero y de Ventura García Calderón en su configuración. Es solo más tarde, desde los años 20 y de modo definitivo desde los años 50, que puede hablarse de la emergencia de un nuevo canon literarioal que el autor propone determinar canon posoligárquico.
Energy Technology Data Exchange (ETDEWEB)
Paris, Mark W. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2018-02-13
The current one-year project allocation (w17 burst) supports the continuation of research performed in the two-year Institutional Computing allocation (w14 bigbangnucleosynthesis). The project has supported development and production runs resulting in several publications[1, 2, 3, 4] in peer-review journals and talks. Most signi cantly, we have recently achieved a signi cant improvement in code performance. This improvement was essential to the prospect of making further progress on this heretofore unsolved multiphysics problem that lies at the intersection of nuclear and particle theory and the kinetic theory of energy transport in a system with internal (quantum) degrees of freedom.
Beyond the Standard Model of Cosmology
International Nuclear Information System (INIS)
Ellis, John; Nanopoulos, D. V.
2004-01-01
Recent cosmological observations of unprecented accuracy, by WMAP in particular, have established a 'Standard Model' of cosmology, just as LEP established the Standard Model of particle physics. Both Standard Models raise open questions whose answers are likely to be linked. The most fundamental problems in both particle physics and cosmology will be resolved only within a framework for Quantum Gravity, for which the only game in town is string theory. We discuss novel ways to model cosmological inflation and late acceleration in a non-critical string approach, and discuss possible astrophysical tests
Nonlocal teleparallel cosmology.
Bahamonde, Sebastian; Capozziello, Salvatore; Faizal, Mir; Nunes, Rafael C
2017-01-01
Even though it is not possible to differentiate general relativity from teleparallel gravity using classical experiments, it could be possible to discriminate between them by quantum gravitational effects. These effects have motivated the introduction of nonlocal deformations of general relativity, and similar effects are also expected to occur in teleparallel gravity. Here, we study nonlocal deformations of teleparallel gravity along with its cosmological solutions. We observe that nonlocal teleparallel gravity (like nonlocal general relativity) is consistent with the present cosmological data obtained by SNe Ia + BAO + CC + [Formula: see text] observations. Along this track, future experiments probing nonlocal effects could be used to test whether general relativity or teleparallel gravity gives the most consistent picture of gravitational interaction.
Nonlocal teleparallel cosmology
Energy Technology Data Exchange (ETDEWEB)
Bahamonde, Sebastian [University College London, Department of Mathematics, London (United Kingdom); Capozziello, Salvatore [Universita di Napoli ' ' Federico II' ' , Dipartimento di Fisica ' ' E. Pancini' ' , Naples (Italy); Gran Sasso Science Institute, L' Aquila (Italy); Compl. Univ. di Monte S. Angelo, Naples (Italy); INFN, Napoli (Italy); Faizal, Mir [University of British Columbia - Okanagan, Irving K. Barber School of Arts and Sciences, Kelowna, BC (Canada); University of Lethbridge, Department of Physics and Astronomy, Lethbridge, AB (Canada); Nunes, Rafael C. [Universidade Federal de Juiz de Fora, Departamento de Fisica, Juiz de Fora, MG (Brazil)
2017-09-15
Even though it is not possible to differentiate general relativity from teleparallel gravity using classical experiments, it could be possible to discriminate between them by quantum gravitational effects. These effects have motivated the introduction of nonlocal deformations of general relativity, and similar effects are also expected to occur in teleparallel gravity. Here, we study nonlocal deformations of teleparallel gravity along with its cosmological solutions. We observe that nonlocal teleparallel gravity (like nonlocal general relativity) is consistent with the present cosmological data obtained by SNe Ia + BAO + CC + H{sub 0} observations. Along this track, future experiments probing nonlocal effects could be used to test whether general relativity or teleparallel gravity gives the most consistent picture of gravitational interaction. (orig.)
Canonical Information Analysis
DEFF Research Database (Denmark)
Vestergaard, Jacob Schack; Nielsen, Allan Aasbjerg
2015-01-01
is replaced by the information theoretical, entropy based measure mutual information, which is a much more general measure of association. We make canonical information analysis feasible for large sample problems, including for example multispectral images, due to the use of a fast kernel density estimator......Canonical correlation analysis is an established multivariate statistical method in which correlation between linear combinations of multivariate sets of variables is maximized. In canonical information analysis introduced here, linear correlation as a measure of association between variables...... for entropy estimation. Canonical information analysis is applied successfully to (1) simple simulated data to illustrate the basic idea and evaluate performance, (2) fusion of weather radar and optical geostationary satellite data in a situation with heavy precipitation, and (3) change detection in optical...
The Higgs boson and cosmology.
Shaposhnikov, Mikhail
2015-01-13
I will discuss how the Higgs field of the Standard Model may have played an important role in cosmology, leading to the homogeneity, isotropy and flatness of the Universe; producing the quantum fluctuations that seed structure formation; triggering the radiation-dominated era of the hot Big Bang; and contributing to the processes of baryogenesis and dark matter production.
Shaposhnikov, Mikhail
2015-01-01
I will discuss how the Higgs field of the Standard Model may have played an important role in cosmology, leading to the homogeneity, isotropy and flatness of the Universe; producing the quantum fluctuations that seed structure formation; triggering the radiation-dominated era of the hot Big Bang; and contributing to the processes of baryogenesis and dark matter production.
Classifying Linear Canonical Relations
Lorand, Jonathan
2015-01-01
In this Master's thesis, we consider the problem of classifying, up to conjugation by linear symplectomorphisms, linear canonical relations (lagrangian correspondences) from a finite-dimensional symplectic vector space to itself. We give an elementary introduction to the theory of linear canonical relations and present partial results toward the classification problem. This exposition should be accessible to undergraduate students with a basic familiarity with linear algebra.
International Nuclear Information System (INIS)
Wesson, P.S.
1979-01-01
The Cosmological Principle states: the universe looks the same to all observers regardless of where they are located. To most astronomers today the Cosmological Principle means the universe looks the same to all observers because density of the galaxies is the same in all places. A new Cosmological Principle is proposed. It is called the Dimensional Cosmological Principle. It uses the properties of matter in the universe: density (rho), pressure (p), and mass (m) within some region of space of length (l). The laws of physics require incorporation of constants for gravity (G) and the speed of light (C). After combining the six parameters into dimensionless numbers, the best choices are: 8πGl 2 rho/c 2 , 8πGl 2 rho/c 4 , and 2 Gm/c 2 l (the Schwarzchild factor). The Dimensional Cosmological Principal came about because old ideas conflicted with the rapidly-growing body of observational evidence indicating that galaxies in the universe have a clumpy rather than uniform distribution
Multi-dimensional cosmology and GUP
Energy Technology Data Exchange (ETDEWEB)
Zeynali, K.; Motavalli, H. [Department of Theoretical Physics and Astrophysics, University of Tabriz, 51666-16471, Tabriz (Iran, Islamic Republic of); Darabi, F., E-mail: k.zeinali@arums.ac.ir, E-mail: f.darabi@azaruniv.edu, E-mail: motavalli@tabrizu.ac.ir [Department of Physics, Azarbaijan Shahid Madani University, 53714-161, Tabriz (Iran, Islamic Republic of)
2012-12-01
We consider a multidimensional cosmological model with FRW type metric having 4-dimensional space-time and d-dimensional Ricci-flat internal space sectors with a higher dimensional cosmological constant. We study the classical cosmology in commutative and GUP cases and obtain the corresponding exact solutions for negative and positive cosmological constants. It is shown that for negative cosmological constant, the commutative and GUP cases result in finite size universes with smaller size and longer ages, and larger size and shorter age, respectively. For positive cosmological constant, the commutative and GUP cases result in infinite size universes having late time accelerating behavior in good agreement with current observations. The accelerating phase starts in the GUP case sooner than the commutative case. In both commutative and GUP cases, and for both negative and positive cosmological constants, the internal space is stabilized to the sub-Planck size, at least within the present age of the universe. Then, we study the quantum cosmology by deriving the Wheeler-DeWitt equation, and obtain the exact solutions in the commutative case and the perturbative solutions in GUP case, to first order in the GUP small parameter, for both negative and positive cosmological constants. It is shown that good correspondence exists between the classical and quantum solutions.
Multi-dimensional cosmology and GUP
International Nuclear Information System (INIS)
Zeynali, K.; Motavalli, H.; Darabi, F.
2012-01-01
We consider a multidimensional cosmological model with FRW type metric having 4-dimensional space-time and d-dimensional Ricci-flat internal space sectors with a higher dimensional cosmological constant. We study the classical cosmology in commutative and GUP cases and obtain the corresponding exact solutions for negative and positive cosmological constants. It is shown that for negative cosmological constant, the commutative and GUP cases result in finite size universes with smaller size and longer ages, and larger size and shorter age, respectively. For positive cosmological constant, the commutative and GUP cases result in infinite size universes having late time accelerating behavior in good agreement with current observations. The accelerating phase starts in the GUP case sooner than the commutative case. In both commutative and GUP cases, and for both negative and positive cosmological constants, the internal space is stabilized to the sub-Planck size, at least within the present age of the universe. Then, we study the quantum cosmology by deriving the Wheeler-DeWitt equation, and obtain the exact solutions in the commutative case and the perturbative solutions in GUP case, to first order in the GUP small parameter, for both negative and positive cosmological constants. It is shown that good correspondence exists between the classical and quantum solutions
Energy Technology Data Exchange (ETDEWEB)
Zuniga Segundo, A. [Instituto Politecnico Nacional, Mexico, D.F. (Mexico)
2001-10-01
In this work we introduce squeezed states with real and complex squeezing parameters directly obtained in the coherent-representation of the harmonic oscillator in quantum phase space. By means of the Fourier transform, we recover the usual coordinate states and compare these states with those obtained by another method in the coordinate representation. In addition we also describe numerically its time evolution in quantum phase space and the variances Q and P. [Spanish] En este trabajo presentamos estados comprimidos con parametros de compresion reales y complejos, obtenidos directamente en la representacion de estado coherente del oscilador armonico en el espacio fase cuantico. Por medio de una transformada de Fourier recuperamos los estados en la representacion de coordenadas y los comparamos con aquellos obtenidos por otro metodo. Ademas describimos numericamente sus evoluciones temporales en el espacio fase cuantico y calculamos las varianzas de Q y P.
Sanders, Robert H
2016-01-01
The advent of sensitive high-resolution observations of the cosmic microwave background radiation and their successful interpretation in terms of the standard cosmological model has led to great confidence in this model's reality. The prevailing attitude is that we now understand the Universe and need only work out the details. In this book, Sanders traces the development and successes of Lambda-CDM, and argues that this triumphalism may be premature. The model's two major components, dark energy and dark matter, have the character of the pre-twentieth-century luminiferous aether. While there is astronomical evidence for these hypothetical fluids, their enigmatic properties call into question our assumptions of the universality of locally determined physical law. Sanders explains how modified Newtonian dynamics (MOND) is a significant challenge for cold dark matter. Overall, the message is hopeful: the field of cosmology has not become frozen, and there is much fundamental work ahead for tomorrow's cosmologis...
Relations between canonical and non-canonical inflation
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Gwyn, Rhiannon [Max-Planck-Institut fuer Gravitationsphysik (Albert-Einstein-Institut), Potsdam (Germany); Rummel, Markus [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Westphal, Alexander [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany). Theory Group
2012-12-15
We look for potential observational degeneracies between canonical and non-canonical models of inflation of a single field {phi}. Non-canonical inflationary models are characterized by higher than linear powers of the standard kinetic term X in the effective Lagrangian p(X,{phi}) and arise for instance in the context of the Dirac-Born-Infeld (DBI) action in string theory. An on-shell transformation is introduced that transforms non-canonical inflationary theories to theories with a canonical kinetic term. The 2-point function observables of the original non-canonical theory and its canonical transform are found to match in the case of DBI inflation.
International Nuclear Information System (INIS)
Kinnebrock, Werner
2011-01-01
The past century changed the classical, scientific way of view enormously. The quantum theory broke with the imagination of continuity of all dynamical processes and gave space to completely new, nearly revolutionary approaches of thinking. Einstein's relativity theory put the absoluteness of time and space as well as the general validity of the Euclidean geometry in question. The absolute calculability, as it was formulated by Laplace, was by the influence of chaos theory proven as illusion. Computers made by the Mandelbrot set the presentation of new esthetic and never seen structures. Hilbert's century program of a complete formalization of mathematics failed because of the famous law of Goedel. It is the demand of this book to present all these theories and conclusions easily understandably and entertainingly.
International Nuclear Information System (INIS)
Dickau, Jonathan J.
2009-01-01
The use of fractals and fractal-like forms to describe or model the universe has had a long and varied history, which begins long before the word fractal was actually coined. Since the introduction of mathematical rigor to the subject of fractals, by Mandelbrot and others, there have been numerous cosmological theories and analyses of astronomical observations which suggest that the universe exhibits fractality or is by nature fractal. In recent years, the term fractal cosmology has come into usage, as a description for those theories and methods of analysis whereby a fractal nature of the cosmos is shown.
Knot theory and a physical state of quantum gravity
International Nuclear Information System (INIS)
Liko, Tomas; Kauffman, Louis H
2006-01-01
We discuss the theory of knots, and describe how knot invariants arise naturally in gravitational physics. The focus of this review is to delineate the relationship between knot theory and the loop representation of non-perturbative canonical quantum general relativity (loop quantum gravity). This leads naturally to a discussion of the Kodama wavefunction, a state which is conjectured to be the ground state of the gravitational field with positive cosmological constant. This review can serve as a self-contained introduction to loop quantum gravity and related areas. Our intent is to make the paper accessible to a wider audience that may include topologists, knot theorists, and other persons innocent of the physical background to this approach to quantum gravity. (topical review)
Enqvist, K
2012-01-01
The very basics of cosmological inflation are discussed. We derive the equations of motion for the inflaton field, introduce the slow-roll parameters, and present the computation of the inflationary perturbations and their connection to the temperature fluctuations of the cosmic microwave background.
Ellis, G F R
1993-01-01
Many topics were covered in the submitted papers, showing much life in this subject at present. They ranged from conventional calculations in specific cosmological models to provocatively speculative work. Space and time restrictions required selecting from them, for summarisation here; the book of Abstracts should be consulted for a full overview.
International Nuclear Information System (INIS)
Chow, Nathan; Khoury, Justin
2009-01-01
We study the cosmology of a galileon scalar-tensor theory, obtained by covariantizing the decoupling Lagrangian of the Dvali-Gabadadze-Poratti (DGP) model. Despite being local in 3+1 dimensions, the resulting cosmological evolution is remarkably similar to that of the full 4+1-dimensional DGP framework, both for the expansion history and the evolution of density perturbations. As in the DGP model, the covariant galileon theory yields two branches of solutions, depending on the sign of the galileon velocity. Perturbations are stable on one branch and ghostlike on the other. An interesting effect uncovered in our analysis is a cosmological version of the Vainshtein screening mechanism: at early times, the galileon dynamics are dominated by self-interaction terms, resulting in its energy density being suppressed compared to matter or radiation; once the matter density has redshifted sufficiently, the galileon becomes an important component of the energy density and contributes to dark energy. We estimate conservatively that the resulting expansion history is consistent with the observed late-time cosmology, provided that the scale of modification satisfies r c > or approx. 15 Gpc.
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Goernitz, T. [Inst. fuer Didaktik der Physik, J.W.Goethe-Univ., Frankfurt/Main (Germany)
2007-07-01
It is common sense between physicists that in the beginning the cosmos is in a narrow relationship to quantum phenomena. Because of the universal validity of quantum theory this relation remains significant in the whole cosmic evolution. Whereas a classical approach is sufficient for the description of many phenomena it is no more useful at last for the case of the ground state of a system. This holds also for the cosmos. The black holes are that part of physics where quantum theory and gravitational theory come into close contact. There a Gedankenexperiment becomes possible that clarifies the fundamental role of abstract quantum information. We give it a new name (Protyposis) because it must be imagined without emitter, receiver and moreover without any concrete meaning. This meaning-free abstract quantum information is defined by means of black holes and cosmology. Protyposis enables a new conception for ''matter'' and makes possible to overcome the problems of the ''Lego-world-view'', which result from the attempt to find the ''simple and therefore basic concepts'' in the range of spatial smallness. Matter can be understood now as ''formed and condensed quantum information''. But on a first view it is nothing to see from its character of being information, as like matter does not appear as ''pure motion'', what it is also because of E=mc{sup 2}. (orig.)
Hoehn, Jessica R.; Finkelstein, Noah D.
2018-06-01
As part of a research study on student reasoning in quantum mechanics, we examine students' use of ontologies, or the way students' categorically organize entities they are reasoning about. In analyzing three episodes of focus group discussions with modern physics students, we present evidence of the dynamic nature of ontologies, and refine prior theoretical frameworks for thinking about dynamic ontologies. We find that in a given reasoning episode ontologies can be dynamic in construction (referring to when the reasoner constructs the ontologies) or application (referring to which ontologies are applied in a given reasoning episode). In our data, we see instances of students flexibly switching back and forth between parallel stable structures as well as constructing and negotiating new ontologies in the moment. Methodologically, we use a collective conceptual blending framework as an analytic tool for capturing student reasoning in groups. In this research, we value the messiness of student reasoning and argue that reasoning in a tentative manner can be productive for students learning quantum mechanics. As such, we shift away from a binary view of student learning which sees students as either having the correct answer or not.
Svenson, Eric Johan
Participants on the Invincible America Assembly in Fairfield, Iowa, and neighboring Maharishi Vedic City, Iowa, practicing Maharishi Transcendental Meditation(TM) (TM) and the TM-Sidhi(TM) programs in large groups, submitted written experiences that they had had during, and in some cases shortly after, their daily practice of the TM and TM-Sidhi programs. Participants were instructed to include in their written experiences only what they observed and to leave out interpretation and analysis. These experiences were then read by the author and compared with principles and phenomena of modern physics, particularly with quantum theory, astrophysics, quantum cosmology, and string theory as well as defining characteristics of higher states of consciousness as described by Maharishi Vedic Science. In all cases, particular principles or phenomena of physics and qualities of higher states of consciousness appeared qualitatively quite similar to the content of the given experience. These experiences are presented in an Appendix, in which the corresponding principles and phenomena of physics are also presented. These physics "commentaries" on the experiences were written largely in layman's terms, without equations, and, in nearly every case, with clear reference to the corresponding sections of the experiences to which a given principle appears to relate. An abundance of similarities were apparent between the subjective experiences during meditation and principles of modern physics. A theoretic framework for understanding these rich similarities may begin with Maharishi's theory of higher states of consciousness provided herein. We conclude that the consistency and richness of detail found in these abundant similarities warrants the further pursuit and development of such a framework.
International Nuclear Information System (INIS)
Desert, F.-Xavier
2004-01-01
After an introduction comprising some definitions, an historical overview, and a discussion of the paradoxical Universe, this course proposes a presentation of fundamental notions and theories, i.e. the restrained relativity and the universal gravitation. The next part addresses the general relativity with the following notions: space-time metrics and principle of generalised covariance, basics of tensor analysis, geodesics, energy-pulse tensor, curvature, Einstein equations, Newtonian limit, Schwarzschild metrics, gravitational waves, gravitational redshift. The next part addresses the standard cosmology with the Friedmann-Robertson-Walker metrics and the Friedmann-Lemaitre equations of the evolution of the Universe. The Universe expansion is then addressed: distances and horizons, Hubble law, determination of the Hubble constant. The next chapter deals with the constituents of the Universe: light matter, baryonic dark matter, black matter, supernovae, Universe acceleration and black energy. Then comes the nuclear evolution of the Universe: thermodynamics of the primordial Universe, the matter-antimatter asymmetry, from quarks to atoms, cosmic abundance, neutron cosmological background, matter-radiation equality, cosmo-chronology or the age of the Universe. The next chapter addresses the cosmological background at 3 K: sky electromagnetic spectrum, measurement of CMB anisotropies, interpretation of anisotropies, growth of perturbations. The last chapter addresses the quantum field theory and inflation: paradoxes of the standard Big Bang, the simple inflation, noticeable consequences
Path integrals for arbitrary canonical transformations
International Nuclear Information System (INIS)
Oliveira, L.A.R. de.
1980-01-01
Some aspects of the path integral formulation of quantum mechanics are studied. This formalism is generalized to arbitrary canonical transformations, by means of an association between path integral probalility amplitudes and classical generators of transformations, analogous to the usual Hamiltonian time development phase space expression. Such association turns out to be equivalent to the Weyl quantization rule, and it is also shown that this formalism furnishes a path integral representation for a Lie algebra of a given set of classical generators. Some physical considerations about the path integral quantization procedure and about the relationship between classical and quantum dynamical structures are also discussed. (Author) [pt
Canonical formulation of general-relativistic theories
International Nuclear Information System (INIS)
Bergmann, P.G.
1987-01-01
With the birth of quantum field theory in the late twenties physicists decided that nature could not be half classical and half quantum, and that the gravitational field ought to be quanticized, just as the electromagnetic field had been. One could accept the group of differomorphisms as a fundamental characteristic of general relativity (and indeed of all general-relativistic theories), and proceed to construct a quantum field-theory that was adapted to that group. Quantization would be attempted by way of a Hamiltonian formulation of the (classical) theory, and quantum commutation relations be patterned after the Poisson brackets arising in that formulation. This program is usually called the canonical quantization program, whereas the weak-field approach is known as covariant quantization. The first steps, conceived entirely within the framework of the classical theory, turned out to be beset with technical and conceptual difficulties, which today are essentially resolved. In this paper the author traces out these initial steps
Cosmological evolution as squeezing: a toy model for group field cosmology
Adjei, Eugene; Gielen, Steffen; Wieland, Wolfgang
2018-05-01
We present a simple model of quantum cosmology based on the group field theory (GFT) approach to quantum gravity. The model is formulated on a subspace of the GFT Fock space for the quanta of geometry, with a fixed volume per quantum. In this Hilbert space, cosmological expansion corresponds to the generation of new quanta. Our main insight is that the evolution of a flat Friedmann–Lemaître–Robertson–Walker universe with a massless scalar field can be described on this Hilbert space as squeezing, familiar from quantum optics. As in GFT cosmology, we find that the three-volume satisfies an effective Friedmann equation similar to the one of loop quantum cosmology, connecting the classical contracting and expanding solutions by a quantum bounce. The only free parameter in the model is identified with Newton’s constant. We also comment on the possible topological interpretation of our squeezed states. This paper can serve as an introduction into the main ideas of GFT cosmology without requiring the full GFT formalism; our results can also motivate new developments in GFT and its cosmological application.
Unified correspondence and canonicity
Zhao, Z.
2018-01-01
Correspondence theory originally arises as the study of the relation between modal formulas and first-order formulas interpreted over Kripke frames. We say that a modal formula and a first-order formula correspond to each other if they are valid on the same class of Kripke frames. Canonicity theory
Luo, Chongliang; Liu, Jin; Dey, Dipak K; Chen, Kun
2016-07-01
In many fields, multi-view datasets, measuring multiple distinct but interrelated sets of characteristics on the same set of subjects, together with data on certain outcomes or phenotypes, are routinely collected. The objective in such a problem is often two-fold: both to explore the association structures of multiple sets of measurements and to develop a parsimonious model for predicting the future outcomes. We study a unified canonical variate regression framework to tackle the two problems simultaneously. The proposed criterion integrates multiple canonical correlation analysis with predictive modeling, balancing between the association strength of the canonical variates and their joint predictive power on the outcomes. Moreover, the proposed criterion seeks multiple sets of canonical variates simultaneously to enable the examination of their joint effects on the outcomes, and is able to handle multivariate and non-Gaussian outcomes. An efficient algorithm based on variable splitting and Lagrangian multipliers is proposed. Simulation studies show the superior performance of the proposed approach. We demonstrate the effectiveness of the proposed approach in an [Formula: see text] intercross mice study and an alcohol dependence study. © The Author 2016. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.
Deviations from Wick's theorem in the canonical ensemble
Schönhammer, K.
2017-07-01
Wick's theorem for the expectation values of products of field operators for a system of noninteracting fermions or bosons plays an important role in the perturbative approach to the quantum many-body problem. A finite-temperature version holds in the framework of the grand canonical ensemble, but not for the canonical ensemble appropriate for systems with fixed particle number such as ultracold quantum gases in optical lattices. Here we present formulas for expectation values of products of field operators in the canonical ensemble using a method in the spirit of Gaudin's proof of Wick's theorem for the grand canonical case. The deviations from Wick's theorem are examined quantitatively for two simple models of noninteracting fermions.
International Nuclear Information System (INIS)
Lachieze-Rey, Marc
2005-01-01
After having recalled that the Platonist and Aristotelian views were the basis of cosmology during the Antiquity and the Middle-Age, the author indicates that these views have been put into question again by Copernicus, Giordano Bruno, Kepler, Galileo and others whose works resulted in Newton physics. The author then follows and comments this history with the emergence of contemporary physics (relativistic and quantum physics) and new concepts for matter, space and time, light, energy, and the Universe with a relativistic cosmology. After having commented these last issues, the author evokes how new results confirmed big-bang models. He also outlines problems to be solved or addressed: observations related to the hidden mass, issue of unification, technological issues to obtain information about what went on more than 13 billions years ago. The author comments the issue of other universes, and issues regarding science, metaphysics and religion raised by these theoretical developments. He also comments the emergence of new physics (supersymmetry, quantum gravity)
Grant, E.; Murdin, P.
2000-11-01
During the early Middle Ages (ca 500 to ca 1130) scholars with an interest in cosmology had little useful and dependable literature. They relied heavily on a partial Latin translation of PLATO's Timaeus by Chalcidius (4th century AD), and on a series of encyclopedic treatises associated with the names of Pliny the Elder (ca AD 23-79), Seneca (4 BC-AD 65), Macrobius (fl 5th century AD), Martianus ...
International Nuclear Information System (INIS)
Partridge, R.B.
1977-01-01
Some sixty years after the development of relativistic cosmology by Einstein and his colleagues, observations are finally beginning to have an important impact on our views of the Universe. The available evidence seems to support one of the simplest cosmological models, the hot Big Bang model. The aim of this paper is to assess the observational support for certain assumptions underlying the hot Big Bang model. These are that the Universe is isobaric and homogeneous on a large scale; that it is expanding from an initial state of high density and temperature; and that the proper theory to describe the dynamics of the Universe is unmodified General Relativity. The properties of the cosmic microwave background radiation and recent observations of the abundance of light elements, in particular, support these assumptions. Also examined here are the data bearing on the related questions of the geometry and the future of the Universe (is it ever-expanding, or fated to recollapse). Finally, some difficulties and faults of the standard model are discussed, particularly various aspects of the 'initial condition' problem. It appears that the simplest Big Bang cosmological model calls for a highly specific set of initial conditions to produce the presently observed properties of the Universe. (Auth.)
the Universe About Cosmology Planck Satellite Launched Cosmology Videos Professor George Smoot's group conducts research on the early universe (cosmology) using the Cosmic Microwave Background radiation (CMB science goals regarding cosmology. George Smoot named Director of Korean Cosmology Institute The GRB
Canonical transformations method in the potential scattering problem
International Nuclear Information System (INIS)
Pavlenko, Yu.G.
1984-01-01
Canonical formalism of the first order is used in the present paper to solve the problem of scattering and other problems of quantum mechanics. The theory of canonical transformations (CT) being the basis of hamiltonian approach permits to develop several methods of integration being beyond the scope of the standard theory of perturbations. In this case it is essential for numerical counting that the theory permits to obtain algorithm for plotting highest approximations
The canonical and grand canonical models for nuclear ...
Indian Academy of Sciences (India)
Many observables seen in intermediate energy heavy-ion collisions can be explained on the basis of statistical equilibrium. Calculations based on statistical equilibrium can be implemented in microcanonical ensemble, canonical ensemble or grand canonical ensemble. This paper deals with calculations with canonical ...
Yurenko, Yevgen P; Zhurakivsky, Roman O; Samijlenko, Svitlana P; Hovorun, Dmytro M
2011-08-01
The aim of this work is to cast some light on the H-bonds in double-stranded DNA in its AI and BI forms. For this purpose, we have performed the MP2 and DFT quantum chemical calculations of the canonical nucleoside conformers, relative to the AI and BI DNA forms, and their Watson-Crick pairs, which were regarded as the simplest models of the double-stranded DNA. Based on the atoms-in-molecules analysis (AIM), five types of the CH···O hydrogen bonds, involving bases and sugar, were detected numerically from 1 to 3 per a conformer: C2'H···O5', C1'H···O2, C6H···O5', C8H···O5', and C6H···O4'. The energy values of H-bonds occupy the range of 2.3-5.6 kcal/mol, surely exceeding the kT value (0.62 kcal/mol). The nucleoside CH···O hydrogen bonds appeared to "survive" turns of bases against the sugar, sometimes in rather large ranges of the angle values, pertinent to certain conformations, which points out to the source of the DNA lability, necessary for the conformational adaptation in processes of its functioning. The calculation of the interactions in the dA·T nucleoside pair gives evidence, that additionally to the N6H···O4 and N1···N3H canonical H-bonds, between the bases adenine and thymine the third one (C2H···O2) is formed, which, though being rather weak (about 1 kcal/mol), satisfies the AIM criteria of H-bonding and may be classified as a true H-bond. The total energy of all the CH···O nontraditional intramolecular H-bonds in DNA nucleoside pairs appeared to be commensurable with the energy of H-bonds between the bases in Watson-Crick pairs, which implies their possible important role in the DNA shaping.
Quaternion Linear Canonical Transform Application
Bahri, Mawardi
2015-01-01
Quaternion linear canonical transform (QLCT) is a generalization of the classical linear canonical transfom (LCT) using quaternion algebra. The focus of this paper is to introduce an application of the QLCT to study of generalized swept-frequency filter
Canonical transformations and generating functionals
Broer, L.J.F.; Kobussen, J.A.
1972-01-01
It is shown that canonical transformations for field variables in hamiltonian partial differential equations can be obtained from generating functionals in the same way as classical canonical transformations from generating functions. A simple proof of the relation between infinitesimal invariant
Wormholes and the cosmological constant problem.
Klebanov, I.
The author reviews the cosmological constant problem and the recently proposed wormhole mechanism for its solution. Summation over wormholes in the Euclidean path integral for gravity turns all the coupling parameters into dynamical variables, sampled from a probability distribution. A formal saddle point analysis results in a distribution with a sharp peak at the cosmological constant equal to zero, which appears to solve the cosmological constant problem. He discusses the instabilities of the gravitational Euclidean path integral and the difficulties with its interpretation. He presents an alternate formalism for baby universes, based on the "third quantization" of the Wheeler-De Witt equation. This approach is analyzed in a minisuperspace model for quantum gravity, where it reduces to simple quantum mechanics. Once again, the coupling parameters become dynamical. Unfortunately, the a priori probability distribution for the cosmological constant and other parameters is typically a smooth function, with no sharp peaks.
Canonical transformations of Kepler trajectories
International Nuclear Information System (INIS)
Mostowski, Jan
2010-01-01
In this paper, canonical transformations generated by constants of motion in the case of the Kepler problem are discussed. It is shown that canonical transformations generated by angular momentum are rotations of the trajectory. Particular attention is paid to canonical transformations generated by the Runge-Lenz vector. It is shown that these transformations change the eccentricity of the orbit. A method of obtaining elliptic trajectories from the circular ones with the help of canonical trajectories is discussed.
International Nuclear Information System (INIS)
Jones, K.R.W.
1995-01-01
We develop a nonlinear quantum theory of Newtonian gravity consistent with an objective interpretation of the wavefunction. Inspired by the ideas of Schroedinger, and Bell, we seek a dimensional reduction procedure to map complex wavefunctions in configuration space onto a family of observable fields in space-time. Consideration of quasi-classical conservation laws selects the reduced one-body quantities as the basis for an explicit quasi-classical coarse-graining. These we interpret as describing the objective reality of the laboratory. Thereafter, we examine what may stand in the role of the usual Copenhagen observer to localise this quantity against macroscopic dispersion. Only a tiny change is needed, via a generically attractive self-potential. A nonlinear treatment of gravitational self-energy is thus advanced. This term sets a scale for all wavepackets. The Newtonian cosmology is thus closed, without need of an external observer. Finally, the concept of quantisation is re-interpreted as a nonlinear eigenvalue problem. To illustrate, we exhibit an elementary family of gravitationally self-bound solitary waves. Contrasting this theory with its canonically quantised analogue, we find that the given interpretation is empirically distinguishable, in principle. This result encourages deeper study of nonlinear field theories as a testable alternative to canonically quantised gravity. (author). 46 refs., 5 figs
Contextuality in canonical systems of random variables
Dzhafarov, Ehtibar N.; Cervantes, Víctor H.; Kujala, Janne V.
2017-10-01
Random variables representing measurements, broadly understood to include any responses to any inputs, form a system in which each of them is uniquely identified by its content (that which it measures) and its context (the conditions under which it is recorded). Two random variables are jointly distributed if and only if they share a context. In a canonical representation of a system, all random variables are binary, and every content-sharing pair of random variables has a unique maximal coupling (the joint distribution imposed on them so that they coincide with maximal possible probability). The system is contextual if these maximal couplings are incompatible with the joint distributions of the context-sharing random variables. We propose to represent any system of measurements in a canonical form and to consider the system contextual if and only if its canonical representation is contextual. As an illustration, we establish a criterion for contextuality of the canonical system consisting of all dichotomizations of a single pair of content-sharing categorical random variables. This article is part of the themed issue `Second quantum revolution: foundational questions'.
Brandenberger, Robert H.
2008-01-01
String gas cosmology is a string theory-based approach to early universe cosmology which is based on making use of robust features of string theory such as the existence of new states and new symmetries. A first goal of string gas cosmology is to understand how string theory can effect the earliest moments of cosmology before the effective field theory approach which underlies standard and inflationary cosmology becomes valid. String gas cosmology may also provide an alternative to the curren...
Magnetohydrodynamic cosmologies
International Nuclear Information System (INIS)
Portugal, R.; Soares, I.D.
1991-01-01
We analyse a class of cosmological models in magnetohydrodynamic regime extending and completing the results of a previous paper. The material content of the models is a perfect fluid plus electromagnetic fields. The fluid is neutral in average but admits an electrical current which satisfies Ohm's law. All models fulfil the physical requirements of near equilibrium thermodynamics and can be favourably used as a more realistic description of the interior of a collapsing star in a magnetohydrodynamic regime with or without a magnetic field. (author)
Bardeen, J. M.
The last several years have seen a tremendous ferment of activity in astrophysical cosmology. Much of the theoretical impetus has come from particle physics theories of the early universe and candidates for dark matter, but what promise to be even more significant are improved direct observations of high z galaxies and intergalactic matter, deeper and more comprehensive redshift surveys, and the increasing power of computer simulations of the dynamical evolution of large scale structure. Upper limits on the anisotropy of the microwave background radiation are gradually getting tighter and constraining more severely theoretical scenarios for the evolution of the universe.
International Nuclear Information System (INIS)
Bardeen, J.M.
1986-01-01
The last several years have seen a tremendous ferment of activity in astrophysical cosmology. Much of the theoretical impetus has come from particle physics theories of the early universe and candidates for dark matter, but what promise to be even more significant are improved direct observations of high z galaxies and intergalactic matter, deeper and more comprehensive redshift surveys, and the increasing power of computer simulations of the dynamical evolution of large scale structure. Upper limits on the anisotropy of the microwave background radiation are gradually getting tighter and constraining more severely theoretical scenarios for the evolution of the universe. 47 refs
Boeyens, Jan CA
2010-01-01
The composition of the most remote objects brought into view by the Hubble telescope can no longer be reconciled with the nucleogenesis of standard cosmology and the alternative explanation, in terms of the LAMBDA-Cold-Dark-Matter model, has no recognizable chemical basis. A more rational scheme, based on the chemistry and periodicity of atomic matter, opens up an exciting new interpretation of the cosmos in terms of projective geometry and general relativity. The response of atomic structure to environmental pressure predicts non-Doppler cosmical redshifts and equilibrium nucleogenesis by alp
Religion, theology and cosmology
Directory of Open Access Journals (Sweden)
John T. Fitzgerald
2013-10-01
Full Text Available Cosmology is one of the predominant research areas of the contemporary world. Advances in modern cosmology have prompted renewed interest in the intersections between religion, theology and cosmology. This article, which is intended as a brief introduction to the series of studies on theological cosmology in this journal, identifies three general areas of theological interest stemming from the modern scientific study of cosmology: contemporary theology and ethics; cosmology and world religions; and ancient cosmologies. These intersections raise important questions about the relationship of religion and cosmology, which has recently been addressed by William Scott Green and is the focus of the final portion of the article.
Canonical group quantization and boundary conditions
International Nuclear Information System (INIS)
Jung, Florian
2012-01-01
In the present thesis, we study quantization of classical systems with non-trivial phase spaces using the group-theoretical quantization technique proposed by Isham. Our main goal is a better understanding of global and topological aspects of quantum theory. In practice, the group-theoretical approach enables direct quantization of systems subject to constraints and boundary conditions in a natural and physically transparent manner -- cases for which the canonical quantization method of Dirac fails. First, we provide a clarification of the quantization formalism. In contrast to prior treatments, we introduce a sharp distinction between the two group structures that are involved and explain their physical meaning. The benefit is a consistent and conceptually much clearer construction of the Canonical Group. In particular, we shed light upon the 'pathological' case for which the Canonical Group must be defined via a central Lie algebra extension and emphasise the role of the central extension in general. In addition, we study direct quantization of a particle restricted to a half-line with 'hard wall' boundary condition. Despite the apparent simplicity of this example, we show that a naive quantization attempt based on the cotangent bundle over the half-line as classical phase space leads to an incomplete quantum theory; the reflection which is a characteristic aspect of the 'hard wall' is not reproduced. Instead, we propose a different phase space that realises the necessary boundary condition as a topological feature and demonstrate that quantization yields a suitable quantum theory for the half-line model. The insights gained in the present special case improve our understanding of the relation between classical and quantum theory and illustrate how contact interactions may be incorporated.
Canonical group quantization and boundary conditions
Energy Technology Data Exchange (ETDEWEB)
Jung, Florian
2012-07-16
In the present thesis, we study quantization of classical systems with non-trivial phase spaces using the group-theoretical quantization technique proposed by Isham. Our main goal is a better understanding of global and topological aspects of quantum theory. In practice, the group-theoretical approach enables direct quantization of systems subject to constraints and boundary conditions in a natural and physically transparent manner -- cases for which the canonical quantization method of Dirac fails. First, we provide a clarification of the quantization formalism. In contrast to prior treatments, we introduce a sharp distinction between the two group structures that are involved and explain their physical meaning. The benefit is a consistent and conceptually much clearer construction of the Canonical Group. In particular, we shed light upon the 'pathological' case for which the Canonical Group must be defined via a central Lie algebra extension and emphasise the role of the central extension in general. In addition, we study direct quantization of a particle restricted to a half-line with 'hard wall' boundary condition. Despite the apparent simplicity of this example, we show that a naive quantization attempt based on the cotangent bundle over the half-line as classical phase space leads to an incomplete quantum theory; the reflection which is a characteristic aspect of the 'hard wall' is not reproduced. Instead, we propose a different phase space that realises the necessary boundary condition as a topological feature and demonstrate that quantization yields a suitable quantum theory for the half-line model. The insights gained in the present special case improve our understanding of the relation between classical and quantum theory and illustrate how contact interactions may be incorporated.
Whose Canon? Culturalization versus Democratization
Directory of Open Access Journals (Sweden)
Erling Bjurström
2012-06-01
Full Text Available Current accounts – and particularly the critique – of canon formation are primarily based on some form of identity politics. In the 20th century a representational model of social identities replaced cultivation as the primary means to democratize the canons of the fine arts. In a parallel development, the discourse on canons has shifted its focus from processes of inclusion to those of exclusion. This shift corresponds, on the one hand, to the construction of so-called alternative canons or counter-canons, and, on the other hand, to attempts to restore the authority of canons considered to be in a state of crisis or decaying. Regardless of the democratic stance of these efforts, the construction of alternatives or the reestablishment of decaying canons does not seem to achieve their aims, since they break with the explicit and implicit rules of canon formation. Politically motivated attempts to revise or restore a specific canon make the workings of canon formation too visible, transparent and calculated, thereby breaking the spell of its imaginary character. Retracing the history of the canonization of the fine arts reveals that it was originally tied to the disembedding of artists and artworks from social and worldly affairs, whereas debates about canons of the fine arts since the end of the 20th century are heavily dependent on their social, cultural and historical reembedding. The latter has the character of disenchantment, but has also fettered the canon debate in notions of “our” versus “their” culture. However, by emphasizing the dedifferentiation of contemporary processes of culturalization, the advancing canonization of popular culture seems to be able to break with identity politics that foster notions of “our” culture in the present thinking on canons, and push it in a more transgressive, syncretic or hybrid direction.
International Nuclear Information System (INIS)
Chimento, L P; Forte, M; Devecchi, F P; Kremer, G M; Ribas, M O; Samojeden, L L
2011-01-01
In this work we review if fermionic sources could be responsible for accelerated periods during the evolution of a FRW universe. In a first attempt, besides the fermionic source, a matter constituent would answer for the decelerated periods. The coupled differential equations that emerge from the field equations are integrated numerically. The self-interaction potential of the fermionic field is considered as a function of the scalar and pseudo-scalar invariants. It is shown that the fermionic field could behave like an inflaton field in the early universe, giving place to a transition to a matter dominated (decelerated) period. In a second formulation we turn our attention to analytical results, specifically using the idea of form-invariance transformations. These transformations can be used for obtaining accelerated cosmologies starting with conventional cosmological models. Here we reconsider the scalar field case and extend the discussion to fermionic fields. Finally we investigate the role of a Dirac field in a Brans-Dicke (BD) context. The results show that this source, in combination with the BD scalar, promote a final eternal accelerated era, after a matter dominated period.
Quantum mechanics with quantum time
International Nuclear Information System (INIS)
Kapuscik, E.
1984-01-01
Using a non-canonical Lie structure of classical mechanics a new algebra of quantum mechanical observables is constructed. The new algebra, in addition to the notion of classical time, makes it possible to introduce the notion of quantum time. A new type of uncertainty relation is derived. (author)
The Future of Theoretical Physics and Cosmology
Gibbons, G. W.; Shellard, E. P. S.; Rankin, S. J.
2009-08-01
Preface; List of contributors; 1. Introduction; Part I. Popular Symposium: 2. Our complex cosmos and its future Martin J. Rees; 3. Theories of everything and Hawking's wave function of the Universe James B. Hartle; 4. The problem of space-time singularities: implications for quantum gravity? Roger Penrose; 5. Warping spacetime Kip Thorne; 6. 60 years in a nutshell Stephen W. Hawking; Part II. Spacetime Singularities: 7. Cosmological perturbations and singularities George F. R. Ellis; 8. The quantum physics of chronology protection Matt Visser; 9. Energy dominance and the Hawking-Ellis vacuum conservation theorem Brandon Carter; 10. On the instability of extra space dimensions Roger Penrose; Part III. Black Holes: 11. Black hole uniqueness and the inner horizon stability problem Werner Israel; 12. Black holes in the real universe and their prospects as probes of relativistic gravity Martin J. Rees; 13. Primordial black holes Bernard Carr; 14. Black hole pair creation Simon F. Ross; 15. Black holes as accelerators Steven Giddings; Part IV. Hawking Radiation: 16. Black holes and string theory Malcolm Perry; 17. M theory and black hole quantum mechanics Joe Polchinski; 18. Playing with black strings Gary Horowitz; 19. Twenty years of debate with Stephen Leonard Susskind; Part V. Quantum Gravity: 20. Euclidean quantum gravity: the view from 2002 Gary Gibbons; 21. Zeta functions, anomalies and stable branes Ian Moss; 22. Some reflections on the status of conventional quantum theory when applied to quantum gravity Chris Isham; 23. Quantum geometry and its ramifications Abhay Ashtekar; 24. Topology change in quantum gravity Fay Dowker; Part VI. M Theory and Beyond: 25. The past and future of string theory Edward Witten; 26. String theory David Gross; 27. A brief description of string theory Michael Green; 28. The story of M Paul Townsend; 29. Gauged supergravity and holographic field theory Nick Warner; 30. 57 varieties in a NUTshell Chris Pope; Part VII. de Sitter Space
Scalar-tensor cosmology with cosmological constant
International Nuclear Information System (INIS)
Maslanka, K.
1983-01-01
The equations of scalar-tensor theory of gravitation with cosmological constant in the case of homogeneous and isotropic cosmological model can be reduced to dynamical system of three differential equations with unknown functions H=R/R, THETA=phi/phi, S=e/phi. When new variables are introduced the system becomes more symmetrical and cosmological solutions R(t), phi(t), e(t) are found. It is shown that when cosmological constant is introduced large class of solutions which depend also on Dicke-Brans parameter can be obtained. Investigations of these solutions give general limits for cosmological constant and mean density of matter in plane model. (author)
Mahootian, F.
2009-12-01
The rapid convergence of advancing sensor technology, computational power, and knowledge discovery techniques over the past decade has brought unprecedented volumes of astronomical data together with unprecedented capabilities of data assimilation and analysis. A key result is that a new, data-driven "observational-inductive'' framework for scientific inquiry is taking shape and proving viable. The anticipated rise in data flow and processing power will have profound effects, e.g., confirmations and disconfirmations of existing theoretical claims both for and against the big bang model. But beyond enabling new discoveries can new data-driven frameworks of scientific inquiry reshape the epistemic ideals of science? The history of physics offers a comparison. The Bohr-Einstein debate over the "completeness'' of quantum mechanics centered on a question of ideals: what counts as science? We briefly examine lessons from that episode and pose questions about their applicability to cosmology. If the history of 20th century physics is any indication, the abandonment of absolutes (e.g., space, time, simultaneity, continuity, determinacy) can produce fundamental changes in understanding. The classical ideal of science, operative in both physics and cosmology, descends from the European Enlightenment. This ideal has for over 200 years guided science to seek the ultimate order of nature, to pursue the absolute theory, the "theory of everything.'' But now that we have new models of scientific inquiry powered by new technologies and driven more by data than by theory, it is time, finally, to relinquish dreams of a "final'' theory.
CERN. Geneva
2014-01-01
We discuss a corpuscular resolution of inflation. In our treatment, the geometric background is viewed as a composite entity, a type of a coherent state, of the constituent gravitons and inflatons. We show that this picture accounts for all the known semi-classical results, but more importantly predicts new quantum effects that are unaccounted neither by standard loop correction nor by known semi-classical non-perturbative effects. These new effects have important consequences. For example, they place an upper bound on the duration of inflation, which is in conflict with the possibility of self-reproduction and eternal inflation. We discuss various implications of these new quantum phenomena.
Krioukov, Dmitri; Kitsak, Maksim; Sinkovits, Robert S; Rideout, David; Meyer, David; Boguñá, Marián
2012-01-01
Prediction and control of the dynamics of complex networks is a central problem in network science. Structural and dynamical similarities of different real networks suggest that some universal laws might accurately describe the dynamics of these networks, albeit the nature and common origin of such laws remain elusive. Here we show that the causal network representing the large-scale structure of spacetime in our accelerating universe is a power-law graph with strong clustering, similar to many complex networks such as the Internet, social, or biological networks. We prove that this structural similarity is a consequence of the asymptotic equivalence between the large-scale growth dynamics of complex networks and causal networks. This equivalence suggests that unexpectedly similar laws govern the dynamics of complex networks and spacetime in the universe, with implications to network science and cosmology.
Narlikar, Jayant Vishnu
2002-01-01
The third edition of this successful textbook is fully updated and includes important recent developments in cosmology. It begins with an introduction to cosmology and general relativity, and goes on to cover the mathematical models of standard cosmology. The physical aspects of cosmology, including primordial nucleosynthesis, the astroparticle physics of inflation, and the current ideas on structure formation are discussed. Alternative models of cosmology are reviewed, including the model of Quasi-Steady State Cosmology, which has recently been proposed as an alternative to Big Bang Cosmology.
Generalized Canonical Time Warping.
Zhou, Feng; De la Torre, Fernando
2016-02-01
Temporal alignment of human motion has been of recent interest due to its applications in animation, tele-rehabilitation and activity recognition. This paper presents generalized canonical time warping (GCTW), an extension of dynamic time warping (DTW) and canonical correlation analysis (CCA) for temporally aligning multi-modal sequences from multiple subjects performing similar activities. GCTW extends previous work on DTW and CCA in several ways: (1) it combines CCA with DTW to align multi-modal data (e.g., video and motion capture data); (2) it extends DTW by using a linear combination of monotonic functions to represent the warping path, providing a more flexible temporal warp. Unlike exact DTW, which has quadratic complexity, we propose a linear time algorithm to minimize GCTW. (3) GCTW allows simultaneous alignment of multiple sequences. Experimental results on aligning multi-modal data, facial expressions, motion capture data and video illustrate the benefits of GCTW. The code is available at http://humansensing.cs.cmu.edu/ctw.
Application of Canonical Effective Methods to Background-Independent Theories
Buyukcam, Umut
Effective formalisms play an important role in analyzing phenomena above some given length scale when complete theories are not accessible. In diverse exotic but physically important cases, the usual path-integral techniques used in a standard Quantum Field Theory approach seldom serve as adequate tools. This thesis exposes a new effective method for quantum systems, called the Canonical Effective Method, which owns particularly wide applicability in backgroundindependent theories as in the case of gravitational phenomena. The central purpose of this work is to employ these techniques to obtain semi-classical dynamics from canonical quantum gravity theories. Application to non-associative quantum mechanics is developed and testable results are obtained. Types of non-associative algebras relevant for magnetic-monopole systems are discussed. Possible modifications of hypersurface deformation algebra and the emergence of effective space-times are presented. iii.
Action at a distance in physics and cosmology
Hoyle, Fred
1974-01-01
Classical theories of electromagnetism and gravitation ; the absorber theory of Wheeler and Feynman ; the quantum response of the Universe ; direct-particle theories in Riemannian spacetime ; inertia and gravitation treated classically ; cosmology ; problems in the quantization of inertia and gravitation ; further considerations of cosmology.
Canonically conjugate pairs and phase operators
International Nuclear Information System (INIS)
Schoenhammer, K.
2002-01-01
For quantum mechanics on a lattice the position ('particle number') operator and the quasimomentum ('phase') operator obey canonical commutation relations (CCRs) only on a dense set of the Hilbert space. We compare exact numerical results for a particle in a linear and a quadratic potential on the lattice with the expectations, when the CCRs are assumed to be strictly obeyed. Only for sufficiently smooth eigenfunctions does this lead to reasonable results. In the long time limit the use of the CCRs can lead to a qualitatively wrong dynamics even if the initial state is in the dense set
Canonical transformations and hamiltonian path integrals
International Nuclear Information System (INIS)
Prokhorov, L.V.
1982-01-01
Behaviour of the Hamiltonian path integrals under canonical transformations produced by a generator, is investigated. An exact form is determined for the kernel of the unitary operator realizing the corresponding quantum transformation. Equivalence rules are found (the Hamiltonian formalism, one-dimensional case) enabling one to exclude non-standard terms from the action. It is shown that the Hamiltonian path integral changes its form under cononical transformations: in the transformed expression besides the classical Hamiltonian function there appear some non-classical terms
Is Quantum Gravity a Super-Quantum Theory?
Chang, Lay Nam; Lewis, Zachary; Minic, Djordje; Takeuchi, Tatsu
2013-01-01
We argue that quantum gravity should be a super-quantum theory, that is, a theory whose non-local correlations are stronger than those of canonical quantum theory. As a super-quantum theory, quantum gravity should display distinct experimentally observable super-correlations of entangled stringy states.
Groups of automorphisms of the canonical commutation and anticommutation relations
International Nuclear Information System (INIS)
Grosse, H.; Pittner, L.
1987-01-01
Observables of supersymmetric quantum mechanics are coded by taking the antisymmetric tensor product with anticommuting parameters. Next we define superunitary transformations, which mix bosonic and fermionic degrees of freedom, in order to construct automorphisms of the canonical (anti-) commutation relations. Conversely, every automorphism of the C(A)CR is implemented by an essentially unique superunitary transformation. 12 refs. (Author)
IUS CONNUBII: Canonical Dimension
Directory of Open Access Journals (Sweden)
Silma Mendes Berti
2018-03-01
Full Text Available anon Law, in regulating under Can.1058 the "ius connubii", lays down that: "All those who are not prohibited from doing so by law may contract matrimony." This disposition, although apparently simple, has a wide and deep range of implications, questionings and possibilities for investigation, especially as it involves an extremely delicate relationship. A perfect combination of law and sacrament, the "ius connubii", in its close relationship with the constitution of the family, which is the sanctuary of Love, is an important problem, which faces the legislator, both in the legislation of the State, specifically in Civil Law, and in that of the Church. As the general principle of the canonical matrimonial system, "ius connubii' is the source of interpretation of all rules concerning matrimony, especially when it comes to the distinction between sacramental reality and liturgical ceremony. This is the fact, which is the basis of our reflections.
Development of the Universe and New Cosmology
Sakharov, Alexander S
2003-01-01
Cosmology is undergoing an explosive period of activity, fueled both by new, accurate astrophysical data and by innovative theoretical developments. Cosmological parameters such as the total density of the Universe and the rate of cosmological expansion are being precisely measured for the first time, and a consistent standard picture of the Universe is beginning to emerge. Recent developments in cosmology give rise the intriguing possibility that all structures in the Universe, from superclusters to planets, had a quantum-mechanical origin in its earliest moments. Furthermore, these ideas are not idle theorizing, but predictive, and subject to meaningful experimental test. We review the concordance model of the development of the Universe, as well as evidence for the observational revolution that this field is going through. This already provides us with important information on particle physics, which is inaccessible to accelerators.
Nonlinear quantum gravity on the constant mean curvature foliation
International Nuclear Information System (INIS)
Wang, Charles H-T
2005-01-01
A new approach to quantum gravity is presented based on a nonlinear quantization scheme for canonical field theories with an implicitly defined Hamiltonian. The constant mean curvature foliation is employed to eliminate the momentum constraints in canonical general relativity. It is, however, argued that the Hamiltonian constraint may be advantageously retained in the reduced classical system to be quantized. This permits the Hamiltonian constraint equation to be consistently turned into an expectation value equation on quantization that describes the scale factor on each spatial hypersurface characterized by a constant mean exterior curvature. This expectation value equation augments the dynamical quantum evolution of the unconstrained conformal three-geometry with a transverse traceless momentum tensor density. The resulting quantum theory is inherently nonlinear. Nonetheless, it is unitary and free from a nonlocal and implicit description of the Hamiltonian operator. Finally, by imposing additional homogeneity symmetries, a broad class of Bianchi cosmological models are analysed as nonlinear quantum minisuperspaces in the context of the proposed theory
Quantum group gauge theory on quantum spaces
International Nuclear Information System (INIS)
Brzezinski, T.; Majid, S.
1993-01-01
We construct quantum group-valued canonical connections on quantum homogeneous spaces, including a q-deformed Dirac monopole on the quantum sphere of Podles quantum differential coming from the 3-D calculus of Woronowicz on SU q (2). The construction is presented within the setting of a general theory of quantum principal bundles with quantum group (Hopf algebra) fiber, associated quantum vector bundles and connection one-forms. Both the base space (spacetime) and the total space are non-commutative algebras (quantum spaces). (orig.)
Dimensional cosmological principles
International Nuclear Information System (INIS)
Chi, L.K.
1985-01-01
The dimensional cosmological principles proposed by Wesson require that the density, pressure, and mass of cosmological models be functions of the dimensionless variables which are themselves combinations of the gravitational constant, the speed of light, and the spacetime coordinates. The space coordinate is not the comoving coordinate. In this paper, the dimensional cosmological principle and the dimensional perfect cosmological principle are reformulated by using the comoving coordinate. The dimensional perfect cosmological principle is further modified to allow the possibility that mass creation may occur. Self-similar spacetimes are found to be models obeying the new dimensional cosmological principle
Cosmology and particle physics
International Nuclear Information System (INIS)
Turner, M.S.
1985-01-01
The author reviews the standard cosmology, focusing on primordial nucleosynthesis, and discusses how the standard cosmology has been used to place constraints on the properties of various particles. Baryogenesis is examined in which the B, C, CP violating interactions in GUTs provide a dynamical explanation for the predominance of matter over antimatter and the present baryon-to-baryon ratio. Monoposes, cosmology and astrophysics are reviewed. The author also discusses supersymmetry/supergravity and cosmology, superstrings and cosmology in extra dimensions, and axions, astrophics, and cosmology
Nonsingular bouncing cosmologies in light of BICEP2
International Nuclear Information System (INIS)
Cai, Yi-Fu; Quintin, Jerome; Saridakis, Emmanuel N.; Wilson-Ewing, Edward
2014-01-01
We confront various nonsingular bouncing cosmologies with the recently released BICEP2 data and investigate the observational constraints on their parameter space. In particular, within the context of the effective field approach, we analyze the constraints on the matter bounce curvaton scenario with a light scalar field, and the new matter bounce cosmology model in which the universe successively experiences a period of matter contraction and an ekpyrotic phase. Additionally, we consider three nonsingular bouncing cosmologies obtained in the framework of modified gravity theories, namely the Hořava-Lifshitz bounce model, the f(T) bounce model, and loop quantum cosmology
New constraints for canonical general relativity
International Nuclear Information System (INIS)
Reisenberger, M.P.
1995-01-01
Ashtekar's canonical theory of classical complex Euclidean GR (no Lorentzian reality conditions) is found to be invariant under the full algebra of infinitesimal 4-diffeomorphisms, but non-invariant under some finite proper 4-diffeos when the densitized dreibein, E a i , is degenerate. The breakdown of 4-diffeo invariance appears to be due to the inability of the Ashtekar Hamiltonian to generate births and deaths of E flux loops (leaving open the possibility that a new 'causality condition' forbidding the birth of flux loops might justify the non-invariance of the theory).A fully 4-diffeo invariant canonical theory in Ashtekar's variables, derived from Plebanski's action, is found to have constraints that are stronger than Ashtekar's for rank E< 2. The corresponding Hamiltonian generates births and deaths of E flux loops.It is argued that this implies a finite amplitude for births and deaths of loops in the physical states of quantum GR in the loop representation, thus modifying this (partly defined) theory substantially.Some of the new constraints are second class, leading to difficulties in quantization in the connection representation. This problem might be overcome in a very nice way by transforming to the classical loop variables, or the 'Faraday line' variables of Newman and Rovelli, and then solving the offending constraints.Note that, though motivated by quantum considerations, the present paper is classical in substance. (orig.)
Effects of heavy fields on inflationary cosmology
Ortiz, Pablo
2014-01-01
Cosmological inflation is the most successful theory that explains the homogeneity and flatness of the early universe. It also provides a quantum origin for the primordial perturbations that we observe in the Cosmic Microwave Background Radiation (CMB). The simplest models make use of a single
Deparametrization and path integral quantization of cosmological models
Simeone, Claudio
2001-01-01
The problem of time is a central feature of quantum cosmology: differing from ordinary quantum mechanics, in cosmology there is nothing "outside" the system which plays the role of clock, and this makes difficult the obtention of a consistent quantization. A possible solution is to assume that a subset of the variables describing the state of the universe can be a clock for the remaining of the system. Following this line, in this book a new proposal consisting in the previous identification of time by means of gauge fixation is applied to the quantization of homogeneous cosmological models. B
Symmetric minimally entangled typical thermal states for canonical and grand-canonical ensembles
Binder, Moritz; Barthel, Thomas
2017-05-01
Based on the density matrix renormalization group (DMRG), strongly correlated quantum many-body systems at finite temperatures can be simulated by sampling over a certain class of pure matrix product states (MPS) called minimally entangled typical thermal states (METTS). When a system features symmetries, these can be utilized to substantially reduce MPS computation costs. It is conceptually straightforward to simulate canonical ensembles using symmetric METTS. In practice, it is important to alternate between different symmetric collapse bases to decrease autocorrelations in the Markov chain of METTS. To this purpose, we introduce symmetric Fourier and Haar-random block bases that are efficiently mixing. We also show how grand-canonical ensembles can be simulated efficiently with symmetric METTS. We demonstrate these approaches for spin-1 /2 X X Z chains and discuss how the choice of the collapse bases influences autocorrelations as well as the distribution of measurement values and, hence, convergence speeds.
Canonical symmetry of a constrained Hamiltonian system and canonical Ward identity
International Nuclear Information System (INIS)
Li, Zi-ping
1995-01-01
An algorithm for the construction of the generators of the gauge transformation of a constrained Hamiltonian system is given. The relationships among the coefficients connecting the first constraints in the generator are made clear. Starting from the phase space generating function of the Green function, the Ward identity in canonical formalism is deduced. We point out that the quantum equations of motion in canonical form for a system with singular Lagrangian differ from the classical ones whether Dirac's conjecture holds true or not. Applications of the present formulation to the Abelian and non-Abelian gauge theories are given. The expressions for PCAC and generalized PCAC of the AVV vertex are derived exactly from another point of view. A new form of the Ward identity for gauge-ghost proper vertices is obtained which differs from the usual Ward-Takahashi identity arising from the BRS invariance
International Nuclear Information System (INIS)
Gaisser, T.K.; Shafi, Q.; Barr, S.M.; Seckel, D.; Rusjan, E.; Fletcher, R.S.
1991-01-01
This report discusses research of professor at Bartol research institute in the following general areas: particle phenomenology and non-accelerator physics; particle physics and cosmology; theories with higher symmetry; and particle astrophysics and cosmology
International Nuclear Information System (INIS)
Heller, M.
1985-01-01
Two Friedman's cosmological papers (1922, 1924) and his own interpretation of the obtained results are briefly reviewed. Discussion follows of Friedman's role in the early development of relativistic cosmology. 18 refs. (author)
Kunze, Kerstin E.
2016-12-20
Cosmology is becoming an important tool to test particle physics models. We provide an overview of the standard model of cosmology with an emphasis on the observations relevant for testing fundamental physics.
Energy Technology Data Exchange (ETDEWEB)
Lamon, Raphael
2010-06-29
Quantum gravity is an attempt to unify general relativity with quantum mechanics which are the two highly successful fundamental theories of theoretical physics. The main difficulty in this unification arises from the fact that, while general relativity describes gravity as a macroscopic geometrical theory, quantum mechanics explains microscopic phenomena. As a further complication, not only do both theories describe different scales but also their philosophical ramifications and the mathematics used to describe them differ in a dramatic way. Consequently, one possible starting point of an attempt at a unification is quantum mechanics, i.e. particle physics, and try to incorporate gravitation. This pathway has been chosen by particle physicists which led to string theory. On the other hand, loop quantum gravity (LQG) chooses the other possibility, i.e. it takes the geometrical aspects of gravity seriously and quantizes geometry. The first part of this thesis deals with a generalization of loop quantum cosmology (LQC) to toroidal topologies. LQC is a quantization of homogenous solutions of Einstein's field equations using tools from LQG. First the general concepts of closed topologies is introduced with special emphasis on Thurston's theorem and its consequences. It is shown that new degrees of freedom called Teichmueller parameters come into play and their dynamics can be described by a Hamiltonian. Several numerical solutions for a toroidal universe are presented and discussed. Following the guidelines of LQG this dynamics are rewritten using the Ashtekar variables and numerical solutions are shown. However, in order to find a suitable Hilbert space a canonical transformation must be performed. On the other hand this transformation makes the quantization of geometrical quantities less tractable such that two different ways are presented. It is shown that in both cases the spectrum of such geometrical operators depends on the initial value problem
International Nuclear Information System (INIS)
Lamon, Raphael
2010-01-01
Quantum gravity is an attempt to unify general relativity with quantum mechanics which are the two highly successful fundamental theories of theoretical physics. The main difficulty in this unification arises from the fact that, while general relativity describes gravity as a macroscopic geometrical theory, quantum mechanics explains microscopic phenomena. As a further complication, not only do both theories describe different scales but also their philosophical ramifications and the mathematics used to describe them differ in a dramatic way. Consequently, one possible starting point of an attempt at a unification is quantum mechanics, i.e. particle physics, and try to incorporate gravitation. This pathway has been chosen by particle physicists which led to string theory. On the other hand, loop quantum gravity (LQG) chooses the other possibility, i.e. it takes the geometrical aspects of gravity seriously and quantizes geometry. The first part of this thesis deals with a generalization of loop quantum cosmology (LQC) to toroidal topologies. LQC is a quantization of homogenous solutions of Einstein's field equations using tools from LQG. First the general concepts of closed topologies is introduced with special emphasis on Thurston's theorem and its consequences. It is shown that new degrees of freedom called Teichmueller parameters come into play and their dynamics can be described by a Hamiltonian. Several numerical solutions for a toroidal universe are presented and discussed. Following the guidelines of LQG this dynamics are rewritten using the Ashtekar variables and numerical solutions are shown. However, in order to find a suitable Hilbert space a canonical transformation must be performed. On the other hand this transformation makes the quantization of geometrical quantities less tractable such that two different ways are presented. It is shown that in both cases the spectrum of such geometrical operators depends on the initial value problem. Furthermore, we
Roos, Matts
2015-01-01
The Fourth Edition of Introduction to Cosmology provides a concise, authoritative study of cosmology at an introductory level. Starting from elementary principles and the early history of cosmology, the text carefully guides the student on to curved spacetimes, special and general relativity, gravitational lensing, the thermal history of the Universe, and cosmological models, including extended gravity models, black holes and Hawking's recent conjectures on the not-so-black holes.
On the effect of renormalization group improvement on the cosmological power spectrum
Energy Technology Data Exchange (ETDEWEB)
Moti, R. [University of Tehran, Department of Physics, Tehran (Iran, Islamic Republic of); Shojai, A. [University of Tehran, Department of Physics, Tehran (Iran, Islamic Republic of); Institute for Research in Fundamental Sciences (IPM), Foundations of Physics Group, School of Physics, Tehran (Iran, Islamic Republic of)
2018-01-15
Asymptotically safe quantum gravity predicts running gravitational and cosmological constants, while it remains a meaningful quantum field theory because of the existence of a finite number of non-Gaussian ultraviolet fixed points. We have investigated the effect of such running couplings on the cosmological perturbations. We have obtained the improved Mukhanov-Sassaki equation and solved it for two models. The effect of such running of the coupling constants on the cosmological power spectrum is also studied. (orig.)
Cosmological models in energy-momentum-squared gravity
Board, Charles V. R.; Barrow, John D.
2017-12-01
We study the cosmological effects of adding terms of higher order in the usual energy-momentum tensor to the matter Lagrangian of general relativity. This is in contrast to most studies of higher-order gravity which focus on generalizing the Einstein-Hilbert curvature contribution to the Lagrangian. The resulting cosmological theories give rise to field equations of similar form to several particular theories with different fundamental bases, including bulk viscous cosmology, loop quantum gravity, k -essence, and brane-world cosmologies. We find a range of exact solutions for isotropic universes, discuss their behaviors with reference to the early- and late-time evolution, accelerated expansion, and the occurrence or avoidance of singularities. We briefly discuss extensions to anisotropic cosmologies and delineate the situations where the higher-order matter terms will dominate over anisotropies on approach to cosmological singularities.
Phantom cosmologies and fermions
International Nuclear Information System (INIS)
Chimento, Luis P; Forte, Monica; Devecchi, Fernando P; Kremer, Gilberto M
2008-01-01
Form invariance transformations can be used for constructing phantom cosmologies starting with conventional cosmological models. In this work we reconsider the scalar field case and extend the discussion to fermionic fields, where the 'phantomization' process exhibits a new class of possible accelerated regimes. As an application we analyze the cosmological constant group for a fermionic seed fluid
Particle physics and cosmology
International Nuclear Information System (INIS)
Schramm, D.N.; Turner, M.S.
1982-06-01
work is described in these areas: cosmological baryon production; cosmological production of free quarks and other exotic particle species; the quark-hadron transition in the early universe; astrophysical and cosmological constraints on particle properties; massive neutrinos; phase transitions in the early universe; and astrophysical implications of an axion-like particle
. ______________________________________________________________________________________ Nobelist George Smoot to Direct Korean Cosmology Institute Nobel Laureate George Smoot has been appointed director of a new cosmology institute in South Korea that will work closely with the year-old Berkeley the Early Universe (IEU) at EWHA Womans University in Seoul, Korea will provide cosmology education
International Nuclear Information System (INIS)
Davies, P.
1991-01-01
The main concepts of cosmology are discussed, and some of the misconceptions are clarified. The features of big bang cosmology are examined, and it is noted that the existence of the cosmic background radiation provides welcome confirmation of the big bang theory. Calculations of relative abundances of the elements conform with observations, further strengthening the confidence in the basic ideas of big bang cosmology
CERN. Geneva. Audiovisual Unit
2001-01-01
Cosmology and particle physics have enjoyed a useful relationship over the entire histories of both subjects. Today, ideas and techniques in cosmology are frequently used to elucidate and constrain theories of elementary particles. These lectures give an elementary overview of the essential elements of cosmology, which is necessary to understand this relationship.
CERN. Geneva
1999-01-01
Cosmology and particle physics have enjoyed a useful relationship over the entire histories of both subjects. Today, ideas and techniques in cosmology are frequently used to elucidate and constrain theories of elementary particles. These lectures give an elementary overview of the essential elements of cosmology, which is necessary to understand this relationship.
International Nuclear Information System (INIS)
Langer, M.
2007-01-01
This is a very concise introductory lecture to Cosmology. We start by reviewing the basics of homogeneous and isotropic cosmology. We then spend some time on the description of the Cosmic Microwave Background. Finally, a small section is devoted to the discussion of the cosmological constant and of some of the related problems
Al-Khalili, Jim
2003-01-01
In this lively look at quantum science, a physicist takes you on an entertaining and enlightening journey through the basics of subatomic physics. Along the way, he examines the paradox of quantum mechanics--beautifully mathematical in theory but confoundingly unpredictable in the real world. Marvel at the Dual Slit experiment as a tiny atom passes through two separate openings at the same time. Ponder the peculiar communication of quantum particles, which can remain in touch no matter how far apart. Join the genius jewel thief as he carries out a quantum measurement on a diamond without ever touching the object in question. Baffle yourself with the bizzareness of quantum tunneling, the equivalent of traveling partway up a hill, only to disappear then reappear traveling down the opposite side. With its clean, colorful layout and conversational tone, this text will hook you into the conundrum that is quantum mechanics.
An alternative path integral for quantum gravity
Energy Technology Data Exchange (ETDEWEB)
Krishnan, Chethan; Kumar, K.V. Pavan; Raju, Avinash [Center for High Energy Physics, Indian Institute of Science,Bangalore 560012 (India)
2016-10-10
We define a (semi-classical) path integral for gravity with Neumann boundary conditions in D dimensions, and show how to relate this new partition function to the usual picture of Euclidean quantum gravity. We also write down the action in ADM Hamiltonian formulation and use it to reproduce the entropy of black holes and cosmological horizons. A comparison between the (background-subtracted) covariant and Hamiltonian ways of semi-classically evaluating this path integral in flat space reproduces the generalized Smarr formula and the first law. This “Neumann ensemble” perspective on gravitational thermodynamics is parallel to the canonical (Dirichlet) ensemble of Gibbons-Hawking and the microcanonical approach of Brown-York.
Discrete Hamiltonian evolution and quantum gravity
International Nuclear Information System (INIS)
Husain, Viqar; Winkler, Oliver
2004-01-01
We study constrained Hamiltonian systems by utilizing general forms of time discretization. We show that for explicit discretizations, the requirement of preserving the canonical Poisson bracket under discrete evolution imposes strong conditions on both allowable discretizations and Hamiltonians. These conditions permit time discretizations for a limited class of Hamiltonians, which does not include homogeneous cosmological models. We also present two general classes of implicit discretizations which preserve Poisson brackets for any Hamiltonian. Both types of discretizations generically do not preserve first class constraint algebras. Using this observation, we show that time discretization provides a complicated time gauge fixing for quantum gravity models, which may be compared with the alternative procedure of gauge fixing before discretization
Quantum Gravity (Cambridge Monographs on Mathematical Physics)
International Nuclear Information System (INIS)
Kiefer, C
2005-01-01
The most difficult unsolved problem in fundamental theoretical physics is the consistent implementation of the gravitational interaction into a quantum framework, which would lead to a theory of quantum gravity. Although a final answer is still pending, several promising attempts do exist. Despite the general title, this book is about one of them - loop quantum gravity. This approach proceeds from the idea that a direct quantization of Einstein's theory of general relativity is possible. In contrast to string theory, it presupposes that the unification of all interactions is not needed as a prerequisite for quantum gravity. Usually one divides theories of quantum general relativity into covariant and canonical approaches. Covariant theories employ four-dimensional concepts in its formulation, one example being the path integral approach. Canonical theories start from a classical Hamiltonian version of the theory in which spacetime is foliated into spacelike hypersurfaces. Loop quantum gravity is a variant of the canonical approach, the oldest being quantum geometrodynamics where the fundamental configuration variable is the three-metric. Loop quantum gravity has developed from a new choice of canonical variables introduced by Abhay Ashtekar in 1986, the new configuration variable being a connection defined on a three-manifold. Instead of the connection itself, the loop approach employs a non-local version in which the connection is integrated over closed loops. This is similar to the Wilson loops used in gauge theories. Carlo Rovelli is one of the pioneers of loop quantum gravity which he started to develop with Lee Smolin in two papers written in 1988 and 1990. In his book, he presents a comprehensive and competent overview of this approach and provides at the same time the necessary technical background in order to make the treatment self-contained. In fact, half of the book is devoted to 'preparations' giving a detailed account of Hamiltonian mechanics, quantum
Anisotropic cosmological constant and the CMB quadrupole anomaly
International Nuclear Information System (INIS)
Rodrigues, Davi C.
2008-01-01
There are evidences that the cosmic microwave background (CMB) large-angle anomalies imply a departure from statistical isotropy and hence from the standard cosmological model. We propose a ΛCDM model extension whose dark energy component preserves its nondynamical character but wields anisotropic vacuum pressure. Exact solutions for the cosmological scale factors are presented, upper bounds for the deformation parameter are evaluated and its value is estimated considering the elliptical universe proposal to solve the quadrupole anomaly. This model can be constructed from a Bianchi I cosmology with a cosmological constant from two different ways: (i) a straightforward anisotropic modification of the vacuum pressure consistently with energy-momentum conservation; (ii) a Poisson structure deformation between canonical momenta such that the dynamics remain invariant under scale factors rescalings
Philosophical Roots of Cosmology
Ivanovic, M.
2008-10-01
We shall consider the philosophical roots of cosmology in the earlier Greek philosophy. Our goal is to answer the question: Are earlier Greek theories of pure philosophical-mythological character, as often philosophers cited it, or they have scientific character. On the bases of methodological criteria, we shall contend that the latter is the case. In order to answer the question about contemporary situation of the relation philosophy-cosmology, we shall consider the next question: Is contemporary cosmology completely independent of philosophical conjectures? The answer demands consideration of methodological character about scientific status of contemporary cosmology. We also consider some aspects of the relation contemporary philosophy-cosmology.
Cosmological production of noncommutative black holes
International Nuclear Information System (INIS)
Mann, Robert B.; Nicolini, Piero
2011-01-01
We investigate the pair creation of noncommutative black holes in a background with a positive cosmological constant. As a first step we derive the noncommutative geometry inspired Schwarzschild-de Sitter solution. By varying the mass and the cosmological constant parameters, we find several spacetimes compatible with the new solution: positive-mass spacetimes admit one cosmological horizon and two, one, or no black hole horizons, while negative-mass spacetimes have just a cosmological horizon. These new black holes share the properties of the corresponding asymptotically flat solutions, including the nonsingular core and thermodynamic stability in the final phase of the evaporation. As a second step we determine the action which generates the matter sector of gravitational field equations and we construct instantons describing the pair production of black holes and the other admissible topologies. As a result we find that for current values of the cosmological constant the de Sitter background is quantum mechanically stable according to experience. However, positive-mass noncommutative black holes and solitons would have plentifully been produced during inflationary times for Planckian values of the cosmological constant. As a special result we find that, in these early epochs of the Universe, Planck size black holes production would have been largely disfavored. We also find a potential instability for production of negative-mass solitons.
Canonical Labelling of Site Graphs
Directory of Open Access Journals (Sweden)
Nicolas Oury
2013-06-01
Full Text Available We investigate algorithms for canonical labelling of site graphs, i.e. graphs in which edges bind vertices on sites with locally unique names. We first show that the problem of canonical labelling of site graphs reduces to the problem of canonical labelling of graphs with edge colourings. We then present two canonical labelling algorithms based on edge enumeration, and a third based on an extension of Hopcroft's partition refinement algorithm. All run in quadratic worst case time individually. However, one of the edge enumeration algorithms runs in sub-quadratic time for graphs with "many" automorphisms, and the partition refinement algorithm runs in sub-quadratic time for graphs with "few" bisimulation equivalences. This suite of algorithms was chosen based on the expectation that graphs fall in one of those two categories. If that is the case, a combined algorithm runs in sub-quadratic worst case time. Whether this expectation is reasonable remains an interesting open problem.
Backlund transformations as canonical transformations
International Nuclear Information System (INIS)
Villani, A.; Zimerman, A.H.
1977-01-01
Toda and Wadati as well as Kodama and Wadati have shown that the Backlund transformations, for the exponential lattice equation, sine-Gordon equation, K-dV (Korteweg de Vries) equation and modifies K-dV equation, are canonical transformation. It is shown that the Backlund transformation for the Boussinesq equation, for a generalized K-dV equation, for a model equation for shallow water waves and for the nonlinear Schroedinger equation are also canonical transformations [pt
Introduction to particle cosmology the standard model of cosmology and its open problems
Bambi, Cosimo
2016-01-01
This book introduces the basic concepts of particle cosmology and covers all the main aspects of the Big Bang Model (expansion of the Universe, Big Bang Nucleosynthesis, Cosmic Microwave Background, large scale structures) and the search for new physics (inflation, baryogenesis, dark matter, dark energy). It also includes the majority of recent discoveries, such as the precise determination of cosmological parameters using experiments like WMAP and Planck, the discovery of the Higgs boson at LHC, the non-discovery to date of supersymmetric particles, and the search for the imprint of gravitational waves on the CMB polarization by Planck and BICEP. This textbook is based on the authors’ courses on Cosmology, and aims at introducing Particle Cosmology to senior undergraduate and graduate students. It has been especially written to be accessible even for those students who do not have a strong background in General Relativity and quantum field theory. The content of this book is organized in an easy-to-use ...
Energy Technology Data Exchange (ETDEWEB)
Barbour, J B [Department of Physics and Astronomy, University of Rochester (United States)
2007-02-07
the standard model though he has difficulties with X-ray clusters) and the observer Michael Disney, who expresses radical doubts about the concordance model and cites a paper of his (astro-ph/0009020) that is entertaining and hard hitting. But is it worth buying 278 pages for the sake of at most 20? I welcomed the opportunity to review this book since I have stuck my neck out even further than Narlikar and Disney, and this journal has even published an article by me in which I question whether the universe is actually expanding (Classical and Quantum Gravity 20 1571). I wanted to see if there were any chinks in the armour of the standard model. I have to say that having read this book, three modern books on cosmology and attended the recent Cosmic Frontiers conference in Durham (UK), I have to agree with Blanchard when he says: 'When I try to find what the weaknesses of the standard big bang are, I get rather more convinced of its robustness{exclamation_point}' However, I was glad to see that he does not regard inflation as part of the model, and I do think Disney is right to be sceptical about exaggerated claims for the specific concordance model (rather than the basic big-bang idea). However, what I find immensely impressive is how the one simple idea of the expanding universe has proved so fruitful and successful. (book review)
International Nuclear Information System (INIS)
Barbour, J B
2007-01-01
about the concordance model and cites a paper of his (astro-ph/0009020) that is entertaining and hard hitting. But is it worth buying 278 pages for the sake of at most 20? I welcomed the opportunity to review this book since I have stuck my neck out even further than Narlikar and Disney, and this journal has even published an article by me in which I question whether the universe is actually expanding (Classical and Quantum Gravity 20 1571). I wanted to see if there were any chinks in the armour of the standard model. I have to say that having read this book, three modern books on cosmology and attended the recent Cosmic Frontiers conference in Durham (UK), I have to agree with Blanchard when he says: 'When I try to find what the weaknesses of the standard big bang are, I get rather more convinced of its robustness!' However, I was glad to see that he does not regard inflation as part of the model, and I do think Disney is right to be sceptical about exaggerated claims for the specific concordance model (rather than the basic big-bang idea). However, what I find immensely impressive is how the one simple idea of the expanding universe has proved so fruitful and successful. (book review)
Roberts, Alex
2016-08-01
Recently, a new framework for describing the multiverse has been proposed which is based on the principles of quantum mechanics. The framework allows for well-defined predictions, both regarding global properties of the universe and outcomes of particular experiments, according to a single probability formula. This provides complete unification of the eternally inflating multiverse and many worlds in quantum mechanics. We elucidate how cosmological parameters can be calculated in this framework, and study the probability distribution for the value of the cosmological constant. We consider both positive and negative values, and find that the observed value is consistent with the calculated distribution at an order of magnitude level. In particular, in contrast to the case of earlier measure proposals, our framework prefers a positive cosmological constant over a negative one. These results depend only moderately on how we model galaxy formation and life evolution therein. We explore supersymmetric theories in which the Higgs mass is boosted by the non-decoupling D-terms of an extended U(1) X gauge symmetry, defined here to be a general linear combination of hypercharge, baryon number, and lepton number. Crucially, the gauge coupling, gX, is bounded from below to accommodate the Higgs mass, while the quarks and leptons are required by gauge invariance to carry non-zero charge under U(1)X. This induces an irreducible rate, sigmaBR, for pp → X → ll relevant to existing and future resonance searches, and gives rise to higher dimension operators that are stringently constrained by precision electroweak measurements. Combined, these bounds define a maximally allowed region in the space of observables, (sigmaBR, mX), outside of which is excluded by naturalness and experimental limits. If natural supersymmetry utilizes non-decoupling D-terms, then the associated X boson can only be observed within this window, providing a model independent 'litmus test' for this broad
Energy Technology Data Exchange (ETDEWEB)
Schramm, D.N.
1992-03-01
The cosmological dark matter problem is reviewed. The Big Bang Nucleosynthesis constraints on the baryon density are compared with the densities implied by visible matter, dark halos, dynamics of clusters, gravitational lenses, large-scale velocity flows, and the {Omega} = 1 flatness/inflation argument. It is shown that (1) the majority of baryons are dark; and (2) non-baryonic dark matter is probably required on large scales. It is also noted that halo dark matter could be either baryonic or non-baryonic. Descrimination between ``cold`` and ``hot`` non-baryonic candidates is shown to depend on the assumed ``seeds`` that stimulate structure formation. Gaussian density fluctuations, such as those induced by quantum fluctuations, favor cold dark matter, whereas topological defects such as strings, textures or domain walls may work equally or better with hot dark matter. A possible connection between cold dark matter, globular cluster ages and the Hubble constant is mentioned. Recent large-scale structure measurements, coupled with microwave anisotropy limits, are shown to raise some questions for the previously favored density fluctuation picture. Accelerator and underground limits on dark matter candidates are also reviewed.
Energy Technology Data Exchange (ETDEWEB)
Schramm, D.N.
1992-03-01
The cosmological dark matter problem is reviewed. The Big Bang Nucleosynthesis constraints on the baryon density are compared with the densities implied by visible matter, dark halos, dynamics of clusters, gravitational lenses, large-scale velocity flows, and the {Omega} = 1 flatness/inflation argument. It is shown that (1) the majority of baryons are dark; and (2) non-baryonic dark matter is probably required on large scales. It is also noted that halo dark matter could be either baryonic or non-baryonic. Descrimination between cold'' and hot'' non-baryonic candidates is shown to depend on the assumed seeds'' that stimulate structure formation. Gaussian density fluctuations, such as those induced by quantum fluctuations, favor cold dark matter, whereas topological defects such as strings, textures or domain walls may work equally or better with hot dark matter. A possible connection between cold dark matter, globular cluster ages and the Hubble constant is mentioned. Recent large-scale structure measurements, coupled with microwave anisotropy limits, are shown to raise some questions for the previously favored density fluctuation picture. Accelerator and underground limits on dark matter candidates are also reviewed.
International Nuclear Information System (INIS)
Schramm, D.N.
1992-03-01
The cosmological dark matter problem is reviewed. The Big Bang Nucleosynthesis constraints on the baryon density are compared with the densities implied by visible matter, dark halos, dynamics of clusters, gravitational lenses, large-scale velocity flows, and the Ω = 1 flatness/inflation argument. It is shown that (1) the majority of baryons are dark; and (2) non-baryonic dark matter is probably required on large scales. It is also noted that halo dark matter could be either baryonic or non-baryonic. Descrimination between ''cold'' and ''hot'' non-baryonic candidates is shown to depend on the assumed ''seeds'' that stimulate structure formation. Gaussian density fluctuations, such as those induced by quantum fluctuations, favor cold dark matter, whereas topological defects such as strings, textures or domain walls may work equally or better with hot dark matter. A possible connection between cold dark matter, globular cluster ages and the Hubble constant is mentioned. Recent large-scale structure measurements, coupled with microwave anisotropy limits, are shown to raise some questions for the previously favored density fluctuation picture. Accelerator and underground limits on dark matter candidates are also reviewed
Emergent symmetries in the canonical tensor model
Obster, Dennis; Sasakura, Naoki
2018-04-01
The canonical tensor model (CTM) is a tensor model proposing a classically and quantum mechanically consistent description of gravity, formulated as a first-class constraint system with structural similarities to the ADM formalism of general relativity. The classical CTM produces a general relativistic system in a formal continuum limit, the emergence of which should be explained by the quantum CTM. In this paper we study the symmetry properties of a wave function that exactly solves the quantum constraints of the CTM. We have found that it has strong peaks at configurations invariant under some Lie groups, as predicted by a mechanism described in our previous paper. A surprising result is the preference for configurations invariant not only under Lie groups with positive definite signature, but also with Lorentzian signature. Such symmetries could characterize the global structures of spacetimes, and our results are encouraging towards showing spacetime emergence in the CTM. To verify the asymptotic convergence of the wave function we have also analyzed the asymptotic behavior, which for the most part seems to be well under control.
Singularity resolution in quantum gravity
International Nuclear Information System (INIS)
Husain, Viqar; Winkler, Oliver
2004-01-01
We examine the singularity resolution issue in quantum gravity by studying a new quantization of standard Friedmann-Robertson-Walker geometrodynamics. The quantization procedure is inspired by the loop quantum gravity program, and is based on an alternative to the Schroedinger representation normally used in metric variable quantum cosmology. We show that in this representation for quantum geometrodynamics there exists a densely defined inverse scale factor operator, and that the Hamiltonian constraint acts as a difference operator on the basis states. We find that the cosmological singularity is avoided in the quantum dynamics. We discuss these results with a view to identifying the criteria that constitute 'singularity resolution' in quantum gravity
Consistency of canonical formulation of Horava gravity
International Nuclear Information System (INIS)
Soo, Chopin
2011-01-01
Both the non-projectable and projectable version of Horava gravity face serious challenges. In the non-projectable version, the constraint algebra is seemingly inconsistent. The projectable version lacks a local Hamiltonian constraint, thus allowing for an extra graviton mode which can be problematic. A new formulation (based on arXiv:1007.1563) of Horava gravity which is naturally realized as a representation of the master constraint algebra (instead of the Dirac algebra) studied by loop quantum gravity researchers is presented. This formulation yields a consistent canonical theory with first class constraints; and captures the essence of Horava gravity in retaining only spatial diffeomorphisms as the physically relevant non-trivial gauge symmetry. At the same time the local Hamiltonian constraint is equivalently enforced by the master constraint.
Consistency of canonical formulation of Horava gravity
Energy Technology Data Exchange (ETDEWEB)
Soo, Chopin, E-mail: cpsoo@mail.ncku.edu.tw [Department of Physics, National Cheng Kung University, Tainan, Taiwan (China)
2011-09-22
Both the non-projectable and projectable version of Horava gravity face serious challenges. In the non-projectable version, the constraint algebra is seemingly inconsistent. The projectable version lacks a local Hamiltonian constraint, thus allowing for an extra graviton mode which can be problematic. A new formulation (based on arXiv:1007.1563) of Horava gravity which is naturally realized as a representation of the master constraint algebra (instead of the Dirac algebra) studied by loop quantum gravity researchers is presented. This formulation yields a consistent canonical theory with first class constraints; and captures the essence of Horava gravity in retaining only spatial diffeomorphisms as the physically relevant non-trivial gauge symmetry. At the same time the local Hamiltonian constraint is equivalently enforced by the master constraint.
Linear canonical transforms theory and applications
Kutay, M; Ozaktas, Haldun; Sheridan, John
2016-01-01
This book provides a clear and accessible introduction to the essential mathematical foundations of linear canonical transforms from a signals and systems perspective. Substantial attention is devoted to how these transforms relate to optical systems and wave propagation. There is extensive coverage of sampling theory and fast algorithms for numerically approximating the family of transforms. Chapters on topics ranging from digital holography to speckle metrology provide a window on the wide range of applications. This volume will serve as a reference for researchers in the fields of image and signal processing, wave propagation, optical information processing and holography, optical system design and modeling, and quantum optics. It will be of use to graduate students in physics and engineering, as well as for scientists in other areas seeking to learn more about this important yet relatively unfamiliar class of integral transformations.
Space distribution of extragalactic sources - Cosmology versus evolution
International Nuclear Information System (INIS)
Cavaliere, A.; Maccacaro, T.
1990-01-01
Alternative cosmologies have been recurrently invoked to explain in terms of global spacetime structure the apparent large increase, with increasing redshift, in the average luminosity of active galactic nuclei. These models interestingly seek to avoid the complexities of the canonical interpretation in terms of intrinsic population evolutions in a Friedmann universe. However, a problem of consistency for these cosmologies is pointed out, since they have to include also other classes of extragalactic sources, such as clusters of galaxies and BL Lac objects, for which there is preliminary evidence of a different behavior. 40 refs
Extending cosmology: the metric approach
Mendoza, S.
2012-01-01
Comment: 2012, Extending Cosmology: The Metric Approach, Open Questions in Cosmology; Review article for an Intech "Open questions in cosmology" book chapter (19 pages, 3 figures). Available from: http://www.intechopen.com/books/open-questions-in-cosmology/extending-cosmology-the-metric-approach
Macroscopic quantum phenomena from the large N perspective
International Nuclear Information System (INIS)
Chou, C H; Hu, B L; Subasi, Y
2011-01-01
Macroscopic quantum phenomena (MQP) is a relatively new research venue, with exciting ongoing experiments and bright prospects, yet with surprisingly little theoretical activity. What makes MQP intellectually stimulating is because it is counterpoised against the traditional view that macroscopic means classical. This simplistic and hitherto rarely challenged view need be scrutinized anew, perhaps with much of the conventional wisdoms repealed. In this series of papers we report on a systematic investigation into some key foundational issues of MQP, with the hope of constructing a viable theoretical framework for this new endeavour. The three major themes discussed in these three essays are the large N expansion, the correlation hierarchy and quantum entanglement for systems of 'large' sizes, with many components or degrees of freedom. In this paper we use different theories in a variety of contexts to examine the conditions or criteria whereby a macroscopic quantum system may take on classical attributes, and, more interestingly, that it keeps some of its quantum features. The theories we consider here are, the O(N) quantum mechanical model, semiclassical stochastic gravity and gauge / string theories; the contexts include that of a 'quantum roll' in inflationary cosmology, entropy generation in quantum Vlasov equation for plasmas, the leading order and next-to-leading order large N behaviour, and hydrodynamic / thermodynamic limits. The criteria for classicality in our consideration include the use of uncertainty relations, the correlation between classical canonical variables, randomization of quantum phase, environment-induced decoherence, decoherent history of hydrodynamic variables, etc. All this exercise is to ask only one simple question: Is it really so surprising that quantum features can appear in macroscopic objects? By examining different representative systems where detailed theoretical analysis has been carried out, we find that there is no a priori
Feynman diagrams coupled to three-dimensional quantum gravity
International Nuclear Information System (INIS)
Barrett, John W
2006-01-01
A framework for quantum field theory coupled to three-dimensional quantum gravity is proposed. The coupling with quantum gravity regulates the Feynman diagrams. One recovers the usual Feynman amplitudes in the limit as the cosmological constant tends to zero
Cosmological simulations of multicomponent cold dark matter.
Medvedev, Mikhail V
2014-08-15
The nature of dark matter is unknown. A number of dark matter candidates are quantum flavor-mixed particles but this property has never been accounted for in cosmology. Here we explore this possibility from the first principles via extensive N-body cosmological simulations and demonstrate that the two-component dark matter model agrees with observational data at all scales. Substantial reduction of substructure and flattening of density profiles in the centers of dark matter halos found in simulations can simultaneously resolve several outstanding puzzles of modern cosmology. The model shares the "why now?" fine-tuning caveat pertinent to all self-interacting models. Predictions for direct and indirect detection dark matter experiments are made.
Fast optimization algorithms and the cosmological constant
Bao, Ning; Bousso, Raphael; Jordan, Stephen; Lackey, Brad
2017-11-01
Denef and Douglas have observed that in certain landscape models the problem of finding small values of the cosmological constant is a large instance of a problem that is hard for the complexity class NP (Nondeterministic Polynomial-time). The number of elementary operations (quantum gates) needed to solve this problem by brute force search exceeds the estimated computational capacity of the observable Universe. Here we describe a way out of this puzzling circumstance: despite being NP-hard, the problem of finding a small cosmological constant can be attacked by more sophisticated algorithms whose performance vastly exceeds brute force search. In fact, in some parameter regimes the average-case complexity is polynomial. We demonstrate this by explicitly finding a cosmological constant of order 10-120 in a randomly generated 1 09-dimensional Arkani-Hamed-Dimopoulos-Kachru landscape.
Inflation after COBE: Lectures on inflationary cosmology
International Nuclear Information System (INIS)
Turner, M.S.
1992-01-01
In these lectures I review the standard hot big-bang cosmology, emphasizing its successes, its shortcomings, and its major challenge-a detailed understanding of the formation of structure in the Universe. I then discuss the motivations for and the fundamentals of inflationary cosmology, particularly emphasizing the quantum origin of metric (density and gravity-wave) perturbations. Inflation addresses the shortcomings of the standard cosmology and provides the ''initial data'' for structure formation. I conclude by addressing the implications of inflation for structure formation, evaluating the various cold dark matter models in the light of the recent detection of temperature anisotropies in the cosmic background radiation by COBE. In the near term, the study of structure formation offers a powerful probe of inflation, as well as specific inflationary models
Inflation after COBE: Lectures on inflationary cosmology
Energy Technology Data Exchange (ETDEWEB)
Turner, M.S. [Chicago Univ., IL (United States). Enrico Fermi Inst.]|[Fermi National Accelerator Lab., Batavia, IL (United States)
1992-12-31
In these lectures I review the standard hot big-bang cosmology, emphasizing its successes, its shortcomings, and its major challenge-a detailed understanding of the formation of structure in the Universe. I then discuss the motivations for and the fundamentals of inflationary cosmology, particularly emphasizing the quantum origin of metric (density and gravity-wave) perturbations. Inflation addresses the shortcomings of the standard cosmology and provides the ``initial data`` for structure formation. I conclude by addressing the implications of inflation for structure formation, evaluating the various cold dark matter models in the light of the recent detection of temperature anisotropies in the cosmic background radiation by COBE. In the near term, the study of structure formation offers a powerful probe of inflation, as well as specific inflationary models.
Some reference formulas for the generating functions of canonical transformations
Energy Technology Data Exchange (ETDEWEB)
Anselmi, Damiano [Universita di Pisa, Dipartimento di Fisica ' ' Enrico Fermi' ' , Pisa (Italy); INFN, Sezione di Pisa, Pisa (Italy)
2016-02-15
We study some properties of the canonical transformations in classical mechanics and quantum field theory and give a number of practical formulas concerning their generating functions. First, we give a diagrammatic formula for the perturbative expansion of the composition law around the identity map. Then we propose a standard way to express the generating function of a canonical transformation by means of a certain ''componential'' map, which obeys the Baker-Campbell-Hausdorff formula. We derive the diagrammatic interpretation of the componential map, work out its relation with the solution of the Hamilton-Jacobi equation and derive its time-ordered version. Finally, we generalize the results to the Batalin-Vilkovisky formalism, where the conjugate variables may have both bosonic and fermionic statistics, and describe applications to quantum field theory. (orig.)
Directory of Open Access Journals (Sweden)
Balbi Amedeo
2013-09-01
Full Text Available Time has always played a crucial role in cosmology. I review some of the aspects of the present cosmological model which are more directly related to time, such as: the definition of a cosmic time; the existence of typical timescales and epochs in an expanding universe; the problem of the initial singularity and the origin of time; the cosmological arrow of time.
International Nuclear Information System (INIS)
Surdin, M.
1980-01-01
It is shown that viewed from the 'outside', our universe is a black hole. Hence the 'inside' cosmology considered is termed as the Bright Universe Cosmology. The model proposed avoids the singularities of cosmologies of the Big Bang variety, it gives a good account of the redshifts, the cosmic background radiation, the number counts; it also gives a satisfactory explanation of the 'large numbers coincidence' and of the variation in time of fundamental constants. (Auth.)
International Nuclear Information System (INIS)
Feng, Jonathan L.
2005-01-01
Cosmology now provides unambiguous, quantitative evidence for new particle physics. I discuss the implications of cosmology for supersymmetry and vice versa. Topics include: motivations for supersymmetry; supersymmetry breaking; dark energy; freeze out and WIMPs; neutralino dark matter; cosmologically preferred regions of minimal supergravity; direct and indirect detection of neutralinos; the DAMA and HEAT signals; inflation and reheating; gravitino dark matter; Big Bang nucleosynthesis; and the cosmic microwave background. I conclude with speculations about the prospects for a microscopic description of the dark universe, stressing the necessity of diverse experiments on both sides of the particle physics/cosmology interface
International Nuclear Information System (INIS)
Sasaki, Misao
1983-01-01
We review the recent status of the inflationary cosmology. After exhibiting the essence of difficulties associated with the horizon, flatness and baryon number problems in the standard big-bang cosmology, we discuss that the inflationary universe scenario is one of the most plausible solutions to these fundamental cosmological problems. Since there are two qualitatively different versions of the inflationary universe scenario, we review each of them separately and discuss merits and demerits of each version. The Hawking radiation in de Sitter space is also reviewed since it may play an essential role in the inflationary cosmology. (author)
Roos, Matts
2003-01-01
The Third Edition of the hugely successful Introduction to Cosmology provides a concise, authoritative study of cosmology at an introductory level. Starting from elementary principles and the history of cosmology, the text carefully guides the student on to curved spacetimes, general relativity, black holes, cosmological models, particles and symmetries, and phase transitions. Extensively revised, this latest edition includes broader and updated coverage of distance measures, gravitational lensing and waves, dark energy and quintessence, the thermal history of the Universe, inflation,
Axions in inflationary cosmology
International Nuclear Information System (INIS)
Linde, A.
1991-01-01
The problem of the cosmological constraints on the axion mass is re-examined. It is argued that in the context of inflationary cosmology the constraint m a > or approx.10 -5 eV can be avoided even when the axion perturbations produced during inflation are taken into account. It is shown also that in most axion models the effective parameter f a rapidly changes during inflation. This modifies some earlier statements concerning isothermal perturbations in the axion cosmology. A hybrid inflation scenario is proposed which combines some advantages of chaotic inflation with specific features of new and/or extended inflation. Its implications for the axion cosmology are discussed. (orig.)
Canonical action-angle formalism for quantized nonlinear fields
International Nuclear Information System (INIS)
Garbaczewki, P.
1987-01-01
The canonical quantizations of field and action-angle coordinates which (locally) parameterize the phase manifold for the same nonlinear field theory model (e.g. sine-Gordon and nonlinear Schrodinger with the attractive coupling) are reconciled on the common for both cases state space. The classical-quantum relationship is maintained in the mean: coherent state expectation values of operators give rise to classical objects
Puzzles in studies of quantum chaos
International Nuclear Information System (INIS)
Xu Gongou
1994-01-01
Puzzles in studies of quantum chaos are discussed. From the view of global properties of quantum states, it is clarified that quantum chaos originates from the break-down of invariant properties of quantum canonical transformations. There exist precise correspondences between quantum and classical chaos
Periodicity, the Canon and Sport
Directory of Open Access Journals (Sweden)
Thomas F. Scanlon
2015-10-01
Full Text Available The topic according to this title is admittedly a broad one, embracing two very general concepts of time and of the cultural valuation of artistic products. Both phenomena are, in the present view, largely constructed by their contemporary cultures, and given authority to a great extent from the prestige of the past. The antiquity of tradition brings with it a certain cachet. Even though there may be peripheral debates in any given society which question the specifics of periodization or canonicity, individuals generally accept the consensus designation of a sequence of historical periods and they accept a list of highly valued artistic works as canonical or authoritative. We will first examine some of the processes of periodization and of canon-formation, after which we will discuss some specific examples of how these processes have worked in the sport of two ancient cultures, namely Greece and Mesoamerica.
Quaternionic quantum field theory
International Nuclear Information System (INIS)
Adler, S.L.
1986-01-01
In this paper the author describes a new kind of quantum mechanics or quantum field theory based on quaternions. Quaternionic quantum mechanics has a Schrodinger equation, a Dirac transformation theory, and a functional integral. Quaternionic quantum mechanics does not seem to have (except in the complex quantum mechanics specialization): A correspondence principle, and beyond this a commuting tensor product, asymptotic states, an S-matrix, a canonical formalism, coherent states or a Euclidean continuation. A new kind of quantum mechanics exists. There are many interesting formal questions to study, which should enable one to decide whether quaternionic quantum field theory is relevant for particle physics
Stability of the Einstein static universe in open cosmological models
International Nuclear Information System (INIS)
Canonico, Rosangela; Parisi, Luca
2010-01-01
The stability properties of the Einstein static solution of general relativity are altered when corrective terms arising from modification of the underlying gravitational theory appear in the cosmological equations. In this paper the existence and stability of static solutions are considered in the framework of two recently proposed quantum gravity models. The previously known analysis of the Einstein static solutions in the semiclassical regime of loop quantum cosmology with modifications to the gravitational sector is extended to open cosmological models where a static neutrally stable solution is found. A similar analysis is also performed in the framework of Horava-Lifshitz gravity under detailed balance and projectability conditions. In the case of open cosmological models the two solutions found can be either unstable or neutrally stable according to the admitted values of the parameters.