Scalar potentials out of canonical quantum cosmology
Guzman, W; Socorro, J; Urena-Lopez, L A
2005-01-01
Using canonical quantization of a flat FRW cosmological model containing a real scalar field $\\phi$ endowed with a scalar potential $V(\\phi)$, we are able to obtain exact and semiclassical solutions of the so called Wheeler-DeWitt equation for a particular family of scalar potentials. Some features of the solutions and their classical limit are discussed.
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
Bojowald, Martin
the Appearance of a Classical World in Quantum TheorySpringerBerlin0855.0000310.1007/978-3-662-03263-3Giulini, D., Kiefer, C., Joos, E., Kupsch, J., Stamatescu, I.O., Zeh, H.D.: Decoherence and the Appearance of a Classical World in Quantum Theory. Springer, Berlin (1996) 2.Bojowald, M., Brizuela, D., Hernandez, H.H., Koop, M.J., Morales-Técotl, H.A.:arXiv:1011.3022 3.J.P.GazeauJ.Klauder1999J. Phys. A: Math. Gen.3212316685761999JPhA...32..123G0919.4706110.1088/0305-4470/32/1/013arXiv:1011.3022Gazeau, J.P., Klauder, J.: J. Phys. A: Math. Gen. 32, 123 (1999) 4.M.NovelloS.E.P.Bergliaffa2008Phys. Rep.46312724370502008PhR...463..127N10.1016/j.physrep.2008.04.006Novello, M., Bergliaffa, S.E.P.: Phys. Rep. 463, 127 (2008) 5.M.Bojowald2010Canonical Gravity and Applications: Cosmology, Black Holes, and Quantum GravityCambridge University PressCambridge10.1017/CBO9780511921759Bojowald, M.: Canonical Gravity and Applications: Cosmology, Black Holes, and Quantum Gravity. Cambridge University Press, Cambridge (2010) 6.A.Ashtekar1987Phys. Rev. D36615879096671987PhRvD..36.1587A10.1103/PhysRevD.36.1587Ashtekar, A.: Phys. Rev. D 36(6), 1587 (1987) 7.Barbero G.J.F., (1995) Phys. Rev. D 51(10): 5507 8.G.Immirzi1997Class. Quantum Grav.14L 17714765391997CQGra..14L.177I10.1088/0264-9381/14/10/002Immirzi, G.: Class. Quantum Grav. 14, L 177 (1997) 9.J.LewandowskiE.T.NewmanC.Rovelli1993J. Math. Phys.34464612359631993JMP....34.4646L0790.5305710.1063/1.530362Lewandowski, J., Newman, E.T., Rovelli, C.: J. Math. Phys. 34, 4646 (1993) 10.C.RovelliL.Smolin1990Nucl. Phys. B3318010444931990NuPhB.331...80R10.1016/0550-3213(90)90019-ARovelli, C., Smolin, L.: Nucl. Phys. B 331, 80 (1990) 11.A.CorichiK.Krasnov1998Mod. Phys. Lett. A13133916358811998MPLA...13.1339C10.1142/S0217732398001406hep-th/9703177Corichi, A., Krasnov, K.: Mod. Phys. Lett. A 13, 1339 (1998). hep-th/9703177 12.A.AshtekarJ.LewandowskiD.MarolfJ.Mour aoT.Thiemann1995J. Math. Phys.3611645613559161995JMP....36.6456A0856
Bojowald, Martin
1999-01-01
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.
Singularities in loop quantum cosmology.
Cailleteau, Thomas; Cardoso, Antonio; Vandersloot, Kevin; Wands, David
2008-12-19
We show that simple scalar field models can give rise to curvature singularities in the effective Friedmann dynamics of loop quantum cosmology (LQC). We find singular solutions for spatially flat Friedmann-Robertson-Walker cosmologies with a canonical scalar field and a negative exponential potential, or with a phantom scalar field and a positive potential. While LQC avoids big bang or big rip type singularities, we find sudden singularities where the Hubble rate is bounded, but the Ricci curvature scalar diverges. We conclude that the effective equations of LQC are not in themselves sufficient to avoid the occurrence of curvature singularities.
Testing loop quantum cosmology
Wilson-Ewing, Edward
2017-03-01
Loop quantum cosmology predicts that quantum gravity effects resolve the big-bang singularity and replace it by a cosmic bounce. Furthermore, loop quantum cosmology can also modify the form of primordial cosmological perturbations, for example by reducing power at large scales in inflationary models or by suppressing the tensor-to-scalar ratio in the matter bounce scenario; these two effects are potential observational tests for loop quantum cosmology. In this article, I review these predictions and others, and also briefly discuss three open problems in loop quantum cosmology: its relation to loop quantum gravity, the trans-Planckian problem, and a possible transition from a Lorentzian to a Euclidean space-time around the bounce point.
Quantum Cosmology: Effective Theory
Bojowald, Martin
2012-01-01
Quantum cosmology has traditionally been studied at the level of symmetry-reduced minisuperspace models, analyzing the behavior of wave functions. However, in the absence of a complete full setting of quantum gravity and detailed knowledge of specific properties of quantum states, it remained difficult to make testable predictions. For quantum cosmology to be part of empirical science, it must allow for a systematic framework in which corrections to well-tested classical equations can be derived, with any ambiguities and ignorance sufficiently parameterized. As in particle and condensed-matter physics, a successful viewpoint is one of effective theories, adapted to specific issues one encounters in quantum cosmology. This review presents such an effective framework of quantum cosmology, taking into account, among other things, space-time structures, covariance, the problem of time and the anomaly issue.
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
Page, Don N
2011-01-01
The total canonical (Liouville-Henneaux-Gibbons-Hawking-Stewart) measure is finite for completely nonsingular Friedmann-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 FRW-Lambda-phi 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-revers...
Macroscopically-Discrete Quantum Cosmology
Chew, Geoffrey F
2008-01-01
To Milne's Lorentz-group-based spacetime and Gelfand-Naimark unitary representations of this group we associate a Fock space of 'cosmological preons'-quantum-theoretic universe constituents. Milne's 'cosmological principle' relies on Lorentz invariance of 'age'--global time. We divide Milne's spacetime into 'slices' of fixed macroscopic width in age, with 'cosmological rays' defined on (hyperbolic) slice boundaries-Fock space attaching only to these exceptional universe ages. Each (fixed-age) preon locates within a 6-dimensional manifold, one of whose 3 'extra' dimensions associates in Dirac sense to a self-adjoint operator that represents preon (continuous) local time, the operator canonically-conjugate thereto representing preon (total) energy. Self-adjoint-operator expectations at any spacetime-slice boundary prescribe throughout the following slice a non-fluctuating 'mundane reality'- electromagnetic and gravitational potentials 'tethered' to current densities of locally-conserved electric charge and ener...
Quantum cosmological metroland model
Anderson, E.; Franzen, A.T.
2010-01-01
Relational particle mechanics is useful for modelling whole-universe issues such as quantum cosmology or the problem of time in quantum gravity, including some aspects outside the reach of comparably complex mini-superspace models. In this paper, we consider the mechanics of pure shape and not scale
Bojowald, Martin
2016-01-01
A cosmological model with two global internal times shows that time reparameterization invariance, and therefore covariance, is not guaranteed by deparameterization. In particular, it is impossible to derive proper-time effective equations from a single deparameterized model if quantum corrections from fluctuations and higher moments are included. The framework of effective constraints shows how proper-time evolution can consistently be defined in quantum cosmological systems, such that it is time reparameterization invariant when compared with other choices of coordinate time. At the same time, it allows transformations of moment corrections in different deparameterizations of the same model, indicating partial time reparameterization of internal-time evolution. However, in addition to corrections from moments such as quantum fluctuations, also factor ordering corrections may appear. The latter generically break covariance in internal-time formulations. Fluctuation effects in quantum cosmology are therefore ...
Vidotto, Francesca
2015-01-01
The application of quantum theory to cosmology raises a number of conceptual questions, such as the role of the quantum-mechanical notion of "observer" or the absence of a time variable in the Wheeler-DeWitt equation. I point out that a relational formulation of quantum mechanics, and more in general the observation that evolution is always relational, provides a coherent solution to this tangle of problems.
Non-standard loop quantum cosmology
Piechocki, Wlodzimierz
2010-01-01
We present results concerning the nature of the cosmological big bounce(BB) transition within the loop geometry underlying loop quantum cosmology (LQC). Our canonical quantization method is an alternative to the standard LQC. An evolution parameter we use has clear interpretation both at classical and quantum levels. The physical volume operator has discrete spectrum which is bounded from below. The minimum gap in the spectrum defines a quantum of the volume. The spectra of operators are parametrized by a free parameter to be determined.
Group field cosmology: a cosmological field theory of quantum geometry
Calcagni, Gianluca; Oriti, Daniele
2012-01-01
Following the idea of a field quantization of gravity as realized in group field theory, we construct a minisuperspace model where the wavefunction of canonical quantum cosmology (either Wheeler-DeWitt or loop quantum cosmology) is promoted to a field, the coordinates are minisuperspace variables, the kinetic operator is the Hamiltonian constraint operator, and the action features a nonlinear and possibly nonlocal interaction term. We discuss free-field classical solutions, the quantum propagator, and a mean-field approximation linearizing the equation of motion and augmenting the Hamiltonian constraint by an effective term mixing gravitational and matter variables. Depending on the choice of interaction, this can reproduce, for example, a cosmological constant, a scalar-field potential, or a curvature contribution.
Noncommutative Quantum Cosmology
García-Compéan, H; Ramírez, C
2001-01-01
We propose a model for noncommutative quantum cosmology by means of a deformation of minisuperspace. For the Kantowski-Sachs metric we are able to find the exact solution to the deformed Wheeler-DeWitt equation. We construct wave packets and show that noncommutativity could remarkably modify the quantum behavior of the universe. We discuss the relation with space-time noncommutativity and exhibit a program to search for the influence of noncommutativity at early times in the universe.
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.
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.
Cosmological quantum entanglement
Martin-Martinez, Eduardo
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 trans...
Loop Quantum Cosmology Gravitational Baryogenesis
Odintsov, S D
2016-01-01
Loop Quantum Cosmology is an appealing quantum completion of classical cosmology, which brings along various theoretical features which in many cases offer remedy or modify various classical cosmology aspects. In this paper we address the gravitational baryogenesis mechanism in the context of Loop Quantum Cosmology. As we demonstrate, when Loop Quantum Cosmology effects are taken into account in the resulting Friedmann equations for a flat Friedmann-Robertson-Walker Universe, then even for a radiation dominated Universe, the predicted baryon-to-entropy ratio from the gravitational baryogenesis mechanism is non-zero, in contrast to the Einstein-Hilbert case, in which case the baryon-to-entropy ratio is zero. We also discuss various other cases apart from the radiation domination case, and we discuss how the baryon-to-entropy ratio is affected from the parameters of the quantum theory. In addition, we use illustrative exact solutions of Loop Quantum Cosmology and we investigate under which circumstances the bar...
Higher dimensional loop quantum cosmology
Zhang, Xiangdong
2016-07-01
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.
Holography from quantum cosmology
Rashki, M
2014-01-01
The Weyl-Wigner-Groenewold-Moyal formalism of deformation quantization is applied to the closed Friedmann-Lema\\^itre-Robertson-Walker (FLRW) cosmological model. We show that the phase space average for the surface of the apparent horizon is quantized in units of the Planck's surface, and that the total entropy of the universe is also quantized. Taking into account these two concepts, it is shown that 't Hooft conjecture on the cosmological holographic principle (CHP) in radiation and dust dominated quantum universes is satisfied as a manifestation of quantization. This suggests that the entire universe (not only inside the apparent horizon) can be seen as a two-dimensional information structure encoded on the apparent horizon.
$\\Psi$-Epistemic Quantum Cosmology?
Evans, Peter W; Thébault, Karim P Y
2016-01-01
This paper provides a prospectus for a new way of thinking about the wavefunction of the universe: a $\\Psi$-epistemic quantum cosmology. We present a proposal that, if successfully implemented, would resolve the cosmological measurement problem and simultaneously allow us to think sensibly about probability and evolution in quantum cosmology. Our analysis draws upon recent work on the problem of time in quantum gravity, upon causally-symmetric local hidden variable theories, and upon a dynamical origin for the cosmological arrow of time. Our conclusion weighs the strengths and weaknesses of the approach and points towards paths for future development.
Phenomenology of loop quantum cosmology
Sakellariadou, Mairi
2010-01-01
After introducing the basic ingredients of Loop Quantum Cosmology, I will briefly discuss some of its phenomenological aspects. Those can give some useful insight about the full Loop Quantum Gravity theory and provide an answer to some long-standing questions in early universe cosmology.
Quantum cosmological metroland model
Energy Technology Data Exchange (ETDEWEB)
Anderson, Edward [DAMTP, Cambridge (United Kingdom); Franzen, Anne, E-mail: ea212@cam.ac.u, E-mail: a.t.franzen@uu.n [Spinoza Institute, Utrecht (Netherlands)
2010-02-21
Relational particle mechanics is useful for modelling whole-universe issues such as quantum cosmology or the problem of time in quantum gravity, including some aspects outside the reach of comparably complex mini-superspace models. In this paper, we consider the mechanics of pure shape and not scale of four particles on a line, so that the only physically significant quantities are ratios of relative separations between the constituents' physical objects. Many of our ideas and workings extend to the N-particle case. As such models' configurations resemble depictions of metro lines in public transport maps, we term them 'N-stop metrolands'. This 4-stop model's configuration space is a 2-sphere, from which our metroland mechanics interpretation is via the 'cubic' tessellation. This model yields conserved quantities which are mathematically SO(3) objects like angular momenta but are physically relative dilational momenta (i.e. coordinates dotted with momenta). We provide and interpret various exact and approximate classical and quantum solutions for 4-stop metroland; from these results one can construct expectations and spreads of shape operators that admit interpretations as relative sizes and the 'homogeneity of the model universe's contents', and also objects of significance for the problem of time in quantum gravity (e.g. in the naive Schroedinger and records theory timeless approaches).
Mannelli, L
2005-01-01
The main theme of this Thesis is the connection between Quantum Gravity and Cosmology. In the First Part (Chapters 1 to 5) I give an introduction to the Holographic Principle. The Second Part is a collection of my research work and it is articulated as follows. Chapter 7 is to an analysis of the renormalization properties of quantum field theories in de Sitter space. It is shown that only two of the maximally invariant vacuum states of free fields lead to consistent perturbation expansions. In Chapter 8 I first present a complete quantum mechanical description of a flat FRW universe with equation of state p = ρ. Then I show a detailed correspondence with an heuristic picture of such a universe as a dense black hole fluid. In the end it is explained how features of the geometry are derived from purely quantum input. Chapter 9 studies the problem of infrared renormalization of particle masses in de Sitter space. It is shown, in a toy model in which the graviton is replaced with a minimally coupled massl...
The consistent histories approach to loop quantum cosmology
Craig, David A
2016-01-01
We review the application of the consistent (or decoherent) histories formulation of quantum theory to canonical loop quantum cosmology. Conventional quantum theory relies crucially on "measurements" to convert unrealized quantum potentialities into physical outcomes that can be assigned probabilities. In the early universe and other physical contexts in which there are no observers or measuring apparatus (or indeed, in any closed quantum system), what criteria determine which alternative outcomes may be realized and what their probabilities are? In the consistent histories formulation it is the vanishing of interference between the branch wave functions describing alternative histories -- as determined by the system's decoherence functional -- that determines which alternatives may be assigned probabilities. We describe the consistent histories formulation and how it may be applied to canonical loop quantum cosmology, describing in detail the application to homogeneous and isotropic cosmological models with ...
Hamiltonian cosmological perturbation theory with loop quantum gravity corrections
Bojowald, M; Kagan, M; Singh, P; Skirzewski, A; Bojowald, Martin; Hern\\'andez, Hector H.; Kagan, Mikhail; Singh, Parampreet; Skirzewski, Aureliano
2006-01-01
Cosmological perturbation equations are derived systematically in a canonical scheme based on Ashtekar variables. A comparison with the covariant derivation and various subtleties in the calculation and choice of gauges are pointed out. Nevertheless, the treatment is more systematic when correction terms of canonical quantum gravity are to be included. This is done throughout the paper for one characteristic modification expected from loop quantum gravity.
Noncommutative quantum cosmology
Energy Technology Data Exchange (ETDEWEB)
Bastos, C; Bertolami, O [Departamento de Fisica, Institute Superior Teico, Avenida Rovisco Pais 1, 1049-001 Lisboa (Portugal); Dias, N C; Prata, J N, E-mail: cbastos@fisica.ist.utl.p, E-mail: orfeu@cosmos.ist.utl.p, E-mail: ncdias@mail.telepac.p, E-mail: joao.prata@mail.telepac.p [Departamento de Matematica, Universidade Lusofona de Humanidades e Tecnologias, Avenida Campo Grande, 376, 1749-024 Lisboa (Portugal)
2009-06-01
We present a phase-space noncommutative extension of Quantum Cosmology in the context of a Kantowski-Sachs (KS) minisuperspace model. We obtain the Wheeler-DeWitt (WDW) equation for the noncommutative system through the ADM formalism and a suitable Seiberg-Witten map. The resulting WDW equation explicitly depends on the phase-space noncommutative parameters, theta and eta. Numerical solutions of the noncommutative WDW equation are found and, interestingly, also bounds on the values of the nonommutative parameters. Moreover, we conclude that the noncommutativity in the momenta sector lead to a damped wave function implying that this type of noncommutativity can be relevant for a selection of possible initial states for the universe.
BOOK REVIEW: Modern Canonical Quantum General Relativity
Kiefer, Claus
2008-06-01
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. In his own words: 'loop quantum gravity is an attempt to construct a mathematically rigorous, background-independent, non-perturbative quantum field theory of Lorentzian general relativity and all known matter in four spacetime dimensions, not more and not less'. 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
Notes in quantum noncommutativity in quantum cosmology
Energy Technology Data Exchange (ETDEWEB)
Oliveira-Neto, Gil de [Universidade Federal de Juiz de Fora (ICE/UFJF), MG (Brazil). Dept. de Fisica; Monerat, Germano A.; Silva, Eduardo V. Correa; Neves, Clifford; Ferreira Filho, Luiz G. [Universidade do Estado do Rio de Janeiro (FAT/UERJ), RJ (Brazil). Dept. de Matematica, Fisica e Computacao
2013-07-01
Full text: In the present work, we study the noncommutative version of a quantum cosmology model. The model has a Friedmann-Robertson-Walker (FRW) geometry, the matter content is a radiative perfect fluid and the spatial sections have positive constant curvatures. We work in the Schutz's variational formalism. The noncommutativity that we are about to propose is not the typical noncommutativity between usual spatial coordinates. We are describing a FRW model using the Hamiltonian formalism, therefore the present model phase space is given by the canonical variables and conjugated momenta:{ a, P_a, τ, P_τ}. Then, the noncommutativity, at the quantum level, we are about to propose will be between these phase space variables. Since these variables are functions of the time coordinate t, this procedure is a generalization of the typical noncommutativity between usual spatial coordinates. The noncommutativity between those types of phase space variables have already been proposed in the literature. We quantize the model and obtain the appropriate Wheeler-DeWitt equation. In this model the states are bounded therefore we compute the discrete energy spectrum and the corresponding eigenfunctions. The energies depend on a noncommutative parameter. We observe that, due to the boundary conditions, the noncommutativity forces the universe to start expanding from an initial scale factor greater than zero. We also notice that, one can only construct wave-packets if the noncommutative parameter is discrete, with a well-defined mathematical expression, in a certain region of its domain. (author)
Cosmological perturbations in teleparallel Loop Quantum Cosmology
Haro, Jaime
2013-01-01
Cosmological perturbations in Loop Quantum Cosmology (LQC) could be studied from two totally different ways. The first one, called holonomy corrected LQC, is performed in the Hamiltonian framework, where the Asthekar connection is replaced by a suitable sinus function (holonomy correction), in order to have a well-defined quantum analogue. The alternative approach is based in the fact that isotropic LQC could be also obtained as a particular case of teleparallel $F(T)$ gravity (teleparallel LQC). Then, working in the Lagrangian framework and using the well-know perturbation equations in $F(T)$ gravity, we have obtained, in teleparallel LQC, the equations for scalar and tensor perturbations, and the corresponding Mukhanov-Sasaki equations. For scalar perturbations, our equation only differs from the one obtained by holonomy corrections in the velocity of sound, leading both formulations, essentially to the same scale invariant power spectrum when a matter-dominated universe is considered. However for tensor pe...
Discrete canonical analysis of three dimensional gravity with cosmological constant
Berra-Montiel, J
2014-01-01
We discuss the interplay between standard canonical analysis and canonical discretization in three-dimensional gravity with cosmological constant. By using the Hamiltonian analysis, we find that the continuum local symmetries of the theory are given by the on-shell space-time diffeomorphisms, which at the action level, corresponds to the Kalb-Ramond transformations. At the time of discretization, although this symmetry is explicitly broken, we prove that the theory still preserves certain gauge freedom generated by a constant curvature relation in terms of holonomies and the Gauss's law in the lattice approach.
Phase-Space Noncommutative Quantum Cosmology
Bastos, Catarina; Dias, Nuno Costa; Prata, João Nuno
2007-01-01
We present a noncommutative extension of Quantum Cosmology and study the Kantowski-Sachs (KS) cosmological model requiring that the two scale factors of the KS metric, the coordinates of the system, and their conjugate canonical momenta do not commute. Through the ADM formalism, we obtain the Wheeler-DeWitt (WDW) equation for the noncommutative system. The Seiberg-Witten map is used to transform the noncommutative equation into a commutative one, i.e. into an equation with commutative variables, which depend on the noncommutative parameters, $\\theta$ and $\\eta$. Numerical solutions are found both for the classical and the quantum formulations of the system. These solutions are used to characterize the dynamics and the state of the universe. From the classical solutions we obtain the behavior of quantities such as the volume expansion, the shear and the characteristic volume. However the analysis of these quantities does not lead to any restriction on the value of the noncommutative parameters, $\\theta$ and $\\...
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.
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.
Classical and quantum cosmology of minimal massive bigravity
Darabi, F
2015-01-01
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's representations of perfect fluid and find the solutions. Moreover, we study the quantum cosmology using the canonical quantization procedure 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 cosmological considerations. Similar to the study of Hartle-Hawking no-boundary proposal in the quantum cosmology of de...
Quantum Cosmology for Tunneling Universes
Kim, Sang Pyo
2004-01-01
In a quantum cosmological model consisting of a Euclidean region and a Lorentzian region, Hartle-Hawking's no-bounary wave function, and Linde's wave function and Vilenkin's tunneling wave function are briefly described and compared with each other. We put a particular emphasis on semiclassical gravity from quantum cosmology and compare it with the conventional quantum field theory in curved spacetimes. Finally, we discuss the recent debate on catastrophic particle production in the tunneling universe between Rubakov and Vilenkin within the semiclassical gravity.
Consistent Histories in Quantum Cosmology
Craig, David A; 10.1007/s10701-010-9422-6
2010-01-01
We illustrate the crucial role played by decoherence (consistency of quantum histories) in extracting consistent quantum probabilities for alternative histories in quantum cosmology. Specifically, within a Wheeler-DeWitt quantization of a flat Friedmann-Robertson-Walker cosmological model sourced with a free massless scalar field, we calculate the probability that the univese is singular in the sense that it assumes zero volume. Classical solutions of this model are a disjoint set of expanding and contracting singular branches. A naive assessment of the behavior of quantum states which are superpositions of expanding and contracting universes may suggest that a "quantum bounce" is possible i.e. that the wave function of the universe may remain peaked on a non-singular classical solution throughout its history. However, a more careful consistent histories analysis shows that for arbitrary states in the physical Hilbert space the probability of this Wheeler-DeWitt quantum universe encountering the big bang/crun...
The quantum mechanics of cosmology.
Hartle, James B.
The following sections are included: * INTRODUCTION * POST-EVERETT QUANTUM MECHANICS * Probability * Probabilities in general * Probabilities in Quantum Mechanics * Decoherent Histories * Fine and Coarse Grained Histories * Decohering Sets of Coarse Grained Histories * No Moment by Moment Definition of Decoherence * Prediction, Retrodiction, and History * Prediction and Retrodiction * The Reconstruction of History * Branches (Illustrated by a Pure ρ) * Sets of Histories with the Same Probabilities * The Origins of Decoherence in Our Universe * On What Does Decoherence Depend? * Two Slit Model * The Caldeira-Leggett Oscillator Model * The Evolution of Reduced Density Matrices * Towards a Classical Domain * The Branch Dependence of Decoherence * Measurement * The Ideal Measurement Model and the Copenhagen Approximation to Quantum Mechanics * Approximate Probabilities Again * Complex Adaptive Systems * Open Questions * GENERALIZED QUANTUM MECHANICS * General Features * Hamiltonian Quantum Mechanics * Sum-Over-Histories Quantum Mechanics for Theories with a Time * Differences and Equivalences between Hamiltonian and Sum-Over-Histories Quantum Mechanics for Theories with a Time * Classical Physics and the Classical Limit of Quantum Mechanics * Generalizations of Hamiltonian Quantum Mechanics * TIME IN QUANTUM MECHANICS * Observables on Spacetime Regions * The Arrow of Time in Quantum Mechanics * Topology in Time * The Generality of Sum Over Histories Quantum Mechanics * THE QUANTUM MECHANICS OF SPACETIME * The Problem of Time * General Covariance and Time in Hamiltonian Quantum Mechanics * The "Marvelous Moment" * A Quantum Mechanics for Spacetime * What we Need * Sum-Over-Histories Quantum Mechanics for Theories Without a Time * Sum-Over-Spacetime-Histories Quantum Mechanics * Extensions and Contractions * The Construction of Sums Over Spacetime Histories * Some Open Questions * PRACTICAL QUANTUM COSMOLOGY * The Semiclassical Regime * The Semiclassical Approximation
Quantum Weyl invariance and cosmology
Directory of Open Access Journals (Sweden)
Atish Dabholkar
2016-09-01
Full Text Available Equations for cosmological evolution are formulated in a Weyl invariant formalism to take into account possible Weyl anomalies. Near two dimensions, the renormalized cosmological term leads to a nonlocal energy-momentum tensor and a slowly decaying vacuum energy. A natural generalization to four dimensions implies a quantum modification of Einstein field equations at long distances. It offers a new perspective on time-dependence of couplings and naturalness with potentially far-reaching consequences for the cosmological constant problem, inflation, and dark energy.
Quantum cosmology near two dimensions
Bautista, Teresa; Dabholkar, Atish
2016-08-01
We consider a Weyl-invariant formulation of gravity with a cosmological constant in d -dimensional spacetime and show that near two dimensions the classical action reduces to the timelike Liouville action. We show that the renormalized cosmological term leads to a nonlocal quantum momentum tensor which satisfies the Ward identities in a nontrivial way. The resulting evolution equations for an isotropic, homogeneous universe lead to slowly decaying vacuum energy and power-law expansion. We outline the implications for the cosmological constant problem, inflation, and dark energy.
Quantum Weyl invariance and cosmology
Dabholkar, Atish
2016-09-01
Equations for cosmological evolution are formulated in a Weyl invariant formalism to take into account possible Weyl anomalies. Near two dimensions, the renormalized cosmological term leads to a nonlocal energy-momentum tensor and a slowly decaying vacuum energy. A natural generalization to four dimensions implies a quantum modification of Einstein field equations at long distances. It offers a new perspective on time-dependence of couplings and naturalness with potentially far-reaching consequences for the cosmological constant problem, inflation, and dark energy.
Noncommutative Quantum Mechanics and Quantum Cosmology
Bastos, Catarina; Dias, Nuno; Prata, Joao Nuno
2009-01-01
We present a phase-space noncommutative version of quantum mechanics and apply this extension to Quantum Cosmology. We motivate this type of noncommutative algebra through the gravitational quantum well (GQW) where the noncommutativity between momenta is shown to be relevant. We also discuss some qualitative features of the GQW such as the Berry phase. In the context of quantum cosmology we consider a Kantowski-Sachs cosmological model and obtain the Wheeler-DeWitt (WDW) equation for the noncommutative system through the ADM formalism and a suitable Seiberg-Witten (SW) map. The WDW equation is explicitly dependent on the noncommutative parameters, $\\theta$ and $\\eta$. We obtain numerical solutions of the noncommutative WDW equation for different values of the noncommutative parameters. We conclude that the noncommutativity in the momenta sector leads to a damped wave function implying that this type of noncommmutativity can be relevant for a selection of possible initial states for the universe.
Quantum cosmology in an anisotropic n-dimensional universe
Alves-Júnior, F A P; Barreto, A B; Romero, C
2016-01-01
We investigate quantum cosmological models in an n-dimensional anisotropic universe in the presence of a massless scalar field. Our basic inspiration comes from Chodos and Detweiler's classical model which predicts an interesting behaviour of the extra dimension, shrinking down as time goes by. We work in the framework of a recent geometrical scalar-tensor theory of gravity. Classically, we obtain two distinct type of solutions. One of them has an initial singularity while the other represents a static universe considered as a whole. By using the canonical approach to quantum cosmology, we investigate how quantum effects could have had an influence in the past history of these universes.
Global canonical symmetry in a quantum system
Institute of Scientific and Technical Information of China (English)
李子平
1996-01-01
Based on the phase-space path integral for a system with a regular or singular Lagrangian the generalized canonical Ward identities under the global symmetry transformation in extended phase space are deduced respectively, thus the relations among Green functions can be found. The connection between canonical symmetries and conservation laws at the quantum level is established. It is pointed out that this connection in classical theories, in general, is no longer always preserved in quantum theories. The advantage of our formulation is that we do not need to carry out the integration over the canonical momenta in phase-space generating functional as usually performed. A precise discussion of quantization for a nonlinear sigma model with Hopf and Chern-Simons terms is reexamined. The property of fractional spin at quantum level has been clarified.
Quantum Cosmology of f( R, T) gravity
Xu, Min-Xing; Harko, Tiberiu; Liang, Shi-Dong
2016-08-01
Modified gravity theories have the potential of explaining the recent acceleration of the Universe without resorting to the mysterious concept of dark energy. In particular, it has been pointed out that matter-geometry coupling may be responsible for the recent cosmological dynamics of the Universe, and matter itself may play a more fundamental role in the description of the gravitational processes that usually assumed. In the present paper we study the quantum cosmology of the f( R, T) theory of gravity, in which the effective Lagrangian of the gravitational field is given by an arbitrary function of the Ricci scalar, and the trace of the matter energy-momentum tensor, respectively. For the background geometry we adopt the Friedmann-Robertson-Walker metric, and we assume that matter content of the Universe consists of a perfect fluid. In this framework we obtain the general form of the gravitational Hamiltonian, of the quantum potential, and of the canonical momenta, respectively. This allows us to formulate the full Wheeler-de Witt equation describing the quantum properties of this modified gravity model. As a specific application we consider in detail the quantum cosmology of the f(R,T)=F^0(R)+θ RT model, in which F^0(R) is an arbitrary function of the Ricci scalar, and θ is a function of the scale factor only. The Hamiltonian form of the equations of motion, and the Wheeler-de Witt equations are obtained, and a time parameter for the corresponding dynamical system is identified, which allows one to formulate the Schrödinger-Wheeler-de Witt equation for the quantum-mechanical description of the model under consideration. A perturbative approach for the study of this equation is developed, and the energy levels of the Universe are obtained by using a twofold degenerate perturbation approach. A second quantization approach for the description of quantum time is also proposed and briefly discussed.
Uncertainty Principle in Loop Quantum Cosmology by Moyal Formalism
Perlov, Leonid
2016-01-01
In this paper we derive the uncertainty principle for the Loop Quantum Cosmology homogeneous and isotropic FLWR model with the holonomy-flux algebra. In our derivation we use the Wigner-Moyal-Groenewold phase space formalism. The formalism uses the characteristic functions and the Wigner transform, which maps the quantum operators to the functions on the phase space. The Wigner-Moyal-Groenewold formalism was originally applied to the Heisenberg algebra of the Quantum Mechanics. One can derive from it both the canonical and path integral QM as well as the uncertainty principle. In this paper we apply the phase-space formalism to the quantum cosmology holonomy-flux algebra in case of the homogeneous and isotropic space to obtain the Loop Quantum Cosmology uncertainty principle.
Canonical Quantum Gravity on Noncommutative Spacetime
Kober, Martin
2014-01-01
In this paper canonical quantum gravity on noncommutative space-time is considered. The corresponding generalized classical theory is formulated by using the moyal star product, which enables the representation of the field quantities depending on noncommuting coordinates by generalized quantities depending on usual coordinates. But not only the classical theory has to be generalized in analogy to other field theories. Besides, the necessity arises to replace the commutator between the gravitational field operator and its canonical conjugated quantity by a corresponding generalized expression on noncommutative space-time. Accordingly the transition to the quantum theory has also to be performed in a generalized way and leads to extended representations of the quantum theoretical operators. If the generalized representations of the operators are inserted to the generalized constraints, one obtains the corresponding generalized quantum constraints including the Hamiltonian constraint as dynamical constraint. Af...
Loop quantum cosmology: Recent progress
Indian Academy of Sciences (India)
Martin Bojowald
2004-10-01
Aspects of the full theory of loop quantum gravity can be studied in a simpler context by reducing to symmetric models like cosmological ones. This leads to several applications where loop effects play a significant role when one is sensitive to the quantum regime. As a consequence, the structure of and the approach to classical singularities are very different from general relativity. The quantum theory is free of singularities, and there are new phenomenological scenarios for the evolution of the very early universe such as inflation. We give an overview of the main effects, focussing on recent results obtained by different groups.
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.
Canonical transforms, quantumness and probability representation of quantum mechanics
Man'ko, Margarita A
2011-01-01
The linear canonical transforms of position and momentum are used to construct the tomographic probability representation of quantum states where the fair probability distribution determines the quantum state instead of the wave function or density matrix. The example of Moshinsky shutter problem is considered.
The consistent histories approach to loop quantum cosmology
Craig, David A.
2016-06-01
We review the application of the consistent (or decoherent) histories formulation of quantum theory to canonical loop quantum cosmology. Conventional quantum theory relies crucially on “measurements” to convert unrealized quantum potentialities into physical outcomes that can be assigned probabilities. In the early universe and other physical contexts in which there are no observers or measuring apparatus (or indeed, in any closed quantum system), what criteria determine which alternative outcomes may be realized and what their probabilities are? In the consistent histories formulation it is the vanishing of interference between the branch wave functions describing alternative histories — as determined by the system’s decoherence functional — that determines which alternatives may be assigned probabilities. We describe the consistent histories formulation and how it may be applied to canonical loop quantum cosmology, describing in detail the application to homogeneous and isotropic cosmological models with scalar matter. We show how the theory may be used to make definite physical predictions in the absence of “observers”. As an application, we demonstrate how the theory predicts that loop quantum models “bounce” from large volume to large volume, while conventional “Wheeler-DeWitt”-quantized universes are invariably singular. We also briefly indicate the relation to other work.
Loop Quantum Cosmology on a Torus
Lamon, Raphael
2009-01-01
In this paper we study the effect of a torus topology on Loop Quantum Cosmology. We first derive the Teichmueller space parametrizing all possible tori using Thurston's theorem and construct a Hamiltonian describing the dynamics of these torus universes. We then compute the Ashtekar variables for a slightly simplified torus such that the Gauss constraint can be solved easily. We perform a canonical transformation so that the holomies along the edges of the torus reduce to a product between almost and strictly periodic functions of the new variables. The drawback of this transformation is that the components of the densitized triad become complicated functions of these variables. Nevertheless we find two ways of quantizing these components, which in both cases leads surprisingly to a continuous spectrum.
Quantum Cosmological Perturbations of Multiple Fluids
Peter, Patrick; Vitenti, Sandro Dias Pinto
2015-01-01
The formalism to treat quantization and evolution of cosmological perturbations of multiple fluids is described. We first construct the Lagrangian for both the gravitational and matter parts, providing the necessary relevant variables and momenta leading to the quadratic Hamiltonian describing linear perturbations. The final Hamiltonian is obtained without assuming any equations of motions for the background variables. This general formalism is applied to the special case of two fluids, having in mind the usual radiation and matter mix which made most of our current Universe history. Quantization is achieved using an adiabatic expansion of the basis functions. This allows for an unambiguous definition of a vacuum state up to the given adiabatic order. Using this basis, we show that particle creation is well defined for a suitable choice of vacuum and canonical variables, so that the time evolution of the corresponding quantum fields is unitary. This provides constraints for setting initial conditions for an a...
Inflation and Loop Quantum Cosmology
Barrau, Aurelien
2010-01-01
On the one hand, inflation is an extremely convincing scenario: it solves most cosmological paradoxes and generates fluctuations that became the seeds for the growth of structures. It, however, suffers from a "naturalness" problem: generating initial conditions for inflation is far from easy. On the other hand, loop quantum cosmology is very successful: it solves the Big Bang singularity through a non-perturbative and background-independent quantization of general relativity. It, however, suffers from a key drawback: it is extremely difficult to test. Recent results can let us hope that inflation and LQC could mutually cure those pathologies: LQC seems to naturally generate inflation and inflation could allow us to test LQC.
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.
Saharian, A. A.
2016-09-01
We investigate the vacuum expectation value of the current density for a charged scalar field on a slice of anti-de Sitter (AdS) space with toroidally compact dimensions. Along the compact dimensions periodicity conditions are imposed on the field operator with general phases and the presence of a constant gauge field is assumed. The latter gives rise to Aharonov-Bohm-like effects on the vacuum currents. The current density along compact dimensions is a periodic function of the gauge field flux with the period equal to the flux quantum. It vanishes on the AdS boundary and, near the horizon, to the leading order, it is conformally related to the corresponding quantity in Minkowski bulk for a massless field. For large values of the length of the compact dimension compared with the AdS curvature radius, the vacuum current decays as power-law for both massless and massive fields. This behavior is essentially different from the corresponding one in Minkowski background, where the currents for a massive field are suppressed exponentially.
Kato expansion in quantum canonical perturbation theory
Nikolaev, A S
2015-01-01
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 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. The corresponding computational algorithm is more efficient for high perturbative orders than the algorithms of Van Vleck and Magnus methods.
Kato expansion in quantum canonical perturbation theory
Nikolaev, Andrey
2016-06-01
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.
Quantum Hamilton-Jacobi Cosmology and Classical-Quantum Correlation
Fathi, M.; Jalalzadeh, S.
2017-07-01
How the time evolution which is typical for classical cosmology emerges from quantum cosmology? The answer is not trivial because the Wheeler-DeWitt equation is time independent. A framework associating the quantum Hamilton-Jacobi to the minisuperspace cosmological models has been introduced in Fathi et al. (Eur. Phys. J. C 76, 527 2016). In this paper we show that time dependence and quantum-classical correspondence both arise naturally in the quantum Hamilton-Jacobi formalism of quantum mechanics, applied to quantum cosmology. We study the quantum Hamilton-Jacobi cosmology of spatially flat homogeneous and isotropic early universe whose matter content is a perfect fluid. The classical cosmology emerge around one Planck time where its linear size is around a few millimeter, without needing any classical inflationary phase afterwards to make it grow to its present size.
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.
Arithmetical Chaos and Quantum Cosmology
Forte, Luca Antonio
2008-01-01
In this note, we present the formalism to start a quantum analysis for the recent billiard representation introduced by Damour, Henneaux and Nicolai in the study of the cosmological singularity. In particular we use the theory of Maass automorphic forms and recent mathematical results about arithmetical dynamical systems. The predictions of the billiard model give precise automorphic properties for the wave function (Maass-Hecke eigenform), the asymptotic number of quantum states (Selberg asymptotics for PSL(2,Z)), the distribution for the level spacing statistics (the Poissonian one) and the absence of scarred states. The most interesting implication of this model is perhaps that the discrete spectrum is fully embedded in the continuous one.
Nonlocal Quantum Effects in Cosmology
Dumin, Yurii V
2014-01-01
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 du...
Will Quantum Cosmology Resurrect Chaotic Inflation Model?
Kim, Sang Pyo; Kim, Won
2016-07-01
The single field chaotic inflation model with a monomial power greater than one seems to be ruled out by the recent Planck and WMAP CMB data while Starobinsky model with a higher curvature term seems to be a viable model. Higher curvature terms being originated from quantum fluctuations, we revisit the quantum cosmology of the Wheeler-DeWitt equation for the chaotic inflation model. The semiclassical cosmology emerges from quantum cosmology with fluctuations of spacetimes and matter when the wave function is peaked around the semiclassical trajectory with quantum corrections a la the de Broglie-Bohm pilot theory.
Will quantum cosmology resurrect chaotic inflation model?
Kim, Sang Pyo
2016-01-01
The single field chaotic inflation model with a monomial power greater than one seems to be ruled out by the recent Planck and WMAP CMB data while Starobinsky model with a higher curvature term seems to be a viable model. Higher curvature terms being originated from quantum fluctuations, we revisit the quantum cosmology of the Wheeler-DeWitt equation for the chaotic inflation model. The semiclassical cosmology emerges from quantum cosmology with fluctuations of spacetimes and matter when the wave function is peaked around the semiclassical trajectory with quantum corrections a la the de Broglie-Bohm pilot theory.
Quantum cosmology and the evolution of inflationary spectra
Kamenshchik, Alexander Y.; Tronconi, Alessandro; Venturi, Giovanni
2016-12-01
We illustrate how it is possible to calculate the quantum gravitational effects on the spectra of primordial scalar/tensor perturbations starting from the canonical, Wheeler-De Witt, approach to quantum cosmology. The composite matter-gravity system is analyzed through a Born-Oppenheimer approach in which gravitation is associated with the heavy degrees of freedom and matter (here represented by a scalar field) with the light ones. Once the independent degrees of freedom are identified, the system is canonically quantized and a semiclassical approximation is used for the scale factor. The differential equation governing the dynamics of the primordial spectra with their quantum-gravitational corrections is then obtained and is applied to diverse inflationary evolutions. Finally, the analytical results are compared to observations through a Monte Carlo Markov chain technique and an estimate of the free parameters of our approach is finally presented and the results obtained are compared with previous ones.
Quantum Cosmology and the Evolution of Inflationary Spectra
Kamenshchik, Alexander Y; Venturi, Giovanni
2016-01-01
We illustrate how it is possible to calculate the quantum gravitational effects on the spectra of primordial scalar/tensor perturbations starting from the canonical, Wheeler-De Witt, approach to quantum cosmology. The composite matter-gravity system is analysed through a Born-Oppenheimer approach in which gravitation is associated with the heavy degrees of freedom and matter (here represented by a scalar field) with the light ones. Once the independent degrees of freedom are identified the system is canonically quantised. The differential equation governing the dynamics of the primordial spectra with its quantum-gravitational corrections is then obtained and is applied to diverse inflationary evolutions. Finally, the analytical results are compared to observations through a Monte Carlo Markov Chain technique and an estimate of the free parameters of our approach is finally presented and the results obtained are compared with previous ones.
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.)
Quantum supersymmetric Bianchi IX cosmology
Damour, Thibault; Spindel, Philippe
2014-11-01
We study the quantum dynamics of a supersymmetric squashed three-sphere by dimensionally reducing (to one timelike dimension) the action of D =4 simple supergravity for a S U (2 ) -homogeneous (Bianchi IX) cosmological model. The quantization of the homogeneous gravitino field leads to a 64-dimensional fermionic Hilbert space. After imposition of the diffeomorphism constraints, the wave function of the Universe becomes a 64-component spinor of spin(8,4) depending on the three squashing parameters, which satisfies Dirac-like, and Klein-Gordon-like, wave equations describing the propagation of a "quantum spinning particle" reflecting off spin-dependent potential walls. The algebra of the supersymmetry constraints and of the Hamiltonian one is found to close. One finds that the quantum Hamiltonian is built from operators that generate a 64-dimensional representation of the (infinite-dimensional) maximally compact subalgebra of the rank-3 hyperbolic Kac-Moody algebra A E3 . The (quartic-in-fermions) squared-mass term μ^ 2 entering the Klein-Gordon-like equation has several remarkable properties: (i) it commutes with all the other (Kac-Moody-related) building blocks of the Hamiltonian; (ii) it is a quadratic function of the fermion number NF; and (iii) it is negative in most of the Hilbert space. The latter property leads to a possible quantum avoidance of the singularity ("cosmological bounce"), and suggests imposing the boundary condition that the wave function of the Universe vanish when the volume of space tends to zero (a type of boundary condition which looks like a final-state condition when considering the big crunch inside a black hole). The space of solutions is a mixture of "discrete-spectrum states" (parametrized by a few constant parameters, and known in explicit form) and of continuous-spectrum states (parametrized by arbitrary functions entering some initial-value problem). The predominantly negative values of the squared-mass term lead to a "bottle
Quantum Supersymmetric Bianchi IX Cosmology
Damour, Thibault
2014-01-01
We study the quantum dynamics of a supersymmetric squashed three-sphere by dimensionally reducing to one timelike dimension the action of D=4 simple supergravity for a Bianchi IX cosmological model. After imposition of the diffeomorphism constraints, the wave function of the Universe becomes a spinor of Spin(8,4) depending on the three squashing parameters, which satisfies Dirac, and Klein-Gordon-like, wave equations describing the propagation of a quantum spinning particle reflecting off spin-dependent potential walls. The algebra of the susy constraints and of the Hamiltonian one is found to close. One finds that the quantum Hamiltonian is built from operators that generate a 64-dimensional representation of the maximally compact sub-algebra of the rank-3 hyperbolic Kac-Moody algebra AE3. The (quartic-in-fermions) squared-mass term entering the Klein-Gordon-like equation has several remarkable properties: 1)it commutes with all the other (Kac-Moody-related) building blocks of the Hamiltonian; 2)it is a quad...
A Cosmological Sector in Loop Quantum Gravity
Koslowski, Tim A
2007-01-01
We use the method of embedding a subsystem (i.e. its observable algebra) into a larger quantum system to extract a cosmological sector from full Loop Quantum Gravity. The application of this method provides a setting for a systematic study of the interplay between diffeomorphism invariance and symmetry reduction. The non-triviality of this relation is shown by extracting a cosmological system that has configurations variables that are very similar to the ones of a super-selection sector of standard Loop Quantum Cosmology. The full operator algebra however turns out to be different from standard Loop Quantum Cosmology. The homogeneous isotropic sector of pure gravity turns out to be quantum mechanics on a circle. The dynamics of our system seems pathological at first sight, and we give both mathematical and physical reasons for this behavior and we explain a strategy to cure these pathologies.
Inflation in multidimensional quantum cosmology
Carugno, E; Occhionero, F; Pollifrone, G; Carugno, Enrico; Litterio, Marco; Occhionero, Franco; Pollifrone, Giuseppe
1996-01-01
We extend to multidimensional cosmology Vilenkin's prescription of tunnelling from nothing for the quantum origin of the observable Universe. Our model consists of a D+4-dimensional spacetime of topology {\\cal R}\\times {\\cal S}^3 \\times{\\cal S}^D, with a scalar field (``chaotic inflaton'') for the matter component. Einstein gravity and Casimir compactification are assumed. The resulting minisuperspace is 3--dimensional. Patchwise we find an approximate analytic solution of the Wheeler--DeWitt equation through which we discuss the tunnelling picture and the probability of nucleation of the classical Universe with compactifying extra dimensions. Our conclusion is that the most likely initial conditions, although they do not lead to the compactification of the internal space, still yield (power-law) inflation for the outer space. The scenario is physically acceptable because the inner space growth is limited to \\sim 10^{11} in 100 e-foldings of inflation, starting from the Planck scale.
Introductory Lectures on Quantum Cosmology (1990)
Halliwell, J J
2009-01-01
We describe the modern approach to quantum cosmology, as initiated by Hartle and Hawking, Linde, Vilenkin and others. The primary aim is to explain how one determines the consequences for the late universe of a given quantum theory of cosmological initial or boundary conditions. An extensive list of references is included, together with a guide to the literature. It also includes a detailed treatment of the WKB interpretation, which is relevant to a forthcoming article by the author on the decoherent histories approach to quantum cosmology.
The Early Universe in Loop Quantum Cosmology
Bojowald, M.
2005-01-01
Loop quantum cosmology applies techniques derived for a background independent quantization of general relativity to cosmological situations and draws conclusions for the very early universe. Direct implications for the singularity problem as well as phenomenology in the context of inflation or bouncing universes result, which will be reviewed here. The discussion focuses on recent new results for structure formation and generalizations of the methods.
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 Exclusion of Positive Cosmological Constant?
Dvali, Gia
2014-01-01
We show that a positive cosmological constant is incompatible with the quantum-corpuscular resolution of de Sitter metric in form of a coherent state. The reason is very general and is due to the quantum self-destruction of the coherent state because of the scattering of constituent graviton quanta. This process creates an irreversible quantum clock, which precludes eternal de Sitter. It also eliminates the possibility of Boltzmann brains and Poincare recurrences. This effect is expected to be part of any microscopic theory that takes into account the quantum corpuscular structure of the cosmological background. This observation puts the cosmological constant problem in a very different light, promoting it, from a naturalness problem, into a question of quantum consistency. We are learning that quantum gravity cannot tolerate exceedingly-classical sources.
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.
Quantum cosmological perturbations of multiple fluids
Peter, Patrick; Pinto-Neto, N.; Vitenti, Sandro D. P.
2016-01-01
The formalism to treat quantization and evolution of cosmological perturbations of multiple fluids is described. We first construct the Lagrangian for both the gravitational and matter parts, providing the necessary relevant variables and momenta leading to the quadratic Hamiltonian describing linear perturbations. The final Hamiltonian is obtained without assuming any equations of motions for the background variables. This general formalism is applied to the special case of two fluids, having in mind the usual radiation and matter mix which made most of our current Universe history. Quantization is achieved using an adiabatic expansion of the basis functions. This allows for an unambiguous definition of a vacuum state up to the given adiabatic order. Using this basis, we show that particle creation is well defined for a suitable choice of vacuum and canonical variables, so that the time evolution of the corresponding quantum fields is unitary. This provides constraints for setting initial conditions for an arbitrary number of fluids and background time evolution. We also show that the common choice of variables for quantization can lead to an ill-defined vacuum definition. Our formalism is not restricted to the case where the coupling between fields is small, but is only required to vary adiabatically with respect to the ultraviolet modes, thus paving the way to consistent descriptions of general models not restricted to single-field (or fluid).
Loop Quantum Cosmology: Anisotropy and singularity resolution
Corichi, Alejandro; Montoya, Edison
2012-01-01
In this contribution we consider the issue of singularity resolution within loop quantum cosmology (LQC) for different homogeneous models. We present results of numerical evolutions of effective equations for both isotropic as well as anisotropic cosmologies, with and without spatial curvature. To address the issue of singularity resolution we examine the time evolution of geometrical and curvature invariants that yield information about the semiclassical spacetime geometry. We discuss generic behavior found for a variety of initial conditions. Finally, we show that the modifications which come from Loop Quantum Cosmology imply a non-chaotic effective behavior in the vacuum Bianchi IX model.
Loop Quantum Cosmology and the CMB
Agullo, Ivan
2017-01-01
This talk will provide an up-to-date summary of phenomenological explorations in loop quantum cosmology. The possibility of a quantum gravity origin of the anomalies observed in the cosmic microwave background at large angular scales will be discussed. The talk will also provide some background material for subsequent contributions in the same session. NSF PHYS-1403943.
Exact Classical Correspondence in Quantum Cosmology
John, Moncy V
2014-01-01
We find a Friedmann model with appropriate matter/energy density such that the solution of the Wheeler-DeWitt equation exactly corresponds to the classical evolution. The well-known problems in quantum cosmology disappear in the resulting coasting evolution. The exact quantum-classical correspondence is demonstrated with the help of the de Broglie-Bohm and modified de Broglie-Bohm approaches to quantum mechanics. It is reassuring that such a solution leads to a robust model for the universe, which agrees well with cosmological expansion indicated by SNe Ia data.
The Quantum Information of Cosmological Correlations
Lim, Eugene A
2014-01-01
It has been shown that the primordial perturbations sourced by inflation are driven to classicality by unitary evolution alone. However, their coupling with the environment such as photons and subsequent decoherence renders the cosmological correlations quantum, losing primordial information in the process. We argue that the quantumness of the resulting cosmological correlations is given by quantum discord, which captures non-classical behavior beyond quantum entanglement. By considering the environment as a quantum channel in which primordial information contained in the perturbations is transmitted to us, we can then ask how much of this information is inaccessible. We show that this amount of information is given by the discord of the joint primordial perturbations-environment system. To illustrate these points, we model the joint system as a mixed bi-modal Gaussian state, and show that quantum discord is dependent on the basis which decoherence occurs.
Loop quantum cosmology and the fate of cosmological singularities
Singh, Parampreet
2015-01-01
Singularities in general relativity such as the big bang and big crunch, and exotic singularities such as the big rip are the boundaries of the classical spacetimes. These events are marked by a divergence in the curvature invariants and the breakdown of the geodesic evolution. Recent progress on implementing techniques of loop quantum gravity to cosmological models reveals that such singularities may be generically resolved because of the quantum gravitational effects. Due to the quantum geometry, which replaces the classical differential geometry at the Planck scale, the big bang is replaced by a big bounce without any assumptions on the matter content or any fine tuning. In this manuscript, we discuss some of the main features of this approach and the results on the generic resolution of singularities for the isotropic as well as anisotropic models. Using effective spacetime description of the quantum theory, we show the way quantum gravitational effects lead to the universal bounds on the energy density, ...
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...
Some Recent Advances in Loop Quantum Cosmology
Ashtekar, Abhay
2012-05-01
In my talk I discussed three recent advances in loop quantum cosmology: 1) Path integral formulation and its WKB approximation; 2) Cosmological spin foams and lessons they provide; and 3) Probability of a slow roll inflationary phase compatible with the 7 year WMAP data. In addition to presenting an overview, this discussion also provides the necessary background for a number of talks in the parallel sessions.
Cosmological perturbation theory and quantum gravity
Brunetti, Romeo; Hack, Thomas-Paul; Pinamonti, Nicola; Rejzner, Katarzyna
2016-01-01
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.
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.
Matrix product purifications for canonical ensembles and quantum number distributions
Barthel, Thomas
2016-09-01
Matrix product purifications (MPPs) are a very efficient tool for the simulation of strongly correlated quantum many-body systems at finite temperatures. When a system features symmetries, these can be used to reduce computation costs substantially. It is straightforward to compute an MPP of a grand-canonical ensemble, also when symmetries are exploited. This paper provides and demonstrates methods for the efficient computation of MPPs of canonical ensembles under utilization of symmetries. Furthermore, we present a scheme for the evaluation of global quantum number distributions using matrix product density operators (MPDOs). We provide exact matrix product representations for canonical infinite-temperature states, and discuss how they can be constructed alternatively by applying matrix product operators to vacuum-type states or by using entangler Hamiltonians. A demonstration of the techniques for Heisenberg spin-1 /2 chains explains why the difference in the energy densities of canonical and grand-canonical ensembles decays as 1 /L .
Nandi, Debottam; Shankaranarayanan, S.
2016-10-01
In this work, we present a consistent Hamiltonian analysis of cosmological perturbations for generalized non-canonical scalar fields. In order to do so, we introduce a new phase-space variable that is uniquely defined for different non-canonical scalar fields. We also show that this is the simplest and efficient way of expressing the Hamiltonian. We extend the Hamiltonian approach of [1] to non-canonical scalar field and obtain an unique expression of speed of sound in terms of phase-space variable. In order to invert generalized phase-space Hamilton's equations to Euler-Lagrange equations of motion, we prescribe a general inversion formulae and show that our approach for non-canonical scalar field is consistent. We also obtain the third and fourth order interaction Hamiltonian for generalized non-canonical scalar fields and briefly discuss the extension of our method to generalized Galilean scalar fields.
Nandi, Debottam
2016-01-01
In this work, we present a consistent Hamiltonian analysis of cosmological perturbations for generalized non-canonical scalar fields. In order to do so, we introduce a new phase-space variable that is uniquely defined for different non-canonical scalar fields. We also show that this is the simplest and efficient way of expressing the Hamiltonian. We extend the Hamiltonian approach of [arXiv:1512.02539] to non-canonical scalar field and obtain a new definition of speed of sound in phase-space. In order to invert generalized phase-space Hamilton's equations to Euler-Lagrange equations of motion, we prescribe a general inversion formulae and show that our approach for non-canonical scalar field is consistent. We also obtain the third and fourth order interaction Hamiltonian for generalized non-canonical scalar fields and briefly discuss the extension of our method to generalized Galilean scalar fields.
Rainbow metric from quantum gravity: anisotropic cosmology
Assanioussi, Mehdi
2016-01-01
In this paper we present a construction of effective cosmological models which describe the propagation of a massive quantum scalar field on a quantum anisotropic cosmological spacetime. Each obtained effective model is represented by a rainbow metric in which particles of distinct momenta propagate on different classical geometries. Our analysis shows that upon certain assumptions and conditions on the parameters determining such anisotropic models, we surprisingly obtain a unique deformation parameter $\\beta$ in the modified dispersion relation of the modes. Hence inducing an isotropic deformation despite the general starting considerations. We then ensure the recovery of the dispersion relation realized in the isotropic case, studied in [arXiv:1412.6000], when some proper symmetry constraints are imposed, and we estimate the value of the deformation parameter for this case in loop quantum cosmology context.
Rainbow metric from quantum gravity: Anisotropic cosmology
Assanioussi, Mehdi; Dapor, Andrea
2017-03-01
In this paper we present a construction of effective cosmological models which describe the propagation of a massive quantum scalar field on a quantum anisotropic cosmological spacetime. Each obtained effective model is represented by a rainbow metric in which particles of distinct momenta propagate on different classical geometries. Our analysis shows that upon certain assumptions and conditions on the parameters determining such anisotropic models, we surprisingly obtain a unique deformation parameter β in the modified dispersion relation of the modes, hence, inducing an isotropic deformation despite the general starting considerations. We then ensure the recovery of the dispersion relation realized in the isotropic case, studied in [M. Assanioussi, A. Dapor, and J. Lewandowski, Phys. Lett. B 751, 302 (2015), 10.1016/j.physletb.2015.10.043], when some proper symmetry constraints are imposed, and we estimate the value of the deformation parameter for this case in loop quantum cosmology context.
Quantum cosmological consistency condition for inflation
Energy Technology Data Exchange (ETDEWEB)
Calcagni, Gianluca [Instituto de Estructura de la Materia, CSIC, calle Serrano 121, 28006 Madrid (Spain); Kiefer, Claus [Institut für Theoretische Physik, Universität zu Köln, Zülpicher Strasse 77, 50937 Köln (Germany); Steinwachs, Christian F., E-mail: calcagni@iem.cfmac.csic.es, E-mail: kiefer@thp.uni-koeln.de, E-mail: christian.steinwachs@physik.uni-freiburg.de [Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Hermann-Herder-Str. 3, 79104 Freiburg (Germany)
2014-10-01
We investigate the quantum cosmological tunneling scenario for inflationary models. Within a path-integral approach, we derive the corresponding tunneling probability distribution. A sharp peak in this distribution can be interpreted as the initial condition for inflation and therefore as a quantum cosmological prediction for its energy scale. This energy scale is also a genuine prediction of any inflationary model by itself, as the primordial gravitons generated during inflation leave their imprint in the B-polarization of the cosmic microwave background. In this way, one can derive a consistency condition for inflationary models that guarantees compatibility with a tunneling origin and can lead to a testable quantum cosmological prediction. The general method is demonstrated explicitly for the model of natural inflation.
Quantum cosmological consistency condition for inflation
Calcagni, Gianluca; Steinwachs, Christian F
2014-01-01
We investigate the quantum cosmological tunneling scenario for inflationary models. Within a path-integral approach, we derive the corresponding tunneling probability distribution. A sharp peak in this distribution can be interpreted as the initial condition for inflation and therefore as a quantum cosmological prediction for its energy scale. This energy scale is also a genuine prediction of any inflationary model by itself, as the primordial gravitons generated during inflation leave their imprint in the B-polarization of the cosmic microwave background. In this way, one can derive a consistency condition for inflationary models that guarantees compatibility with a tunneling origin and can lead to a testable quantum cosmological prediction. The general method is demonstrated explicitly for the model of natural inflation.
Squeezed Wave Packets in Quantum Cosmology
Pedram, Pouria
2010-11-01
We use an appropriate initial condition for constructing squeezed wave packets in the context of Wheeler-DeWitt equation with complete classical description. This choice of initial condition does not alter the classical paths and only affect the quantum mechanical picture. To demonstrate the method, we consider an empty 4+1-dimensional Kaluza-Klein quantum cosmology in the presence of a negative cosmological constant. We show that these wave packets do not disperse and sharply peak on the classical trajectories in the whole configuration space. So, the probability of finding the corresponding physical quantities approaches zero everywhere except on the classical paths.
Third Quantization and Quantum Cosmology.
McGuigan, Michael Deturck
My thesis consists of three separate parts. Part one consists of a study of CP violation in the Kaon decay: K to pi pi gamma . To study the short distance contribution to the matrix element we developed an operator expansion for the effective Hamiltonian. An effective s to dgamma vertex arises through operator mixing. We evaluated several two-loop graphs in order to obtain the coefficient of this operator. We studied the long distance contributions to the matrix element and demonstrated that this was the dominant contribution. This explained why the polarization of the emitted photon is primarily of the magnetic type. Part two of my thesis involves the treatment of string theory at finite temperature. We introduced finite temperature into string theory by compactifying time on a twisted torus of radius beta = 1/kT, the reciprical of the temperature. The twisted torus takes into account the different thermal properties of bosons and fermions. We computed the one-loop vacuum amplitude Lambda(beta) on a twisted torus which is manifestly modular invariant. We found that lnZ(beta) = -betaVLambda (beta) where Z(beta) is the partition function and V the volume of the system. We computed the function sigma(E) which counts the number of multi-string states of total energy E by taking the inverse Laplace transform of Z( beta). We also studied the effect of finite temperature on the effective potentials which determine a string theory's compactification. The third part of my thesis involved the Wheeler DeWitt equation and a new interpretation of quantum cosmology. We examined a proposal by DeWitt for the normalization of solutions to the Wheeler-DeWitt equation. We avoided negative probability problems with this proposal by reinterpreting the Wheeler-DeWitt wave function as a second quantized field. As the arguments of the Wheeler-DeWitt wave functional are second quantized fields this represented a third quantization. We developed a mode decomposition for the third quantized
Quantum Cosmology of f(R, T) gravity
Energy Technology Data Exchange (ETDEWEB)
Xu, Min-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); Guangdong Province Key Laboratory of Display Material and Technology, State Key Laboratory of Optoelectronic Material and Technology, Guangzhou (China)
2016-08-15
Modified gravity theories have the potential of explaining the recent acceleration of the Universe without resorting to the mysterious concept of dark energy. In particular, it has been pointed out that matter-geometry coupling may be responsible for the recent cosmological dynamics of the Universe, and matter itself may play a more fundamental role in the description of the gravitational processes that usually assumed. In the present paper we study the quantum cosmology of the f(R, T) theory of gravity, in which the effective Lagrangian of the gravitational field is given by an arbitrary function of the Ricci scalar, and the trace of the matter energy-momentum tensor, respectively. For the background geometry we adopt the Friedmann-Robertson-Walker metric, and we assume that matter content of the Universe consists of a perfect fluid. In this framework we obtain the general form of the gravitational Hamiltonian, of the quantum potential, and of the canonical momenta, respectively. This allows us to formulate the full Wheeler-de Witt equation describing the quantum properties of this modified gravity model. As a specific application we consider in detail the quantum cosmology of the f(R, T) = F{sup 0}(R) + θ RT model, in which F{sup 0}(R) is a function of the scale factor only. The Hamiltonian form of the equations of motion, and the Wheeler-de Witt equations are obtained, and a time parameter for the corresponding dynamical system is identified, which allows one to formulate the Schroedinger-Wheeler-de Witt equation for the quantum-mechanical description of the model under consideration. A perturbative approach for the study of this equation is developed, and the energy levels of the Universe are obtained by using a twofold degenerate perturbation approach. A second quantization approach for the description of quantum time is also proposed and briefly discussed. (orig.)
Time Symmetry and Asymmetry in Quantum Mechanics and Quantum Cosmology
Gell-Mann, Murray; Gell-Mann, Murray; Hartle, James B.
1993-01-01
We investigate the origin of the arrow of time in quantum mechanics in the context of quantum cosmology. The ``Copenhagen'' quantum mechanics of measured subsystems incorporates a fundamental arrow of time. Extending discussions of Aharonov, Bergmann and Lebovitz, Griffiths, and others we investigate a generalized quantum mechanics for cosmology that utilizes both an initial and a final density matrix to give a time-neutral formulation without a fundamental arrow of time. Time asymmetries can arise for particular universes from differences between their initial and final conditions. Theories for both would be a goal of quantum cosmology. A special initial condition and a final condition of indifference would be sufficient to explain the observed time asymmetries of the universe. In this essay we ask under what circumstances a completely time symmetric universe, with T-symmetric initial and final condition, could be consistent with the time asymmetries of the limited domain of our experience. We discuss the ap...
Quantum cosmology of (loop) quantum gravity condensates: An example
Gielen, Steffen
2014-01-01
Spatially homogeneous universes can be described in (loop) quantum gravity as condensates of elementary excitations of space. Their treatment is easiest in the second-quantised group field theory formalism which allows the adaptation of techniques from the description of Bose-Einstein condensates in condensed matter physics. Dynamical equations for the states can be derived directly from the underlying quantum gravity dynamics. The analogue of the Gross-Pitaevskii equation defines an anisotropic quantum cosmology model, in which the condensate wavefunction becomes a quantum cosmology wavefunction on minisuperspace. To illustrate this general formalism, we give a mapping of the gauge-invariant geometric data for a tetrahedron to a minisuperspace of homogeneous anisotropic 3-metrics. We then study an example for which we give the resulting quantum cosmology model in the general anisotropic case and derive the general analytical solution for isotropic universes. We discuss the interpretation of these solutions a...
The Vertex Expansion in the Consistent Histories Formulation of Spin Foam Loop Quantum Cosmology
Craig, David
2016-01-01
Assignment of consistent quantum probabilities to events in a quantum universe is a fundamental challenge which every quantum cosmology/gravity framework must overcome. In loop quantum cosmology, this issue leads to a fundamental question: What is the probability that the universe undergoes a non-singular bounce? Using the consistent histories formulation, this question was successfully answered recently by the authors for a spatially flat FRW model in the canonical approach. In this manuscript, we obtain a covariant generalization of this result. Our analysis is based on expressing loop quantum cosmology in the spin foam paradigm and using histories defined via volume transitions to compute the amplitudes of transitions obtained using a vertex expansion. We show that the probability for bounce turns out to be unity.
Non-linear (loop) quantum cosmology
Bojowald, Martin; Dantas, Christine C; Jaffe, Matthew; Simpson, David
2012-01-01
Inhomogeneous quantum cosmology is modeled as a dynamical system of discrete patches, whose interacting many-body equations can be mapped to a non-linear minisuperspace equation by methods analogous to Bose-Einstein condensation. Complicated gravitational dynamics can therefore be described by more-manageable equations for finitely many degrees of freedom, for which powerful solution procedures are available, including effective equations. The specific form of non-linear and non-local equations suggests new questions for mathematical and computational investigations, and general properties of non-linear wave equations lead to several new options for physical effects and tests of the consistency of loop quantum gravity. In particular, our quantum cosmological methods show how sizeable quantum corrections in a low-curvature universe can arise from tiny local contributions adding up coherently in large regions.
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
The Cosmological Constant in the Quantum Multiverse
Larsen, Grant; Roberts, H 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.
Signature change in loop quantum cosmology
Mielczarek, Jakub
2012-01-01
The Wick rotation is commonly considered only as an useful computational trick. However, as it was suggested by Hartle and Hawking already in early eighties, Wick rotation may gain physical meaning at the Planck epoch. While such possibility is conceptually interesting, leading to no-boundary proposal, mechanism behind the signature change remains mysterious. We show that the signature change anticipated by Hartle and Hawking naturally appear in loop quantum cosmology. Theory of cosmological perturbations with the effects of quantum holonomies is discussed. It was shown by Cailleteau \\textit{et al.} (Class. Quant. Grav. {\\bf 29} (2012) 095010) that this theory can be uniquely formulated in the anomaly-free manner. The obtained algebra of effective constraints turns out to be modified such that the metric signature is changing from Lorentzian in low curvature regime to Euclidean in high curvature regime. Implications of this phenomenon on propagation of cosmological perturbations are discussed and corrections ...
Loop quantum cosmology: Anisotropies and inhomogeneities
Wilson-Ewing, Edward
In this dissertation we extend the improved dynamics of loop quantum cosmology from the homogeneous and isotropic Friedmann-Lemaitre-Robertson-Walker space-times to cosmological models which allow anisotropies and inhomogeneities. Specifically, we consider the cases of the homogeneous but anisotropic Bianchi type I, II and IX models with a massless scalar field as well as the vacuum, inhomogeneous, linearly polarized Gowdy T3 model. For each case, we derive the Hamiltonian constraint operator and study its properties. In particular, we show how in all of these models the classical big bang and big crunch singularities are resolved due to quantum gravity effects. Since the Bianchi models play a key role in the Belinskii, Khalatnikov and Lifshitz conjecture regarding the nature of generic space-like singularities in general relativity, the quantum dynamics of the Bianchi cosmologies are likely to provide considerable intuition about the fate of such singularities in quantum gravity. In addition, the results obtained here provide an important step toward the full loop quantization of cosmological space-times that allow generic inhomogeneities; this would provide falsifiable predictions that could be compared to observations.
Quantum Cosmology - The Supersymmetric Perspective - Vol. 2
Moniz, Paulo Vargas
What is this book about? What is quantum cosmology with supersymmetry? How is supersymmetry implemented? Is it through the use of (recent developments in) a superstring theory? Why should the very early universe be explored in that manner? Are there enticing and interesting research problems left to solve? How relevant would it be to address and solve them?
Hybrid models in loop quantum cosmology
Elizaga Navascués, Beatriz; Martín-Benito, Mercedes; Mena Marugán, Guillermo A.
2016-06-01
In the framework of Loop Quantum Cosmology (LQC), inhomogeneous models are usually quantized by means of a hybrid approach that combines loop quantization techniques with standard quantum field theory methods. This approach is based on a splitting of the phase space in a homogeneous sector, formed by global, zero-modes and an inhomogeneous sector, formed by the remaining, infinite number of modes, that describe the local degrees of freedom. Then, the hybrid quantization is attained by adopting a loop representation for the homogeneous gravitational sector, while a Fock representation is used for the inhomogeneities. The zero-mode of the Hamiltonian constraint operator couples the homogeneous and inhomogeneous sectors. The hybrid approach, therefore, is expected to provide a suitable quantum theory in regimes where the main quantum effects of the geometry are those affecting the zero-modes, while the inhomogeneities, still being quantum, can be treated in a more conventional way. This hybrid strategy was first proposed for the simplest cosmological midisuperspaces: the Gowdy models, and it has been later applied to the case of cosmological perturbations. This paper reviews the construction and main applications of hybrid LQC.
Affine Coherent States in Quantum Cosmology
Malkiewicz, Przemyslaw
2015-01-01
A brief summary of the application of coherent states in the examination of quantum dynamics of cosmological models is given. We discuss quantization maps, phase space probability distributions and semiclassical phase spaces. The implementation of coherent states based on the affine group resolves the hardest singularities, renders self-adjoint Hamiltonians without boundary conditions and provides a completely consistent semi-classical description of the involved quantum dynamics. We consider three examples: the closed Friedmann model, the anisotropic Bianchi Type I model and the deep quantum domain of the Bianchi Type IX model.
Uniqueness of measures in loop quantum cosmology
Energy Technology Data Exchange (ETDEWEB)
Hanusch, Maximilian, E-mail: hanuschm@fau.edu [Mathematics Department, University of Paderborn, Paderborn (Germany)
2015-09-15
In Ashtekar and Campiglia [Classical Quantum Gravity 29, 242001 (2012)], residual diffeomorphisms have been used to single out the standard representation of the reduced holonomy-flux algebra in homogeneous loop quantum cosmology (LQC). We show that, in the homogeneous isotropic case, unitarity of the translations with respect to the extended ℝ-action (exponentiated reduced fluxes in the standard approach) singles out the Bohr measure on both the standard quantum configuration space ℝ{sub Bohr} as well as on the Fleischhack one (ℝ⊔ℝ{sub Bohr}). Thus, in both situations, the same condition singles out the standard kinematical Hilbert space of LQC.
Discrete canonical analysis of three-dimensional gravity with cosmological constant
Berra-Montiel, J.; E. Rosales-Quintero, J.
2015-05-01
We discuss the interplay between standard canonical analysis and canonical discretization in three-dimensional gravity with cosmological constant. By using the Hamiltonian analysis, we find that the continuum local symmetries of the theory are given by the on-shell space-time diffeomorphisms, which at the action level, correspond to the Kalb-Ramond transformations. At the time of discretization, although this symmetry is explicitly broken, we prove that the theory still preserves certain gauge freedom generated by a constant curvature relation in terms of holonomies and the Gauss's law in the lattice approach.
Classical and Quantum Limits in Bohmian Quantum Cosmology
Shojai, F.; Shirinifard, A.
2005-01-01
In this paper we have investigated the classical limit in Bohmian quantum cosmology. It is observed that in the quantum regime where the quantum potential is greater than the classical one, one has an expansion in terms of negative powers of the Planck constant. But in the classical limit there are regions having positive powers of the Planck constant, and regions having negative powers and also regions having both. The conclusion is that the Bohmian classical limit cannot be obtained by lett...
Quantum cosmology and late-time singularities
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 behaviour 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 o...
Noether symmetries in extended gravity quantum cosmology
Capozziello, Salvatore
2013-01-01
We summarize the use of Noether symmetries in Minisuperspace Quantum Cosmology. In particular, we consider minisuperspace models, showing that the existence of conserved quantities gives selection rules that allow to recover classical behaviors in cosmic evolution according to the so called Hartle criterion. Such a criterion selects correlated regions in the configuration space of dynamical variables whose meaning is related to the emergence of classical observable universes. Some minisuperspace models are worked out starting from Extended Gravity, in particular coming from scalar tensor, f(R) and f(T) theories. Exact cosmological solutions are derived.
Inhomogenous loop quantum cosmology with matter
Blas, Daniel Martín-de; Marugán, Guillermo A Mena; 10.1088/1742-6596/360/1/012032
2013-01-01
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.
WKB-type Approximation to Noncommutative Quantum Cosmology
Mena, E; Sabido, M
2007-01-01
In this work, we develop and apply the WKB approximation to several examples of noncommutative quantum cosmology, obtaining the time evolution of the noncommutative universe, this is done starting from a noncommutative quantum formulation of cosmology where the noncommutativity is introduced by a deformation on the minisuperspace variables. This procedure gives a straightforward algorithm to incorporate noncommutativity to cosmology and inflation.
Loop quantum cosmology and the fate of cosmological singularities
Singh, Parampreet
2014-09-01
Singularities in general relativity such as the big bang and big crunch, and exotic singularities such as the big rip are the boundaries of the classical spacetimes. These events are marked by a divergence in the curvature invariants and the breakdown of the geodesic evolution. Recent progress on implementing techniques of loop quantum gravity to cosmological models reveals that such singularities may be generically resolved because of the quantum gravitational effects. Due to the quantum geometry, which replaces the classical differential geometry at the Planck scale, the big bang is replaced by a big bounce without any assumptions on the matter content or any fine tuning. In this manuscript, we discuss some of the main features of this approach and the results on the generic resolution of singularities for the isotropic as well as anisotropic models. Using effective spacetime description of the quantum theory, we show the way quantum gravitational effects lead to the universal bounds on the energy density, the Hubble rate and the anisotropic shear. We discuss the geodesic completeness in the effective spacetime and the resolution of all of the strong singularities. It turns out that despite the bounds on energy density and the Hubble rate, there can be divergences in the curvature invariants. However such events are geodesically extendible, with tidal forces not strong enough to cause inevitable destruction of the in-falling objects.
The canonical connection in quantum mechanics
Lévai, Peter; Tsutsui, I; Levay, Peter; McMullan, David; Tsutsui, Izumi
1995-01-01
In this paper we investigate the form of induced gauge fields that arises in two types of quantum systems. In the first we consider quantum mechanics on coset spaces G/H, and argue that G-invariance is central to the emergence of the H-connection as induced gauge fields in the different quantum sectors. We then demonstrate why the same connection, now giving rise to the non-abelian generalization of Berry's phase, can also be found in systems which have slow variables taking values in such a coset space.
The canonical connection in quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Levay, P. [Budapesti Mueszaki Egyetem, Budapest (Hungary); Mcmullan, D.; Tsutsui, Izumi
1995-04-01
In this paper we investigate the form of induced gauge fields that arises in two types of quantum systems. In the first we consider quantum mechanics on coset spaces G/H, and argue that G-invariance is central to the emergence of the H-connection as induced gauge fields in the different quantum sectors. We then demonstrate why the same connection, now giving rise to the non-abelian generalization of Berry`s phase, can also be found in systems which have slow variables taking values in such a coset space. (author).
Hybrid Models in Loop Quantum Cosmology
Navascués, B Elizaga; Marugán, G A Mena
2016-01-01
In the framework of Loop Quantum Cosmology, inhomogeneous models are usually quantized by means of a hybrid approach that combines loop quantization techniques with standard quantum field theory methods. This approach is based on a splitting of the phase space in a homogeneous sector, formed by global, zero-modes, and an inhomogeneous sector, formed by the remaining, infinite number of modes, that describe the local degrees of freedom. Then, the hybrid quantization is attained by adopting a loop representation for the homogeneous gravitational sector, while a Fock representation is used for the inhomogeneities. The zero-mode of the Hamiltonian constraint operator couples the homogeneous and inhomogeneous sectors. The hybrid approach, therefore, is expected to provide a suitable quantum theory in regimes where the main quantum effects of the geometry are those affecting the zero-modes, while the inhomogeneities, still being quantum, can be treated in a more conventional way. This hybrid strategy was first prop...
The canonical Kravchuk basis for discrete quantum mechanics
Hakioglu, Tugrul; Wolf, Kurt Bernardo
2000-04-01
The well known Kravchuk formalism of the harmonic oscillator obtained from the direct discretization method is shown to be a new way of formulating discrete quantum phase space. It is shown that the Kravchuk oscillator Hamiltonian has a well defined unitary canonical partner which we identify with the quantum phase of the Kravchuk oscillator. The generalized discrete Wigner function formalism based on the action and angle variables is applied to the Kravchuk oscillator and its continuous limit is examined.
The simplest possible bouncing quantum cosmological model
Peter, Patrick
2016-01-01
We present and expand the simplest possible quantum cosmological model already discussed in a previous work: the trajectory formulation of quantum mechanics applied to cosmology in the FLRW minisuperspace without spatial curvature. The initial conditions that were assumed there were such that the wave function would not change its functional form but instead provide a dynamics to its parameters. Here, we consider a more general situation, in practice consisting of modified Gaussian wave functions, aiming at obtaining a bounce from a contracting phase. Whereas previous works consistently obtain very symmetric bounces, we find that it is possible to produce highly non symmetric solutions, and even cases for which multiple bounces naturally occur. We also introduce a means of treating the shear in this category of models by quantizing in the Bianchi I minisuperpace.
The simplest possible bouncing quantum cosmological model
Peter, Patrick; Vitenti, Sandro D. P.
2016-06-01
We present and expand the simplest possible quantum cosmological bouncing model already discussed in previous works: the trajectory formulation of quantum mechanics applied to cosmology (through the Wheeler-De Witt equation) in the Friedmann-Lemaître-Robertson-Walker (FLRW) minisuperspace without spatial curvature. The initial conditions that were previously assumed were such that the wave function would not change its functional form but instead provide a dynamics to its parameters. Here, we consider a more general situation, in practice consisting of modified Gaussian wave functions, aiming at obtaining a nonsingular bounce from a contracting phase. Whereas previous works consistently obtain very symmetric bounces, we find that it is possible to produce highly non-symmetric solutions, and even cases for which multiple bounces naturally occur. We also introduce a means of treating the shear in this category of models by quantizing in the Bianchi I minisuperspace.
Canonical averaging of the equations of quantum mechanics
Chirkov, A. G.
2005-01-01
The representation of a Schrodinger equations as a classic Hamiltonian system allows to construct a unified perturbation theory both in classic, and in a quantum mechanics grounded on the theory of canonical transformations, and also to receive asymptotic estimations of affinity of the precisian approximated solutions of Schrodinger equations
Relating the quantum mechanics of discrete systems to standard canonical quantum mechanics
Hooft, Gerard t
2012-01-01
Discrete quantum mechanics is here defined to be a quantum theory of wave functions defined on integers P_i and Q_i, while canonical quantum mechanics is assumed to be based on wave functions on the real numbers, R^n. We study reversible mappings from the position operators q_i and their quantum canonical operators p_i of a canonical theory, onto the discrete, commuting operators Q_i and P_i. In this paper we are particularly interested in harmonic oscillators. In the discrete system, these t...
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.
Bouncing cosmologies from quantum gravity condensates
Oriti, Daniele; Wilson-Ewing, Edward
2016-01-01
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 semi-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.
Conserved quantities in isotropic loop quantum cosmology
Cartin, Daniel
2012-01-01
We develop an action principle for those models arising from isotropic loop quantum cosmology, and show that there is a natural conserved quantity $Q$ for the discrete difference equation arising from the Hamiltonian constraint. This quantity $Q$ relates the semi-classical limit of the wavefunction at large values of the spatial volume, but opposite triad orientations. Moreover, there is a similar quantity for generic difference equations of one parameter arising from a self-adjoint operator.
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.
Local spinfoam expansion in loop quantum cosmology
Henderson, Adam; Vidotto, Francesca; Wilson-Ewing, Edward
2010-01-01
The quantum dynamics of the flat Friedmann-Lemaitre-Robertson-Walker and Bianchi I models defined by loop quantum cosmology have recently been translated into a spinfoam-like formalism. The construction is facilitated by the presence of a massless scalar field which is used as an internal clock. The implicit integration over the matter variable leads to a nonlocal spinfoam amplitude. In this paper we consider a vacuum Bianchi I universe and show that by choosing an appropriate regulator a spinfoam expansion can be obtained without selecting a clock variable and that the resulting spinfoam amplitude is local.
Quantum Cosmology of $f(R,T)$ gravity
Xu, Min-Xing; Liang, Shi-Dong
2016-01-01
Modified gravity theories have the potential of explaining the recent acceleration of the Universe without resorting to the mysterious concept of dark energy. In particular, it has been pointed out that matter-geometry coupling may be responsible for the recent cosmological dynamics of the Universe, and matter itself may play a more fundamental role in the description of the gravitational processes that usually assumed. We study the quantum cosmology of the $f(R,T)$ gravity theory, in which the effective Lagrangian of the gravitational field is given by an arbitrary function of the Ricci scalar, and the trace of the matter energy-momentum tensor, respectively. For the background geometry we adopt the Friedmann--Robertson--Walker metric, and we assume that matter content of the Universe consists of a perfect fluid. We obtain the general form of the gravitational Hamiltonian, of the quantum potential, and of the canonical momenta, respectively. This allows us to formulate the full Wheeler-de Witt equation descr...
Replication Regulates Volume Weighting in Quantum Cosmology
Hartle, James
2009-01-01
Probabilities for observations in cosmology are conditioned both on the universe's quantum state and on local data specifying the observational situation. We show the quantum state defines a measure for prediction through such conditional probabilities that is well behaved for spatially large or infinite universes when the probabilities that our data is replicated are taken into account. In histories where our data are rare volume weighting connects top-down probabilities conditioned on both the data and the quantum state to the bottom-up probabilities conditioned on the quantum state alone. We apply these principles to a calculation of the number of inflationary e-folds in a homogeneous, isotropic minisuperspace model with a single scalar field moving in a quadratic potential. We find that volume weighting is justified and the top-down probabilities favor a large number of e-folds.
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)
Quantum canonical tensor model and an exact wave function
Sasakura, Naoki
2013-01-01
Tensor models in various forms are being studied as models of quantum gravity. Among them the canonical tensor model has a canonical pair of rank-three tensors as dynamical variables, and is a pure constraint system with first-class constraints. The Poisson algebra of the first-class constraints has structure functions, and provides an algebraically consistent way of discretizing the Dirac first-class constraint algebra for general relativity. This paper successfully formulates the Wheeler-DeWitt scheme of quantization of the canonical tensor model; the ordering of operators in the constraints is determined without ambiguity by imposing Hermiticity and covariance on the constraints, and the commutation algebra of constraints takes essentially the same from as the classical Poisson algebra, i.e. is first-class. Thus one could consistently obtain, at least locally in the configuration space, wave functions of "universe" by solving the partial differential equations representing the constraints, i.e. the Wheeler...
Asymptotic silence in loop quantum cosmology
Mielczarek, Jakub
2012-01-01
The state of asymptotic silence, characterized by causal disconnection of the space points, emerges from various approaches aiming to describe gravitational phenomena in the limit of large curvatures. In particular, such behavior was anticipated by Belinsky, Khalatnikov and Lifshitz (BKL) in their famous conjecture put forward in the early seventies of the last century. While the BKL conjecture is based on purely classical considerations, one can expect that asymptotic silence should have its quantum counterpart at the level of a more fundamental theory of quantum gravity, which is the relevant description of gravitational phenomena in the limit of large energy densities. Here, we summarize some recent results which give support to such a possibility. More precisely, we discuss occurrence of the asymptotic silence due to polymerization of space at the Planck scale, in the framework of loop quantum cosmology. In the discussed model, the state of asymptotic silence is realized at the energy density $\\rho = \\rho...
Quantum Signature of Cosmological Large Scale Structures
Capozziello, S; De Siena, S; Illuminati, F; Capozziello, Salvatore; Martino, Salvatore De; Siena, Silvio De; Illuminati, Fabrizio
1998-01-01
We demonstrate that to all large scale cosmological structures where gravitation is the only overall relevant interaction assembling the system (e.g. galaxies), there is associated a characteristic unit of action per particle whose order of magnitude coincides with the Planck action constant $h$. This result extends the class of physical systems for which quantum coherence can act on macroscopic scales (as e.g. in superconductivity) and agrees with the absence of screening mechanisms for the gravitational forces, as predicted by some renormalizable quantum field theories of gravity. It also seems to support those lines of thought invoking that large scale structures in the Universe should be connected to quantum primordial perturbations as requested by inflation, that the Newton constant should vary with time and distance and, finally, that gravity should be considered as an effective interaction induced by quantization.
Inflationary cosmology from quantum Conformal Gravity
Jizba, Petr; Scardigli, Fabio
2014-01-01
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'sparameter and the cosmological constant is highlighted and implications for cosmic inflation are briefly discussed and compared with recent PLANCK and BICEP2 data.
Inflationary cosmology from quantum conformal gravity
Energy Technology Data Exchange (ETDEWEB)
Jizba, Petr [Czech Technical University in Prague, FNSPE, Praha 1 (Czech Republic); Freie Universitaet Berlin, ITP, Berlin (Germany); Kleinert, Hagen [Freie Universitaet Berlin, ITP, Berlin (Germany); Scardigli, Fabio [American University of the Middle East, Department of Mathematics, College of Engineering, P.O. Box 220, Dasman (Kuwait); Politecnico di Milano, Dipartimento di Matematica, Milan (Italy)
2015-06-15
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
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.
Canonical quantum gravity on noncommutative space-time
Kober, Martin
2015-06-01
In this paper canonical quantum gravity on noncommutative space-time is considered. The corresponding generalized classical theory is formulated by using the Moyal star product, which enables the representation of the field quantities depending on noncommuting coordinates by generalized quantities depending on usual coordinates. But not only the classical theory has to be generalized in analogy to other field theories. Besides, the necessity arises to replace the commutator between the gravitational field operator and its canonical conjugated quantity by a corresponding generalized expression on noncommutative space-time. Accordingly the transition to the quantum theory has also to be performed in a generalized way and leads to extended representations of the quantum theoretical operators. If the generalized representations of the operators are inserted to the generalized constraints, one obtains the corresponding generalized quantum constraints including the Hamiltonian constraint as dynamical constraint. After considering quantum geometrodynamics under incorporation of a coupling to matter fields, the theory is transferred to the Ashtekar formalism. The holonomy representation of the gravitational field as it is used in loop quantum gravity opens the possibility to calculate the corresponding generalized area operator.
On Perturbative Instability of Cosmology from Quantum Potential
Tawfik, Abdel Nasser; Dahab, Eiman Abou El; Harko, Tiberiu
2016-01-01
Apart from its debatable correctness, we examine the pertubative stability of the recently proposed cosmology from quantum potential. We find that the proposed quantum corrections invoke additional parameters which apparently introduce perturbative instability to the Universe.
Bounce Loop Quantum Cosmology Corrected Gauss-Bonnet Gravity
Haro, J; Myagky, A N; Odintsov, S D; Oikonomou, V K
2015-01-01
We develop a Gauss-Bonnet extension of Loop Quantum Cosmology, by introducing holonomy corrections in modified $F(\\mathcal{G})$ theories of gravity. Within the context of our formalism, we provide a perturbative expansion in the critical density, a parameter characteristic of Loop Quantum Gravity theories, and we result in having leading order corrections to the classical $F(\\mathcal{G})$ theories of gravity. After extensively discussing the formalism, we present a reconstruction method that makes possible to find the Loop Quantum Cosmology corrected $F(\\mathcal{G})$ theory that can realize various cosmological scenarios. Specifically, we studied exponential and power-law bouncing cosmologies, emphasizing on the behavior near the bouncing point and in some cases, the behavior for all the values of the cosmic time is obtained. We exemplify our theoretical constructions by using bouncing cosmologies, and we investigate which Loop Quantum Cosmology corrected Gauss-Bonnet modified gravities can successfully reali...
Instabilities in numerical loop quantum cosmology
Rosen, J; Khanna, G; Jung, Jae-Hun; Khanna, Gaurav; Rosen, Jessica
2006-01-01
In this article we perform von Neumann analysis of the difference equations that arise as a result of loop quantum gravity being applied to models of cosmology and black holes. In particular, we study the numerical stability of Bianchi I LRS (symmetric and non-symmetric constraint) and Schwarzschild interior (symmetric constraint) models, and find that there exist domains over which there are instabilities, generically. We also present explicit evolutions of wave-packets in these models and clearly demonstrate the presence of these instabilities.
Diffeomorphism invariant cosmological symmetry in full quantum gravity
Beetle, Christopher; Engle, Jonathan S.; Hogan, Matthew E.; Mendonça, Phillip
2016-06-01
This paper summarizes a new proposal to define rigorously a sector of loop quantum gravity at the diffeomorphism invariant level corresponding to homogeneous and isotropic cosmologies, thereby enabling a detailed comparison of results in loop quantum gravity and loop quantum cosmology. The key technical steps we have completed are (a) to formulate conditions for homogeneity and isotropy in a diffeomorphism covariant way on the classical phase-space of general relativity, and (b) to translate these conditions consistently using well-understood techniques to loop quantum gravity. Some additional steps, such as constructing a specific embedding of the Hilbert space of loop quantum cosmology into a space of (distributional) states in the full theory, remain incomplete. However, we also describe, as a proof of concept, a complete analysis of an analogous embedding of homogeneous and isotropic loop quantum cosmology into the quantum Bianchi I model of Ashtekar and Wilson-Ewing. Details will appear in a pair of forthcoming papers.
Diffeomorphism invariant cosmological symmetry in full quantum gravity
Beetle, Christopher; Hogan, Matthew E; Mendonca, Phillip
2016-01-01
This paper summarizes a new proposal to define rigorously a sector of loop quantum gravity at the diffeomorphism invariant level corresponding to homogeneous and isotropic cosmologies, thereby enabling a detailed comparison of results in loop quantum gravity and loop quantum cosmology. The key technical steps we have completed are (a) to formulate conditions for homogeneity and isotropy in a diffeomorphism covariant way on the classical phase space of general relativity, and (b) to translate these conditions consistently using well-understood techniques to loop quantum gravity. Some additional steps, such as constructing a specific embedding of the Hilbert space of loop quantum cosmology into a space of (distributional) states in the full theory, remain incomplete. However, we also describe, as a proof of concept, a complete analysis of an analogous embedding of homogeneous and isotropic loop quantum cosmology into the quantum Bianchi I model of Ashtekar and Wilson-Ewing. Details will appear in a pair of fort...
Decoherent Histories Analysis of Minisuperspace Quantum Cosmology
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 analys...
Quantum modified Regge-Teitelboim cosmology
Cordero, Rubén; Molgado, Alberto; Rojas, Efraín
2013-01-01
The quantization of the modified geodetic brane gravity implemented from the Regge-Teitelboim model and the trace of the extrinsic curvature of the brane trajectory, K, is developed. As a second-order derivative model, on the grounds of the Ostrogradski Hamiltonian method and the Dirac's scheme for constrained systems we find suitable first- and second-class constraints which allow for a proper quantization. The first-class constraints obey a sort of truncated Virasoro algebra. The effective quantum potential emerging in our approach is exhaustively studied where it shows that an embryonic epoch is still present. The quantum nucleation is briefly discussed where we observe that it is driven by an effective cosmological constant.
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.
Effective equations for isotropic quantum cosmology including matter
Bojowald, Martin; Skirzewski, Aureliano
2007-01-01
Effective equations often provide powerful tools to develop a systematic understanding of detailed properties of a quantum system. This is especially helpful in quantum cosmology where several conceptual and technical difficulties associated with the full quantum equations can be avoided in this way. Here, effective equations for Wheeler-DeWitt and loop quantizations of spatially flat, isotropic cosmological models sourced by a massive or interacting scalar are derived and studied. The resulting systems are remarkably different from that given for a free, massless scalar. This has implications for the coherence of evolving states and the realization of a bounce in loop quantum cosmology.
Quantum Reduced Loop Gravity and the foundation of Loop Quantum Cosmology
Alesci, Emanuele
2016-01-01
Quantum Reduced Loop Gravity is a promising framework for linking Loop Quantum Gravity and the effective semiclassical dynamics of Loop Quantum Cosmology. We review its basic achievements and its main perspectives, outlining how it provides a quantum description of the Universe in terms of a cuboidal graph which constitutes the proper framework for applying loop techniques in a cosmological setting.
Canonical Group Quantization, Rotation Generators and Quantum Indistinguishability
Benavides, C
2008-01-01
Using the method of canonical group quantization, we construct the angular momentum operators associated to configuration spaces with the topology of (i) a sphere and (ii) a projective plane. In the first case, the obtained angular momentum operators are the quantum version of Poincare's vector, i.e., the physically correct angular momentum operators for an electron coupled to the field of a magnetic monopole. In the second case, the obtained operators represent the angular momentum operators of a system of two indistinguishable spin zero quantum particles in three spatial dimensions. We explicitly show how our formalism relates to the one developed by Berry and Robbins. The relevance of the proposed formalism for an advance in our understanding of the spin-statistics connection in non-relativistic quantum mechanics is discussed.
Big-bounce cosmology from quantum gravity: The case of a cyclical Bianchi I universe
Moriconi, Riccardo; Montani, Giovanni; Capozziello, Salvatore
2016-07-01
We analyze the classical and quantum dynamics of a Bianchi I model in the presence of a small negative cosmological constant characterizing its evolution in term of the dust-time dualism. We demonstrate that in a canonical metric approach, the cosmological singularity is removed in correspondence to a positive defined value of the dust energy density. Furthermore, the quantum big bounce is connected to the Universe's turning point via a well-defined semiclassical limit. Then we can reliably infer that the proposed scenario is compatible with a cyclical universe picture. We also show how, when the contribution of the dust energy density is sufficiently high, the proposed scenario can be extended to the Bianchi IX cosmology and therefore how it can be regarded as a paradigm for the generic cosmological model. Finally, we investigate the origin of the observed cutoff on the cosmological dynamics, demonstrating how the big-bounce evolution can be mimicked by the same semiclassical scenario, where the negative cosmological constant is replaced via a polymer discretization of the Universe's volume. A direct proportionality law between these two parameters is then established.
Embedding loop quantum cosmology without piecewise linearity
Engle, Jonathan
2013-01-01
An important goal is to understand better the relation between full loop quantum gravity (LQG) and the simplified, reduced theory known as loop quantum cosmology (LQC), {\\em directly at the quantum level}. Such a firmer understanding would increase confidence in the reduced theory as a tool for formulating predictions of the full theory, as well as permitting lessons from the reduced theory to guide further development in the full theory. The present paper constructs an embedding of the usual state space of LQC into that of standard LQG, that is, LQG based on \\textit{piecewise analytic paths}. The embedding is well-defined even prior to solving the diffeomorphism constraint, at no point is a graph fixed, and at no point is the piecewise linear category used. This motivates for the first time a definition of operators in LQC corresponding to holonomies along non-piecewise-linear paths, without changing the usual kinematics of LQC in any way. The new embedding intertwines all operators corresponding to such hol...
Embedding loop quantum cosmology without piecewise linearity
Engle, Jonathan
2013-04-01
An important goal is to understand better the relation between full loop quantum gravity (LQG) and the simplified, reduced theory known as loop quantum cosmology (LQC), directly at the quantum level. Such a firmer understanding would increase confidence in the reduced theory as a tool for formulating predictions of the full theory, as well as permitting lessons from the reduced theory to guide further development in the full theory. This paper constructs an embedding of the usual state space of LQC into that of standard LQG, that is, LQG based on piecewise analytic paths. The embedding is well defined even prior to solving the diffeomorphism constraint, at no point is a graph fixed and at no point is the piecewise linear category used. This motivates for the first time a definition of operators in LQC corresponding to holonomies along non-piecewise linear paths, without changing the usual kinematics of LQC in any way. The new embedding intertwines all operators corresponding to such holonomies, and all elements in its image satisfy an operator equation which classically implies homogeneity and isotropy. The construction is made possible by a recent result proven by Fleischhack. Communicated by P Singh
Towards a loop representation for quantum canonical supergravity
Gambini, R; Pullin, J
1995-01-01
We study several aspects of the canonical quantization of supergravity in terms of the Asthekar variables. We cast the theory in terms of a GSU(2) connection and we introduce a loop representation. The solution space is remarkably similar to the loop representation of ordinary gravity, the main difference being the form of the Mandelstam identities. Physical states are in general given by knot invariants that are compatible with the GSU(2) Mandelstam identities. There is an explicit solution to all the quantum constraint equations connected with the Chern-Simons form, which leads to a new knot invariant polynomial in the loop representation.
Probability of boundary conditions in quantum cosmology
Suenobu, Hiroshi; Nambu, Yasusada
2017-02-01
One of the main interest in quantum cosmology is to determine boundary conditions for the wave function of the universe which can predict observational data of our universe. For this purpose, we solve the Wheeler-DeWitt equation for a closed universe with a scalar field numerically and evaluate probabilities for boundary conditions of the wave function of the universe. To impose boundary conditions of the wave function, we use exact solutions of the Wheeler-DeWitt equation with a constant scalar field potential. These exact solutions include wave functions with well known boundary condition proposals, the no-boundary proposal and the tunneling proposal. We specify the exact solutions by introducing two real parameters to discriminate boundary conditions, and obtain the probability for these parameters under the requirement of sufficient e-foldings of the inflation. The probability distribution of boundary conditions prefers the tunneling boundary condition to the no-boundary boundary condition. Furthermore, for large values of a model parameter related to the inflaton mass and the cosmological constant, the probability of boundary conditions selects an unique boundary condition different from the tunneling type.
Probability of boundary conditions in quantum cosmology
Nambu, Yasusada; Suenobu, Hiroshi
2017-08-01
One of the main interest in quantum cosmology is to determine boundary conditions for the wave function of the universe which can predict observational data of our universe. For this purpose, we solve the Wheeler-DeWitt equation for a closed universe with a scalar field numerically and evaluate probabilities for boundary conditions of the wave function of the universe. To impose boundary conditions of the wave function, we use exact solutions of the Wheeler-DeWitt equation with a constant scalar field potential. We specify the exact solutions by introducing two real parameters to discriminate boundary conditions, and obtain the probability for these parameters under the requirement of sufficient e-foldings of the inflation. The probability distribution of boundary conditions prefers the tunneling boundary condition to the no-boundary boundary condition. Furthermore, for large values of a model parameter related to the inflaton mass and the cosmological constant, the probability of boundary conditions selects an unique boundary condition different from the tunneling type.
Loop Quantum Cosmology, Modified Gravity and Extra Dimensions
Directory of Open Access Journals (Sweden)
Xiangdong Zhang
2016-08-01
Full Text Available Loop quantum cosmology (LQC is a framework of quantum cosmology based on the quantization of symmetry reduced models following the quantization techniques of loop quantum gravity (LQG. This paper is devoted to reviewing LQC as well as its various extensions including modified gravity and higher dimensions. For simplicity considerations, we mainly focus on the effective theory, which captures main quantum corrections at the cosmological level. We set up the basic structure of Brans–Dicke (BD and higher dimensional LQC. The effective dynamical equations of these theories are also obtained, which lay a foundation for the future phenomenological investigations to probe possible quantum gravity effects in cosmology. Some outlooks and future extensions are also discussed.
Probability of Boundary Conditions in Quantum Cosmology
Suenobu, Hiroshi
2016-01-01
One of the main interest in quantum cosmology is to determine which type of boundary conditions for the wave function of the universe can predict observational data of our universe. For this purpose, we solve the Wheeler-DeWitt equation numerically and evaluate probabilities for an observable representing evolution of the classical universe, especially, the number of e-foldings of the inflation. To express boundary conditions of the wave function, we use exact solutions of the Wheeler-DeWitt equation with constant scalar field potential. These exact solutions include wave functions with well known boundary condition proposals, the no-boundary proposal and the tunneling proposal. We specify them introducing two real parameters which discriminate boundary conditions and estimate values of these parameters resulting in observationally preferable predictions. We obtain the probability for these parameters under the requirement of the sufficient e-foldings of the inflation.
Loop Quantum Cosmology and Spin Foams
Ashtekar, Abhay; 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 %convergent 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.
Evolution of Primordial Black Holes in Loop Quantum Cosmology
Indian Academy of Sciences (India)
D. Dwivedee; B. Nayak; M. Jamil; L. P. Singh; R. Myrzakulov
2014-03-01
In this work, we study the evolution of primordial black holes within the context of loop quantum cosmology. First we calculate the scale factor and energy density of the Universe for different cosmic era and then taking these as inputs, we study evolution of primordial black holes. From our estimation it is found that accretion of radiation does not affect evolution of primordial black holes in loop quantum cosmology. We also conclude that due to slow variation of scale factor, the upper bound on initial mass fraction of presently evaporating PBHs are much greater in loop quantum cosmology than the standard case.
Phenomenology with fluctuating quantum geometries in loop quantum cosmology
Agullo, Ivan; Gupt, Brajesh
2016-01-01
The goal of this paper is to probe phenomenological implications of large fluctuations of quantum geometry in the Planck era, using cosmology of the early universe. For the background (Friedmann, Lema\\^{i}tre, Robertson, Walker) \\emph{quantum} geometry, we allow `widely spread' states in which the \\emph{relative} dispersions are as large as $168\\%$ in the Planck regime. By introducing suitable methods to overcome the ensuing conceptual and computational issues, we calculate the power spectrum $P_{\\mathcal{R}}(k)$ and the spectral index $n_s(k)$ of primordial curvature perturbations. These results generalize the previous work in loop quantum cosmology which focused on those states which were known to remain sharply peaked throughout the Planck regime. Surprisingly, even though the fluctuations we now consider are large, their presence does not add new features to the final $P_{\\mathcal{R}}(k)$ and $n_s(k)$: Within observational error bars, their effect is degenerate with a different freedom in the theory, name...
Phenomenology with fluctuating quantum geometries in loop quantum cosmology
Agullo, Ivan; Ashtekar, Abhay; Gupt, Brajesh
2017-04-01
The goal of this paper is to probe phenomenological implications of large fluctuations of quantum geometry in the Planck era, using cosmology of the early universe. For the background (Friedmann, Lemaître, Robertson, Walker) quantum geometry, we allow ‘widely spread’ states in which the relative dispersions are as large as 168 % in the Planck regime. By introducing suitable methods to overcome the ensuing conceptual and computational issues, we calculate the power spectrum {{P}R}(k) and the spectral index n s (k) of primordial curvature perturbations. These results generalize the previous work in loop quantum cosmology which focused on those states which were known to remain sharply peaked throughout the Planck regime. Surprisingly, even though the fluctuations we now consider are large, their presence does not add new features to the final {{P}R}(k) and n s (k): within observational error bars, their effect is degenerate with a different freedom in the theory, namely the number of pre-inflationary e-folds {{N}\\text{B\\star}} between the bounce and the onset of inflation. Therefore, with regard to observational consequences, one can simulate the freedom in the choice of states with large fluctuations in the Planck era using the simpler, sharply peaked states, simply by allowing for different values of {{N}\\text{B \\star}} .
Preon model and cosmological quantum-hyperchromodynamic phase transition
Nishimura, H.; Hayashi, Y.
1987-05-01
From the cosmological viewpoint, we investigate whether or not recent preon models are compatible with the picture of the first-order phase transition from the preon phase to the composite quark-lepton phase. It is shown that the current models accepting the 't Hooft anomaly-matching condition together with quantum hyperchromodynamics are consistent with the cosmological first-order phase transition.
Supersymmetric quantum cosmology for Bianchi class A models
Macías, A; Socorro, J; Macías, Alfredo; Mielke, Eckehard W.; Socorro, José
1998-01-01
The canonical theory of (N=1) supergravity, with a matrix representation for the gravitino covector-spinor, is applied to the Bianchi class A spatially homogeneous cosmologies. The full Lorentz constraint and its implications for the wave function of the universe are analyzed in detail. We found that in this model no physical states other than the trivial "rest frame" type occur.
Big-bounce cosmology from quantum gravity: The case of a cyclical Bianchi I universe
Moriconi, Riccardo; Capozziello, Salvatore
2016-01-01
We analyse the classical and quantum dynamics of a Bianchi I model in the presence of a small negative cosmological constant characterizing its evolution in term of the dust-time dualism. We demonstrate that in a canonical metric approach, the cosmological singularity is removed in correspondence to a positive defined value of the dust energy density. Furthermore, the quantum Big-Bounce is connected to the Universe turning point via a well-defined semiclassical limit. Then we can reliably infer that the proposed scenario is compatible with a cyclical Universe picture. We also show how, when the contribution of the dust energy density is sufficiently high, the proposed scenario can be extended to the Bianchi IX cosmology and therefore how it can be regarded as a paradigm for the generic cosmological model. Finally, we investigate the origin of the observed cut-off on the cosmological dynamics, demonstrating how the Big-Bounce evolution can be mimicked by the same semiclassical scenario, where the negative cosm...
Time-dependant cosmological interpretation of quantum mechanics
Moulay, Emmanuel
2015-01-01
The aim of this article is to define a time-dependant cosmological interpretation of quantum mechanics in the context of a multiverse coming from eternal inflation. A common notion of time is defined for observers in similar observable universes by using the holographic principle. It is the time elapsed since the post-inflationary epoch. With this improvement, the cosmological interpretation of quantum mechanics becomes a full interpretation of quantum mechanics where the unitary evolution of quantum states is preserved. Moreover, it is well suited for eternal inflation .
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
Darabi, F.; Mousavi, M.
2016-10-01
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
Directory of Open Access Journals (Sweden)
F. Darabi
2016-10-01
Full Text Available 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.
Quantum cosmology from group field theory condensates: a review
Gielen, Steffen
2016-01-01
We give, in some detail, a critical overview over recent work towards deriving a cosmological phenomenology from the fundamental quantum dynamics of group field theory (GFT), based on the picture of a macroscopic universe as a "condensate" of a large number of quanta of geometry which are given by excitations of the GFT field over a "no-space" vacuum. We emphasise conceptual foundations, relations to other research programmes in GFT and the wider context of loop quantum gravity (LQG), and connections to the quantum physics of real Bose-Einstein condensates. We show how to extract an effective dynamics for GFT condensates from the microscopic GFT physics, and how to compare it with predictions of more conventional quantum cosmology models, in particular loop quantum cosmology (LQC). No detailed familiarity with the GFT formalism is assumed.
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.
Observables in Loop Quantum Gravity with a cosmological constant
Dupuis, Maïté
2013-01-01
An open issue in loop quantum gravity (LQG) is the introduction of a non-vanishing cosmological constant $\\Lambda$. In 3d, Chern-Simons theory provides some guiding lines: $\\Lambda$ appears in the quantum deformation of the gauge group. The Turaev-Viro model, which is an example of spin foam model is also defined in terms of a quantum group. By extension, it is believed that in 4d, a quantum group structure could encode the presence of $\\Lambda\
The quantum general linear supergroup, canonical bases and Kazhdan-Lusztig polynomials
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
Canonical bases of the tensor powers of the natural Uq(glm|n)-module V are constructed by adapting the work of Frenkel, Khovanov and Kirrilov to the quantum supergroup setting. This result is generalized in several directions. We first construct the canonical bases of the Z2-graded symmetric algebra of V and tensor powers of this superalgebra; then construct canonical bases for the superalgebra Oq(Mm|n) of a quantum (m, n) × (m, n)-supermatrix; and finally deduce from the latter result the canonical basis of every irreducible tensor module for Uq(glm|n) by applying a quantum analogue of the Borel-Weil construction.
Dynamical eigenfunctions and critical density in loop quantum cosmology
Craig, David A
2012-01-01
We offer a new, physically transparent argument for the existence of the critical, universal maximum matter density in loop quantum cosmology for the case of a flat Friedmann-Lemaitre-Robertson-Walker cosmology with scalar matter. The argument is based on the existence of a sharp exponential ultraviolet cutoff in momentum space on the eigenfunctions of the quantum cosmological dynamical evolution operator (the gravitational part of the Hamiltonian constraint), attributable to the fundamental discreteness of spatial volume in loop quantum cosmology. The existence of the cutoff is proved directly from recently found exact solutions for the eigenfunctions for this model. As a consequence, the operators corresponding to the momentum of the scalar field and the spatial volume approximately commute. The ultraviolet cutoff then implies that the scalar momentum, though not a bounded operator, is in effect bounded on subspaces of constant volume, leading to the upper bound on the expectation value of the matter densit...
Zero-point quantum fluctuations in cosmology
Hollenstein, Lukas; Maggiore, Michele; Mitsou, Ermis
2011-01-01
We re-examine the classic problem of the renormalization of zero-point quantum fluctuations in a Friedmann-Robertson-Walker background. We discuss a number of issues that arise when regularizing the theory with a momentum-space cutoff, and show explicitly how introducing non-covariant counter-terms allows to obtain covariant results for the renormalized vacuum energy-momentum tensor. We clarify some confusion in the literature concerning the equation of state of vacuum fluctuations. Further, we point out that the general structure of the effective action becomes richer if the theory contains a scalar field phi with mass m smaller than the Hubble parameter H(t). Such an ultra-light particle cannot be integrated out completely to get the effective action. Apart from the volume term and the Einstein-Hilbert term, that are reabsorbed into renormalizations of the cosmological constant and Newton's constant, the effective action in general also has a term proportional to F(phi)R, for some function F(phi). As a resu...
Universal features of quantum bounce in loop quantum cosmology
Zhu, Tao; Kirsten, Klaus; Cleaver, Gerald; Sheng, Qin
2016-01-01
Loop quantum cosmology (LQC) provides an elegant resolution of the classical big bang singularity by a quantum bounce in the deep Planck era. The evolutions of the flat Friedmann-Lemaitre-Robertson-Walker (FLRW) background and its linear scalar and tensor perturbations are universal during the pre-inflationary phase. In this period the potentials of the perturbations can be well approximated by a P\\"oschl-Teller (PT) potential, from which we find analytically the mode functions and then calculate the Bogoliubov coefficients at the onset of the slow-roll inflation, valid for any inflationary models with a single scalar field. Matching them to those given in the slow-roll inflationary phase, we investigate the effects of the quantum bounce on the power spectra and find unique features that can be tested by current and forthcoming observations. In particular, fitting the power spectra to the Planck 2015 data, we find that the universe must have expanded at least 132 e-folds from the bounce until now.
Cosmology and the pilot wave interpretation of quantum mechanics
Tipler, Frank J.
1984-07-01
Bell has recently revived the pilot wave interpretation of de Broglie and Bohm as a possible scheme for interpreting wave functions in quantum cosmology. I argue that the pilot wave interpretation cannot be applied consistently to systems whose wave functions split into macroscopically distinguishable states. At some stage the pilot wave interpretation must either tacitly invoke wave function reduction in the same manner as the Copenhagen interpretation, or else abandon locality by requiring physical particles to move faster than light. Consequently, the many-worlds interpretation is the only known realist interpretation of the quantum mechanical formalism which can be extended to quantum cosmology.
Path Integrals and the WKB approximation in Loop Quantum Cosmology
Ashtekar, Abhay; Henderson, Adam
2010-01-01
We follow the Feynman procedure to obtain a path integral formulation of loop quantum cosmology starting from the Hilbert space framework. Quantum geometry effects modify the weight associated with each path so that the effective measure on the space of paths is different from that used in the Wheeler-DeWitt theory. These differences introduce some conceptual subtleties in arriving at the WKB approximation. But the approximation is well defined and provides intuition for the differences between loop quantum cosmology and the Wheeler-DeWitt theory from a path integral perspective.
Path integrals and the WKB approximation in loop quantum cosmology
Ashtekar, Abhay; Campiglia, Miguel; Henderson, Adam
2010-12-01
We follow the Feynman procedure to obtain a path integral formulation of loop quantum cosmology starting from the Hilbert space framework. Quantum geometry effects modify the weight associated with each path so that the effective measure on the space of paths is different from that used in the Wheeler-DeWitt theory. These differences introduce some conceptual subtleties in arriving at the WKB approximation. But the approximation is well defined and provides intuition for the differences between loop quantum cosmology and the Wheeler-DeWitt theory from a path integral perspective.
Averaged null energy condition in Loop Quantum Cosmology
Li, Li-Fang
2008-01-01
Wormhole and time machine are very interesting objects in general relativity. However, they need exotic matters which are impossible in classical level to support them. But if we introduce the quantum effects of gravity into the stress-energy tensor, these peculiar objects can be constructed self-consistently. Fortunately, loop quantum cosmology (LQC) has the potential to serve as a bridge connecting the classical theory and quantum gravity. Therefore it provides a simple way for the study of quantum effect in the semiclassical case. As is well known, loop quantum cosmology is very successful to deal with the behavior of early universe. In the early stage, if taken the quantum effect into consideration, inflation is natural because of the violation of every kind of local energy conditions. Similar to the inflationary universe, the violation of the averaged null energy condition is the necessary condition for the traversable wormholes. In this paper, we investigate the averaged null energy condition in LQC in ...
Quantum Mechanics in the Light of Quantum Cosmology
Gell-Mann, Murray; Hartle, James B.
We sketch a quantum-mechanical framework for the universe as a whole. Within that framework we propose a program for describing the ultimate origin in quantum cosmology of the "quasiclassical domain" of familiar experience and for characterizing the process of measurement. Predictions in quantum mechanics are made from probabilities for sets of alternative histories. Probabilities (approximately obeying the rules of probability theory) can be assigned only to sets of histories that approximately decohere. Decoherence is defined and the mechanism of decoherence is reviewed. Decoherence requires a sufficiently coarse-grained description of alternative histories of the universe. A quasiclassical domain consists of a branching set of alternative decohering histories, described by a coarse graining that is, in an appropriate sense, maximally refined consistent with decoherence, with individual branches that exhibit a high level of classical correlation in time. We pose the problem of making these notions precise and quantitative. A quasiclassical domain is emergent in the universe as a consequence of the initial condition and the action function of the elementary particles. It is an important question whether all the quasiclassical domains are roughly equivalent or whether there are various essentially inequivalent ones. A measurement is a correlation with variables in a quasiclassical domain. An "observer" (or information gathering and utilizing system) is a complex adaptive system that has evolved to exploit the relative predictability of a quasiclassical domain, or rather a set of such domains among which it cannot discriminate because of its own very coarse graining. We suggest that resolution of many of the problems of interpretation presented by quantum mechanics is to be accomplished, not by further scrutiny of the subject as it applies to reproducible laboratory situations, but rather by an examination of alternative histories of the universe, stemming from its
Cosmological constraints on a classical limit of quantum gravity
Easson, D A; Trodden, M; Wohlfarth, M N R; Easson, Damien A.; Schuller, Frederic P.; Trodden, Mark; Wohlfarth, Mattias N.R.
2005-01-01
We investigate the cosmology of a recently proposed deformation of Einstein gravity, emerging from quantum gravity heuristics. The theory is constructed to have de Sitter space as a vacuum solution, and thus to be relevant to the accelerating universe. However, this solution turns out to be unstable, and the true phase space of cosmological solutions is significantly more complex, displaying two late-time power-law attractors -- one accelerating and the other dramatically decelerating. It is also shown that non-accelerating cosmologies sit on a separatrix between the two basins of attraction of these attractors. Hence it is impossible to pass from a decelerating cosmology to an accelerating one, as required in standard cosmology for consistency with nucleosynthesis and structure formation and compatibility with the data inferred from supernovae Ia. We point out that alternative models of the early universe, such as the one investigated here might provide possible ways to circumvent these requirements.
Loop quantum cosmology of Bianchi type IX models
Wilson-Ewing, Edward
2010-01-01
The loop quantum cosmology "improved dynamics" of the Bianchi type IX model are studied. The action of the Hamiltonian constraint operator is obtained via techniques developed for the Bianchi type I and type II models, no new input is required. It is shown that the big bang and big crunch singularities are resolved by quantum gravity effects. We also present the effective equations which provide modifications to the classical equations of motion due to quantum geometry effects.
Loop quantum cosmology of Bianchi type IX models
Wilson-Ewing, Edward
2010-08-01
The loop quantum cosmology “improved dynamics” of the Bianchi type IX model are studied. The action of the Hamiltonian constraint operator is obtained via techniques developed for the Bianchi type I and type II models, no new input is required. It is shown that the big bang and big crunch singularities are resolved by quantum gravity effects. We also present effective equations which provide quantum geometry corrections to the classical equations of motion.
Origin of Structure in the Universe: Quantum Cosmology Reconsidered
Anderson, Edward
2015-01-01
Based on a more careful canonical analysis, we motivate a reduced quantization of slightly inhomogeneous cosmology in place of the Dirac quantization in the existing literature, and provide it in the vacuum case. This is attained via consideration of configuration space geometries at various levels of reduction. Some of these have the good fortunate of being flat. Geometrically natural coordinates thereupon are interpreted in terms of the original redundant formulation's well-known mode expansion coefficients.
Quantum Cosmology Problems for the 21st Century
Hartle, J B
1997-01-01
Two fundamental laws are needed for prediction in the universe: (1) a basic dynamical law and (2) a law for the cosmological initial condition. Quantum cosmology is the area of basic research concerned with the search for a theory of the initial cosmological state. The issues involved in this search are presented in the form of eight problems. (To appear in Physics 2001, ed. by M. Kumar and in the Proceedings of the 10th Yukawa-Nishinomiya Symposium}, November 7--8, 1996, Nishinomiya, Japan.)
Universal features of quantum bounce in loop quantum cosmology
Zhu, Tao; Wang, Anzhong; Kirsten, Klaus; Cleaver, Gerald; Sheng, Qin
2017-10-01
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.
Dynamical Horizon Entropy Bound Conjecture in Loop Quantum Cosmology
Institute of Scientific and Technical Information of China (English)
李丽仿; 朱建阳
2012-01-01
The covariant entropy bound conjecture is an important hint for the quantum gravity, with several versions available in the literature. For cosmology, Ashtekar and Wilson-Ewing ever show the consistence between the loop gravity theory and one version of this conjecture. Recently, He and Zhang [J. High Energy Phys. 10 （2007） 077] proposed a version for the dynamical horizon of the universe, which validates the entropy bound conjecture for the cosmology filled with perfect fluid in the classical scenario when the universe is far away from the big bang singularity. However, their conjecture breaks down near big bang region. We examine this conjecture in the context of the loop quantum cosmology. With the example of photon gas, this conjecture is protected by the quantum geometry effects as expected.
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.
Cosmological Applications of Algebraic Quantum Field Theory in Curved Spacetimes
Hack, Thomas-Paul
2015-01-01
This monograph provides a largely self--contained and broadly accessible exposition of 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 containing a pedagogical introduction to the subject as well as 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. The target reader should have a basic understanding of General Relativity and QFT on Minkowski spacetime, but does not need to have a background in QFT on curved spacetimes or the algebraic approach to QFT. In particul...
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.
Cosmological implications of modified gravity induced by quantum metric fluctuations
Liu, Xing; Liang, Shi-Dong
2016-01-01
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 nonminimal 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...
Bunao, Joseph
2016-01-01
This study considers the operator $\\hat{T}$ corresponding to the classical spacetime four-volume $T$ of a finite patch of spacetime in the context of Unimodular Loop Quantum Cosmology for the homogeneous and isotropic model with flat spatial sections and without matter sources. Since $T$ is canonically conjugate to the cosmological "constant" $\\Lambda$, the operator $\\hat{T}$ is constructed by solving its canonical commutation relation with $\\hat{\\Lambda}$ - the operator corresponding to $\\Lambda$. %This is done by expanding $\\hat{T}$ in terms of Bender-Dunne-like basis operators $\\hat{T}_{m,n}$ and solving for the expansion coefficients. This conjugacy, along with the action of $\\hat{T}$ on definite volume states reducing to $T$, allows us to interpret that $\\hat{T}$ is indeed a quantum spacetime four-volume operator. The eigenstates $\\Phi_{\\tau}$ are calculated and, considering $\\tau\\in\\mathbb{R}$, we find that the $\\Phi_{\\tau}$'s are normalizable suggesting that the real line $\\mathbb{R}$ is in the discret...
Universe's memory and spontaneous coherence in loop quantum cosmology
Pawłowski, Tomasz
2016-01-01
The quantum bounce a priori connects several (semi)classical epochs of Universe evolution, however determining if and how well the semiclassicality is preserved in this transition is highly nontrivial. We review the present state of knowledge in that regards in the isotropic sector of loop quantum cosmology. This knowledge is next extended by studies of an isotropic universe admitting positive cosmological constant (featuring an infinite chain of large Universe epochs). It is also shown, that such universe always admits a semiclassical epoch thanks to spontaneous spontaneous coherence, provided it is semiclassical in certain constant of motion playing the role of energy.
Probability of inflation in loop quantum cosmology
Ashtekar, Abhay; Sloan, David
2011-12-01
Inflationary models of the early universe provide a natural mechanism for the formation of large scale structure. This success brings to forefront the question of naturalness: Does a sufficiently long slow roll inflation occur generically or does it require a careful fine tuning of initial parameters? In recent years there has been considerable controversy on this issue (Hollands and Wald in Gen Relativ Gravit, 34:2043, 2002; Kofman et al. in J High Energy Phys 10:057, 2002); (Gibbons and Turok in Phys Rev D 77:063516, 2008). In particular, for a quadratic potential, Kofman et al. (J High Energy Phys 10:057, 2002) have argued that the probability of inflation with at least 65 e-foldings is close to one, while Gibbons and Turok (Phys Rev D 77:063516, 2008) have argued that this probability is suppressed by a factor of ~10-85. We first clarify that such dramatically different predictions can arise because the required measure on the space of solutions is intrinsically ambiguous in general relativity. We then show that this ambiguity can be naturally resolved in loop quantum cosmology (LQC) because the big bang is replaced by a big bounce and the bounce surface can be used to introduce the structure necessary to specify a satisfactory measure. The second goal of the paper is to present a detailed analysis of the inflationary dynamics of LQC using analytical and numerical methods. By combining this information with the measure on the space of solutions, we address a sharper question than those investigated in Kofman et al. (J High Energy Phys 10:057, 2002), Gibbons and Turok (Phys Rev D 77:063516, 2008), Ashtekar and Sloan (Phys Lett B 694:108, 2010): What is the probability of a sufficiently long slow roll inflation which is compatible with the seven year WMAP data? We show that the probability is very close to 1. The material is so organized that cosmologists who may be more interested in the inflationary dynamics in LQC than in the subtleties associated with
Canonical Form and Separability of PPT States in 2xMxN Composite Quantum Systems
Wang, X H; Wang, Z X; Wu, K
2003-01-01
We investigate the canonical forms of positive partial transposition (PPT) density matrices in ${\\cal C}^2 \\otimes {\\cal C}^M \\otimes {\\cal C}^N$ composite quantum systems with rank $N$. A general expression for these PPT states are explicitly obtained. From this canonical form a sufficient separability condition is presented.
Towards generic resolution of strong singularities in loop quantum cosmology
Singh, Parampreet
2010-10-01
Singularities are the boundaries of classical spacetime in General Relativity. It has been always hoped that quantum gravitational effects may resolve these singularities. In recent years, progress in loop quantum cosmology has provided insights on the resolution of big bang, big crunch and other spacelike singularities. In this talk we will give an update on the recent status of the generic resolution of strong spacelike singularities in loop quantum cosmology. We will show that for flat and curved Roberston-Walker backgrounds and also for Bianchi-I models, loop quantum gravity effects resolve all strong curvature singularities. However, weak curvature singularities, that is those beyond which geodesics can be continued, may not be resolved.
Tachyon field in Loop Quantum Cosmology: inflation and evolution picture
Xiong, H H; Xiong, Hua-Hui; Zhu, Jian-Yang
2007-01-01
Loop quantum cosmology (LQC) predicts a nonsingular evolution of the universe through a bounce in the high energy region. We show that this is always true in tachyon matter LQC. Different from the classical FRW cosmology, the superinflation can appear in the tachyon matter LQC; furthermore, the inflation can be extended to the region where classical inflation stops. Using numerical method, we give an evolution picture of the tachyon field with an exponential potential in the context of LQC. It indicates that the quantum dynamical solutions have the attractor behavior as the classical solutions does. And, the whole evolution of the tachyon field is that: at the far past, the tachyon field, being in the contracting cosmology, is accelerated to climb up the potential hill with a negative velocity; and then, the tachyon field at the boundary is bounced into an expanding universe with positive velocity rolling down to the bottom of the potential.
Intrinsically Quantum-Mechanical Gravity and the Cosmological Constant Problem
Mannheim, Philip D
2010-01-01
We propose that gravity be intrinsically quantum-mechanical, so that in the absence of quantum mechanics the geometry of the universe would be Minkowski. We show that in such a situation gravity does not require any independent quantization of its own, with it being quantized simply by virtue of its being coupled to the quantized matter fields that serve as its source. We show that when the gravitational and matter fields possess an underlying conformal symmetry, the gravitational field and fermionic matter-field zero-point fluctuations cancel each other identically. Then, when the fermions acquire mass by a dynamical symmetry breaking procedure that induces a cosmological constant in such conformal theories, the zero-point fluctuations readjust so as to cancel the induced cosmological constant identically. The zero-point vacuum problem and the cosmological constant vacuum problems thus mutually solve each other. We illustrate our ideas in a completely solvable conformal-invariant model, namely two-dimensiona...
Non-Schroedinger forces and pilot waves in quantum cosmology
Energy Technology Data Exchange (ETDEWEB)
Tipler, F.J.
1987-09-01
The author argues that the version of the pilot wave interpretation of quantum mechanics which uses a non-local non-Schroedinger force is inconsistent when applied to distributions with small numbers of particles. Thus, no version of the pilot wave interpretation (some-times called the de Broglie-Bohm, or causal, interpretation) can be applied to the wavefunction of quantum cosmology because in any version of this interpretation, there is only one particle, the universe.
A Note in Cosmology and Loop Quantum Gravity
Mora, P
2000-01-01
One possible description of the very early stages of the evolution of the universe is provided by Chaotic Inflationary Cosmology. For that model the role of the inflaton field is played by quantum gravitational effects. We study if such a picture may arise within the framework of Loop Quantum gravity by studying a simple model. While we were unable to reach definitive conclusions we believe the general approach proposed in this paper may prove fruitful in the future.
The Bohmian Approach to the Problems of Cosmological Quantum Fluctuations
Goldstein, Sheldon; Struyve, Ward; Tumulka, Roderich
2015-01-01
There are two kinds of quantum fluctuations relevant to cosmology that we focus on in this article: those that form the seeds for structure formation in the early universe and those giving rise to Boltzmann brains in the late universe. First, structure formation requires slight inhomogeneities in the density of matter in the early universe, which then get amplified by the effect of gravity, leading to clumping of matter into stars and galaxies. According to inflation theory, quantum fluctuati...
The Bohmian Approach to the Problems of Cosmological Quantum Fluctuations
Goldstein, Sheldon; Tumulka, Roderich
2015-01-01
There are two kinds of quantum fluctuations relevant to cosmology that we focus on in this article: those that form the seeds for structure formation in the early universe and those giving rise to Boltzmann brains in the late universe. First, structure formation requires slight inhomogeneities in the density of matter in the early universe, which then get amplified by the effect of gravity, leading to clumping of matter into stars and galaxies. According to inflation theory, quantum fluctuations form the seeds of these inhomogeneities. However, these quantum fluctuations are described by a quantum state which is homogeneous and isotropic, and this raises a problem, connected to the foundations of quantum theory, as the unitary evolution alone cannot break the symmetry of the quantum state. Second, Boltzmann brains are random agglomerates of particles that, by extreme coincidence, form functioning brains. Unlikely as these coincidences are, they seem to be predicted to occur in a quantum universe as vacuum flu...
Quantum cosmology for a quadratic theory of gravity
Pimentel, L O; Pimentel, L O; Obregon, O
1994-01-01
For pure fourth order ({\\cal{L}} \\propto R^2) quantum cosmology the Wheeler-DeWitt equation is solved exactly for the closed homogeneous and isotropic model. It is shown that by imposing as boundary condition that \\Psi = 0 at the origin of the universe the wave functions behave as suggested by Vilenkin.
Interpretation of the triad orientations in loop quantum cosmology
Kiefer, Claus
2012-01-01
Loop quantum cosmology allows for arbitrary superpositions of the triad variable. We show here how these superpositions can become indistinguishable from a classical mixture by the interaction with fermions. We calculate the reduced density matrix for a locally rotationally symmetric Bianchi I model and show that the purity factor for the triads decreases by decoherence. In this way, the Universe assumes a definite orientation.
On Duru-Kleinert Path Integral In Quantum Cosmology
Jafarizadeh, M A; Rastegar, A R
1998-01-01
We show that the Duru-Kleinert fixed energy amplitude leads to the path integral for the propagation amplitude in the closed FRW quantum cosmology with scale factor as one degree of freedom. Then, using the Duru-Kleinert equivalence of corresponding actions, we calculate the tunneling rate, with exact prefactor, through the dilute-instanton approximation to first order in
Gauge-invariance in one-loop quantum cosmology
Vasilevich, D V
1995-01-01
We study the problem of gauge-invariance and gauge-dependence in one-loop quantum cosmology. We formulate some requirements which should be satisfied by boundary conditions in order to give gauge-independent path integral. The case of QED is studied in some detail. We outline difficulties in gauge-invariant quantization of gravitational field in a bounded region.
Singularity resolution in loop quantum cosmology: A brief overview
Energy Technology Data Exchange (ETDEWEB)
Ashtekar, Abhay, E-mail: ashtekar@gravity.psu.ed [Institute for Gravitation and the Cosmos, Penn State, University Park, PA 16802 (United States)
2009-10-01
A brief summary of loop quantum cosmology of homogeneous isotropic models is presented for non-experts with emphasis on the origin of and subtleties associated with the resolution of big bang and big crunch singularities. For further details, and a discussion of some frequently asked questions, the reader is directed to more comprehensive recent reviews.{sup 1}
On solutions of loop quantum cosmology and their thermodynamics properties
Sadjadi, H Mohseni
2012-01-01
Loop quantum cosmology is considered in inflationary era. A slow rolling scalar field solution with power law potential is presented in the neighborhood of transition time, i.e. when the universe enters inflationary phase from super-inflation era. The second and the generalized second laws of thermodynamics and their validities and violations are discussed and elucidated through some examples.
Cold electroweak baryogenesis and quantum cosmological correlations
M.P. van der Meulen
2008-01-01
This thesis describes two subjects from theoretical cosmology. The first concerns the creation of the matter--anti-matter asymmetry, which is generally assumed to be created in the early universe by a process called baryogenesis. The details of this process are yet unknown and there exist many model
Bunao, J.
2017-02-01
This study considers the operator \\hat{T} corresponding to the classical spacetime four-volume \\tilde{T} (on-shell) of a finite patch of spacetime in the context of unimodular loop quantum cosmology for the homogeneous and isotropic model with flat spatial sections and without matter sources. Since the spacetime four-volume is canonically conjugate to the cosmological ‘constant’, the operator \\hat{T} is constructed by solving its canonical commutation relation with {\\hat Λ } —the operator corresponding to the classical cosmological constant on-shell {\\tilde Λ } . This conjugacy, along with the action of \\hat{T} on definite volume states reducing to \\tilde{T} , allows us to interpret that \\hat{T} is indeed a quantum spacetime four-volume operator. The discrete spectrum of \\hat{T} is calculated by considering the set of all τ’s where the eigenvalue equation has a solution {{ Φ }τ} in the domain of \\hat{T} . It turns out that, upon assigning the maximal domain D≤ft(\\hat{T}\\right) to \\hat{T} , we have {{ Φ }τ}\\in D≤ft(\\hat{T}\\right) for all τ \\in {C} so that the spectrum of \\hat{T} is purely discrete and is the entire complex plane. A family of operators {{\\hat{T}}≤ft({{b0},{φ0}\\right)}} was also considered as possible self-adjoint versions of \\hat{T} . They represent the restrictions of \\hat{T} on their respective domains D≤ft({{\\hat{T}}≤ft({{b0},{φ0}\\right)}}\\right) which are just the maximal domain with additional quasi-periodic conditions. Their possible self-adjointness is motivated by their discrete spectra only containing real and discrete numbers {τm} for m=0,+/- 1,+/- 2,... .
Quantum Transitions Between Classical Histories: Bouncing Cosmologies
Hartle, James
2015-01-01
In a quantum theory of gravity spacetime behaves classically when quantum probabilities are high for histories of geometry and field that are correlated in time by the Einstein equation. Probabilities follow from the quantum state. This quantum perspective on classicality has important implications: (a) Classical histories are generally available only in limited patches of the configuration space on which the state lives. (b) In a given patch states generally predict relative probabilities for an ensemble of possible classical histories. (c) In between patches classical predictability breaks down and is replaced by quantum evolution connecting classical histories in different patches. (d) Classical predictability can break down on scales well below the Planck scale, and with no breakdown in the classical equations of motion. We support and illustrate (a)-(d) by calculating the quantum transition across the de Sitter like throat connecting asymptotically classical, inflating histories in the no-boundary quantu...
Casting Loop Quantum Cosmology in the Spin Foam Paradigm
Ashtekar, Abhay; Henderson, Adam
2010-01-01
The goal of spin foam models is to provide a viable path integral formulation of quantum gravity. Because of background independence, their underlying framework has certain novel features that are not shared by path integral formulations of familiar field theories in Minkowski space. As a simple viability test, these features were recently examined through the lens of loop quantum cosmology (LQC). Results of that analysis, reported in a brief communication [1], turned out to provide concrete arguments in support of the spin foam paradigm. We now present detailed proofs of those results. Since the quantum theory of LQC models is well understood, this analysis also serves to shed new light on some long standing issues in the spin foam and group field theory literature. In particular, it suggests an intriguing possibility for addressing the question of why the cosmological constant is positive and small.
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
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.
Covariance and Quantum Cosmology: A Comparison of Two Matter Clocks
Halnon, Theodore; Bojowald, Martin
2017-01-01
In relativity, time is relative between reference frames. However, quantum mechanics requires a specific time coordinate in order to write an evolution equation for wave functions. This difference between the two theories leads to the problem of time in quantum gravity. One method to study quantum relativity is to interpret the dynamics of a matter field as a clock. In order to test the relationship between different reference frames, an isotropic cosmological model with two matter ingredients is introduced. One is given by a scalar field and one by vacuum energy or a cosmological constant. There are two matter fields, and thus two different Hamiltonians are derived from the respective clock rates. Semi-classical solutions are found for these equations and a comparison is made of the physical predictions that they imply. Partial funding from the Ronald E. McNair Postbaccalaureate Achievement Program.
Quantum Chaos on Hyperbolic Manifolds A New Approach to Cosmology
Tomaschitz, R
1992-01-01
We consider classical and quantum motion on multiply connected hyperbolic spaces, which appear as space-like slices in Robertson-Walker cosmologies. The topological structure of these manifolds creates on the one hand bounded chaotic trajectories, and on the other hand quantal bound states whose wave functions can be reconstructed from the chaotic geodesics. We obtain an exact relation between a probabilistic quantum mechanical wave field and the corresponding classical system, which is likewise probabilistic because of the instabilities of the trajectories with respect to the initial conditions. The central part in this reconstruction is played by the fractal limit set of the covering group of the manifold. This limit set determines the bounded chaotic trajectories on the manifold. Its Hausdorff measure and dimension determine the wave function of the quantum mechanical bound state for geodesic motion. We investigate relativistic scalar wave fields in de Sitter cosmologies, coupled to the curvature scalar of...
The quantum general linear supergroup,canonical bases and Kazhdan-Lusztig polynomials
Institute of Scientific and Technical Information of China (English)
ZHANG HeChun
2009-01-01
Canonical bases of the tensor powers of the natural Uq(glm|n)-module V are constructed by adapting the work of Frenkel,Khovanov and Kirrilov to the quantum supergroup setting.This result is generalized in several directions.We first construct the canonical bases of the Z2-graded symmetric algebra of V and tensor powers of this superalgebra;then construct canonical bases for the superalgebra Oq(Mm|n) of a quantum (m,n) x (m,n)-supermatrix;and finally deduce from the latter result the canonical basis of every irreducible tensor module for Uq(glm|n) by applying a quantum analogue of the Borel-Weil construction.
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.)
Chaplygin gas Hořava-Lifshitz quantum cosmology
Ardehali, Hossein; Pedram, Pouria
2016-02-01
In this paper, we study the Chaplygin gas Hořava-Lifshitz quantum cosmology. Using Schutz formalism and Arnowitt-Deser-Misner decomposition, we obtain the corresponding Schrödinger-Wheeler-DeWitt equation. We obtain exact classical and quantum mechanical solutions and construct wave packets to study the time evolution of the expectation value of the scale factor for two cases. We show that unlike classical solutions and upon choosing appropriate initial conditions, the expectation value of the scale factor never tends to the singular point which exhibits the singularity-free behavior of the solutions in the quantum domain.
Chaplygin Gas Ho\\v{r}ava-Lifshitz Quantum Cosmology
Ardehali, Hossein
2016-01-01
In this paper, we study the Chaplygin gas Ho\\v{r}ava-Lifshitz quantum cosmology. Using Schutz formalism and Arnowitt-Deser-Misner decomposition, we obtain the corresponding Schr\\"{o}dinger-Wheeler-DeWitt equation. We obtain exact classical and quantum mechanical solutions and construct wave packets to study the time evolution of the expectation value of the scale factor for two cases. We show that unlike classical solutions and upon choosing appropriate initial conditions, the expectation value of the scale factor never tends to the singular point which exhibits the singularity-free behavior of the solutions in the quantum domain.
Quantum Vacuum and a Matter - Antimatter Cosmology
Rothwarf, F; Rothwarf, Frederick; Roy, Sisir
2007-01-01
A model of the universe as proposed by Allen Rothwarf based upon a degenerate Fermion fluid composed of polarizable particle-antiparticle pairs leads to a big bang model of the universe where the velocity of light varies inversely with the square root of cosmological time, t. This model is here extended to predict a decelerating expansion of the universe and to derive the Tully-Fisher law describing the flat rotation curves of spiral galaxies. The estimated critical acceleration parameter, aoR, is compared to the experimental, critical modified Newtonian Dynamics (MOND) cosmological acceleration constant, obtained by fitting a large number of rotation curves. The present estimated value is much closer to the experimental value than that obtained with the other models. This model for aR(t) allows the derivation of the time dependent radius of the universe as a function of red shift Other cosmological parameters such as the velocity of light, Hubble's constant, the Tully-Fisher relation, and the index of refrac...
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.)
Cosmological implications of modified gravity induced by quantum metric fluctuations
Liu, Xing; Harko, Tiberiu; Liang, Shi-Dong
2016-08-01
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.
Loop quantum cosmology for nonminimally coupled scalar field
Artymowski, Michal; Pawlowski, Tomasz
2013-01-01
We perform a LQC-quantization of the FRW cosmological model with nonminimally coupled scalar field. Making use of a canonical transformation, we recast the theory in the minimally coupled form (Einstein frame), for which standard LQC techniques can be applied to find the physical Hilbert space and the dynamics. We then focus on the semiclassical sector, obtaining a classical effective Hamiltonian, which can be used to study the dynamics. We show that the classical singularity is replaced by a "mexican hat"-shaped bounce, joining the contracting and expanding branches. The model accommodates Higgs-driven inflation, with more than enough e-folding for any physically meaningful initial condition.
Canonical Form and Separability of PPT States on Multiple Quantum Spaces
Wang, X H; Wang, Xiao-Hong; Fei, Shao-Ming
2005-01-01
By using the "subtracting projectors" method in proving the separability of PPT states on multiple quantum spaces, we derive a canonical form of PPT states in ${\\Cb}^{K_1} \\otimes {\\Cb}^{K_2} \\otimes ... \\otimes {\\Cb}^{K_m} \\otimes {\\Cb}^N$ composite quantum systems with rank $N$, from which a sufficient separability condition for these states is presented.
The optimal pure Gaussian state canonically associated to a Gaussian quantum state
Energy Technology Data Exchange (ETDEWEB)
Gosson, Maurice de [Blekinge Institute of Technology, Karlskrona 371 79 (Sweden)]. E-mail: mdg@bth.se
2004-09-20
We show, using the symplectically invariant notion of 'quantum blob', that it is possible to attach a canonical optimal Gaussian pure state to an arbitrary quantum state. When at least one pair of conjugate variables satisfies the minimum uncertainty condition, then the associated Gaussian is uniquely determined up to an overall phase factor.
Reconstructing the Universe Evolution from Loop Quantum Cosmology Scalar Fields
Oikonomou, V K
2016-01-01
We extend the scalar-tensor reconstruction techniques for classical cosmology frameworks, in the context of loop quantum cosmology. After presenting in some detail how the equations are generalized in the loop quantum cosmology case, we discuss which new features and limitations does the quantum framework brings along, and we use various illustrative examples in order to demonstrate how the method works. As we show the energy density has two different classes of solutions, and one of these yields the correct classical limit while the second captures the quantum phenomena. We study in detail the scalar tensor reconstruction method for both these solutions. Also we discuss some scenarios for which the Hubble rate becomes unbounded at finite time, which corresponds for example in a case that a Big Rip occurs. As we show this issue is non-trivial and we discuss how this case should be treated in a consistent way. Finally, we investigate how the classical stability conditions for the scalar-tensor solutions are ge...
The quantum-to-classical transition of primordial cosmological perturbations
Pinto-Neto, Nelson; Struyve, Ward
2011-01-01
There is a widespread belief that the classical small inhomogeneities which gave rise to all structures in the Universe through gravitational instability originated from primordial quantum cosmological fluctuations. However, this transition from quantum to classical fluctuations is plagued with important conceptual issues, most of them related to the application of standard quantum theory to the Universe as a whole. In this paper, we show how these issues can easily be overcome in the framework of the de Broglie-Bohm quantum theory. This theory is an alternative to standard quantum theory that provides an objective description of physical reality, where rather ambiguous notions of measurement or observer play no fundamental role, and which can hence be applied to the Universe as a whole. In addition, it allows for a simple and unambiguous characterization of the classical limit.
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.
Slow-roll approximation in loop quantum cosmology
Luc, Joanna
2016-01-01
The slow-roll approximation is an analytical approach to study dynamical properties of the inflationary universe. In this article, systematic construction of the slow-roll expansion for effective loop quantum cosmology is presented. The analysis is performed up to the fourth order in both slow-roll parameters and the parameter controlling the strength of deviation from the classical case. The expansion is performed for three types of the slow-roll parameters: Hubble slow-roll parameters, Hubble flow parameters and potential slow-roll parameters. An accuracy of the approximation is verified by comparison with the numerical phase space trajectories for the case with a massive potential term. The results obtained in this article may be helpful in the search for the subtle quantum gravitational effects with use of the cosmological data.
Noether symmetric classical and quantum scalar field cosmology
Vakili, Babak
2011-01-01
We study the evolution of a two dimensional minisuperspace cosmological model in classical and quantum levels by the Noether symmetry approach. The phase space variables turn out to correspond to the scale factor of a Friedmann-Robertson-Walker (FRW) model and a scalar field with which the action of the model is augmented. It is shown that the minisuperspace of such a model is a two dimensional manifold with vanishing Ricci scalar. We present a coordinate transformation which cast the corresponding minisuper metric to a Minkowskian or Euclidean one according to the choices of an ordinary or phantom model for the scalar field. Then, the Noether symmetry of such a cosmological model is investigated by utilizing the behavior of the corresponding Lagrangian under the infinitesimal generators of the desired symmetry. We explicitly calculate the form of the scalar field potential functions for which such symmetries exist. For these potential functions, the exact classical and quantum solutions in the cases where th...
Slow-roll approximation in loop quantum cosmology
Luc, Joanna; Mielczarek, Jakub
2017-01-01
The slow-roll approximation is an analytical approach to study dynamical properties of the inflationary universe. In this article, systematic construction of the slow-roll expansion for effective loop quantum cosmology is presented. The analysis is performed up to the fourth order in both slow-roll parameters and the parameter controlling the strength of deviation from the classical case. The expansion is performed for three types of the slow-roll parameters: Hubble slow-roll parameters, Hubble flow parameters and potential slow-roll parameters. An accuracy of the approximation is verified by comparison with the numerical phase space trajectories for the case with a massive potential term. The results obtained in this article may be helpful in the search for the subtle quantum gravitational effects with use of the cosmological data.
Aspects of nonlocality in quantum field theory, quantum gravity and cosmology
Barvinsky, A. O.
2015-02-01
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. 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 (dS) cosmological evolution at an arbitrary value of Λ — a model of dark energy with the dynamical scale selected by a kind of a scaling symmetry breaking mechanism. This model is shown to interpolate between the superhorizon phase of a scalar mediated gravity and the short distance general relativistic limit in a special metric frame related by a nonlocal conformal transformation to the original metric.
Canonical simulations of supersymmetric SU(N) Yang-Mills quantum mechanics
Bergner, Georg; Wenger, Urs
2015-01-01
The fermion loop formulation naturally separates partition functions into their canonical sectors. Here we discuss various strategies to make use of this for supersymmetric SU(N) Yang-Mills quantum mechanics obtained from dimensional reduction in various dimensions and present numerical results for the separate canonical sectors with fixed fermion numbers. We comment on potential problems due to the sign of the contributions from the fermions and due to flat directions.
Non-Schroedinger forces and pilot waves in quantum cosmology
Tipler, Frank J.
1987-09-01
The version of the pilot wave interpretation of quantum mechanics using a nonlocal non-Schroedinger force is found to be inconsistent when applied to distributions with small numbers of particles. Any version of the pilot wave interpretation is shown to require the universe to move along a single trajectory. It is suggested that no version of the pilot wave interpretation can be applied to the wavefunction of quantum cosmology, because in any version of this interpretation there is only one particle, the universe.
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.
Cosmological implications of quantum entanglement in the multiverse
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 scale dependent modulations may enter the spectrum for the case of initially non-entangled state due to quantum interference. 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
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.
Loop quantum cosmology, non-Gaussianity, and CMB power asymmetry
Agullo, Ivan
2015-01-01
We argue that the anomalous power asymmetry observed in the cosmic microwave background (CMB) may have originated in a cosmic bounce preceding inflation. In loop quantum cosmology (LQC) the big bang singularity is generically replaced by a bounce due to quantum gravitational effects. We compute the spectrum of inflationary non-Gaussianity and show that strong correlation between observable scales and modes with longer (super-horizon) wavelength arise as a consequence of the evolution of perturbations across the LQC bounce. These correlations are strongly scale dependent and induce a dipole-dominated modulation on large angular scales in the CMB, in agreement with observations.
Canonical pairs, Spatially Confined Motion and the Quantum Time of Arrival Problem
Galapon, E A
2000-01-01
It has always been believed that no self-adjoint and canonical time of arrival operator can be constructed within the confines of standard quantum mechanics. In this Letter we demonstrate the otherwise. We do so by pointing out that there is no a priori reason in demanding that canonical pairs form a system of imprimitivities. We then proceed to show that a class of self-adjoint and canonical time of arrival (TOA) operators can be constructed for a spatially confined free particle. And then discuss the relatiobship between the non-self-adjointess of the TOA operator for the unconfined particle and the self-adjointness of the confined one.
Quantum Cosmological Approach to 2d Dilaton Gravity
Navarro-Salas, J
1994-01-01
We study the canonical quantization of the induced 2d-gravity and the pure gravity CGHS-model on a closed spatial section. The Wheeler-DeWitt equations are solved in (spatially homogeneous) choices of the internal time variable and the space of solutions is properly truncated to provide the physical Hilbert space. We establish the quantum equivalence of both models and relate the results with the covariant phase-space quantization. We also discuss the relation between the quantum wavefunctions and the classical space-time solutions and propose the wave function representing the ground state.
Loop quantum cosmology with self-dual variables
Wilson-Ewing, Edward
2015-01-01
Using the complex-valued self-dual connection variables, the loop quantum cosmology of a closed Friedmann universe 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 measure for the inner product in 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 holonomy-like operators, some of which are well-defined; these operators in turn are used in the definition of a Hamiltonian constraint operator where the scalar field can be used as a relational clock. The resulting quantum dynamics are similar, 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 remai...
Generalized quantum gravity condensates for homogeneous geometries and cosmology
Oriti, Daniele; Ryan, James P; Sindoni, Lorenzo
2015-01-01
We construct a generalized class of quantum gravity condensate states, that allows the description of continuum homogeneous quantum geometries within the full theory. They are based on similar ideas already applied to extract effective cosmological dynamics from the group field theory formalism, and thus also from loop quantum gravity. However, they represent an improvement over the simplest condensates used in the literature, in that they are defined by an infinite superposition of graph-based states encoding in a precise way the topology of the spatial manifold. The construction is based on the definition of refinement operators on spin network states, written in a second quantized language. The construction lends itself easily to be applied also to the case of spherically symmetric quantum geometries.
Cosmological Constant, Quantum Measurement, and the Problem of Time
Banerjee, Shreya; Singh, Tejinder P
2015-01-01
Three of the big puzzles of theoretical physics are the following: (i) There is apparently no time evolution in the dynamics of quantum general relativity, because the allowed quantum states must obey the Hamiltonian constraint. (ii) During a quantum measurement, the state of the quantum system randomly collapses from being in a linear superposition of the eigenstates of the measured observable, to just one of the eigenstates, in apparent violation of the predictions of the deterministic, linear Schr\\"{o}dinger equation. (iii) The observed value of the cosmological constant is exceedingly small, compared to its natural value, creating a serious fine-tuning problem. In this essay we propose a novel idea to show how the three problems help solve each other.
The Causal Interpretation of Conformally Coupled Scalar Field Quantum Cosmology
De Barros, J A; Sagioro-Leal, M A
2000-01-01
We apply the causal interpretation of quantum mechanics to homogeneous and isotropic quantum cosmology, where the source of the gravitational field is a conformally coupled scalar field, and the maximally symmetric hypersurfaces are flat. The classical solutions are expanding or contracting singular universes. The general solution of the Wheeler-DeWitt equation is a discrete superposition of Hermite polynomials multiplied by complex exponentials. Superpositions with up to two parcels are studied, and the phase diagrams of their corresponding Bohmian trajectories are analyzed in detail. Nonsingular periodic quantum solutions are found. They are nonclassical but they can be arbitrarily big. Some of them can represent the universe we live in but the majority present too small oscillations. We also find that singular quantum solutions present an inflation era in the begining of the universe. Numerical calculations indicates that these results remain valid for general superpositions.
Inflation with the Starobinsky potential in Loop Quantum Cosmology
Bonga, Béatrice
2015-01-01
A self-consistent pre-inflationary extension of the inflationary scenario with the Starobinksy potential, favored by Planck data, is studied using techniques from loop quantum cosmology (LQC). The results are compared with the quadratic potential previously studied. Planck scale completion of the inflationary paradigm and observable signatures of LQC are found to be robust under the change of the inflaton potential. The entire evolution, from the quantum bounce all the way to the end of inflation, is compatible with observations. Occurrence of desired slow-roll phase is almost inevitable and natural initial conditions exist for both the background and perturbations for which the resulting power spectrum agrees with recent observations. There exist initial data for which the quantum gravitational corrections to the power spectrum are potentially observable. Furthermore, the quantum geometry alters the behavior of super horizon modes. This feature is unique to the Starobinsky potential.
Spin Foams and Canonical Quantization
Alexandrov, Sergei; Noui, Karim
2011-01-01
This review is devoted to the analysis of the mutual consistency of the spin foam and canonical loop quantizations in three and four spacetime dimensions. In the three-dimensional context, where the two approaches are in good agreement, we show how the canonical quantization \\`a la Witten of Riemannian gravity with a positive cosmological constant is related to the Turaev-Viro spin foam model, and how the Ponzano-Regge amplitudes are related to the physical scalar product of Riemannian loop quantum gravity without cosmological constant. In the four-dimensional case, we recall a Lorentz-covariant formulation of loop quantum gravity using projected spin networks, compare it with the new spin foam models, and identify interesting relations and their pitfalls. Finally, we discuss the properties which a spin foam model is expected to possess in order to be consistent with the canonical quantization, and suggest a new model illustrating these results.
Aspects of Nonlocality in Quantum Field Theory, Quantum Gravity and Cosmology
Barvinsky, A. O.
2014-01-01
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...
Semiclassical momentum representation in quantum cosmology
Coutant, Antonin
2016-02-01
It is well known that the standard WKB approximation fails to provide semiclassical solutions in the vicinity of turning points. However, turning points arise in many cosmological scenarios. In a previous work, we obtained a new class of semiclassical solutions of the Wheeler-DeWitt equation using the conjugate momentum to the geometric variable. We present here a detailed study of their main properties. We carefully compare them to usual WKB solutions and turning point resolutions using Airy functions. We show that the momentum representation possesses many advantages that are absent in other approaches. In particular, this framework has a key application in tackling the problem of time. It allows us to use curvature as a time variable, and control the corresponding domain of validity, i.e., under which conditions it provides a good clock. We consider several applications, and in particular show how this allows us to obtain semiclassical solutions of the Wheeler-DeWitt equation parametrized by York time.
Mathematical Structure of Loop Quantum Cosmology: Homogeneous Models
Directory of Open Access Journals (Sweden)
Martin Bojowald
2013-12-01
Full Text Available The mathematical structure of homogeneous loop quantum cosmology is analyzed, starting with and taking into account the general classification of homogeneous connections not restricted to be Abelian. As a first consequence, it is seen that the usual approach of quantizing Abelian models using spaces of functions on the Bohr compactification of the real line does not capture all properties of homogeneous connections. A new, more general quantization is introduced which applies to non-Abelian models and, in the Abelian case, can be mapped by an isometric, but not unitary, algebra morphism onto common representations making use of the Bohr compactification. Physically, the Bohr compactification of spaces of Abelian connections leads to a degeneracy of edge lengths and representations of holonomies. Lifting this degeneracy, the new quantization gives rise to several dynamical properties, including lattice refinement seen as a direct consequence of state-dependent regularizations of the Hamiltonian constraint of loop quantum gravity. The representation of basic operators - holonomies and fluxes - can be derived from the full theory specialized to lattices. With the new methods of this article, loop quantum cosmology comes closer to the full theory and is in a better position to produce reliable predictions when all quantum effects of the theory are taken into account.
Superbounce and Loop Quantum Cosmology Ekpyrosis from Modified Gravity
Oikonomou, V K
2014-01-01
As is known, in modified cosmological theories of gravity many of the cosmologies which could not be generated by standard Einstein gravity, can be consistently described by $F(R)$ theories. Using known reconstruction techniques, we investigate which $F(R)$ theories can lead to a Hubble parameter describing two types of cosmological bounces, the superbounce model, related to supergravity and non-supersymmetric models of contracting ekpyrosis and also the Loop Quantum Cosmology modified ekpyrotic model. Since our method is an approximate method, we investigate the problem at large and small curvatures. As we evince, both models yield power law reconstructed $F(R)$ gravities, with the most interesting new feature being that both lead to an $R+aR^2$ gravity in the large curvature approximation. As we explicitly show, this result is not accidental and we study the general case which, within the approximations imposed by the employed reconstruction method, always leads to an $R^2$ in the large curvature limit. As ...
A Calculation of Cosmological Scale from Quantum Coherence
Energy Technology Data Exchange (ETDEWEB)
Lindesay, J
2004-07-23
We use general arguments to examine the energy scales for which a quantum coherent description of gravitating quantum energy units is necessary. The cosmological dark energy density is expected to decouple from the Friedman-Lemaitre energy density when the Friedman-Robertson-Walker scale expansion becomes sub-luminal at R = c, at which time the usual microscopic interactions of relativistic quantum mechanics (QED, QCD, etc) open new degrees of freedom. We assume that these microscopic interactions cannot signal with superluminal exchanges, only superluminal quantum correlations. The expected gravitational vacuum energy density at that scale would be expected to freeze out due to the loss of gravitational coherence. We define the vacuum energy which generates this cosmological constant to be that of a zero temperature Bose condensate at this gravitational de-coherence scale. We presume a universality throughout the universe in the available degrees of freedom determined by fundamental constants during its evolution. Examining the reverse evolution of the universe from the present, long before reaching Planck scale dynamics one expects major modifications from the de-coherent thermal equations of state, suggesting that the pre-coherent phase has global coherence properties. Since the arguments presented involve primarily counting of degrees of freedom, we expect the statistical equilibrium states of causally disconnected regions of space to be independently identical. Thus, there is no horizon problem associated with the lack of causal influences between spatially separated regions in this approach. The scale of the amplitude of fluctuations produced during de-coherence of cosmological vacuum energy are found to evolve to values consistent with those observed in cosmic microwave background radiation and galactic clustering.
Detecting quantum gravitational effects of loop quantum cosmology in the early universe
Zhu, Tao; Cleaver, Gerald; Kirsten, Klaus; Sheng, Qin; Wu, Qiang
2015-01-01
We derive the primordial power spectra and spectral indexes of the density fluctuations and gravitational waves in the framework of loop quantum cosmology (LQC) with holonomy and inverse-volume corrections, by using the uniform asymptotic approximation method to its third-order, at which the upper error bounds are $\\lesssim 0.15\\%$, accurate enough for the current and forthcoming cosmological observations. Then, using the Planck, BAO and SN data we obtain new constraints on quantum gravitational effects from LQC corrections, and find that such effects could be well within the detection of the current and forthcoming experiments.
Chimera: A hybrid approach to numerical loop quantum cosmology
Diener, Peter; Singh, Parampreet
2013-01-01
The existence of a quantum bounce in isotropic spacetimes is a key result in loop quantum cosmology (LQC), which has been demonstrated to arise in all the models studied so far. In most of the models, the bounce has been studied using numerical simulations involving states which are sharply peaked and which bounce at volumes much larger than the Planck volume. An important issue is to confirm the existence of the bounce for states which have a wide spread, or which bounce closer to the Planck volume. Numerical simulations with such states demand large computational domains, making them very expensive and practically infeasible with the techniques which have been implemented so far. To overcome these difficulties, we present an efficient hybrid numerical scheme using the property that at the small spacetime curvature, the quantum Hamiltonian constraint in LQC, which is a difference equation with uniform discretization in volume, can be approximated by a Wheeler-DeWitt differential equation. By carefully choosi...
What can quantum cosmology say about the inflationary universe?
Calcagni, Gianluca; Steinwachs, Christian F
2015-01-01
We propose a method to extract predictions from quantum cosmology for inflation that can be confronted with observations. Employing the tunneling boundary condition in quantum geometrodynamics, we derive a probability distribution for the inflaton field. A sharp peak in this distribution can be interpreted as setting the initial conditions for the subsequent phase of inflation. In this way, the peak sets the energy scale at which the inflationary phase has started. This energy scale must be consistent with the energy scale found from the inflationary potential and with the scale found from a potential observation of primordial gravitational waves. Demanding a consistent history of the universe from its quantum origin to its present state, which includes decoherence, we derive a condition that allows one to constrain the parameter space of the underlying model of inflation. We demonstrate our method by applying it to two models: Higgs inflation and natural inflation.
Loop quantum cosmology: from pre-inflationary dynamics to observations
Ashtekar, Abhay; Barrau, Aurélien
2015-12-01
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.
Curved momentum spaces from quantum groups with cosmological constant
Ballesteros, Á.; Gubitosi, G.; Gutiérrez-Sagredo, I.; Herranz, F. J.
2017-10-01
We bring the concept that quantum symmetries describe theories with nontrivial momentum space properties one step further, looking at quantum symmetries of spacetime in presence of a nonvanishing cosmological constant Λ. In particular, the momentum space associated to the κ-deformation of the de Sitter algebra in (1 + 1) and (2 + 1) dimensions is explicitly constructed as a dual Poisson-Lie group manifold parametrized by Λ. Such momentum space includes both the momenta associated to spacetime translations and the 'hyperbolic' momenta associated to boost transformations, and has the geometry of (half of) a de Sitter manifold. Known results for the momentum space of the κ-Poincaré algebra are smoothly recovered in the limit Λ → 0, where hyperbolic momenta decouple from translational momenta. The approach here presented is general and can be applied to other quantum deformations of kinematical symmetries, including (3 + 1)-dimensional ones.
Observational Selection Effects in Quantum Cosmology
Page, Don N
2007-01-01
Scientific theories need to be testable by observations, say using Bayes' theorem. A complete theory needs at least the three parts of dynamical laws for specified physical variables, the correct solution of the dynamical laws (boundary conditions), and the connection with observations or experience or conscious perceptions (laws of psycho-physical parallelism). Principles are proposed for Bayesian meta-theories. One framework that obeys these principles is Sensible Quantum Mechanics (SQM), which is discussed. In principle, it allows one to test between single-history and many-worlds theories, and to discuss threats to certain theories from fake universes and Boltzmann brains. The threat of fake universes may be dismissed if one doubts the substrate-independence of consciousness, which seems very implausible in the SQM framework. Boltzmann brains seem more problematic, though there are many conceivable solutions. SQM also suggests the possibility that past steps along our evolutionary ancestry may be so rare ...
Quantum cosmology based on discrete Feynman paths
Energy Technology Data Exchange (ETDEWEB)
Chew, Geoffrey F.
2002-10-10
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''.
Inclusion of matter in inhomogeneous loop quantum cosmology
Blas, Daniel Martín-de; Marugán, Guillermo A Mena; 10.1063/1.4734461
2013-01-01
We study the hybrid quantization of the linearly polarized Gowdy $T^3$ model with a massless scalar field with the same symmetries as the metric. For simplicity, we quantize its restriction to the model with local rotational symmetry. Using this hybrid approach, the homogeneous degrees of freedom of the geometry are quantized \\`a la loop, leading to the resolution of the cosmological singularity. A Fock quantization is employed both for the matter and the 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, providing a perfect scenario to study the quantum back-reaction of the inhomogeneities on the polymeric homogeneous and isotropic background.
Quantum Deformed Canonical Transformations, W_{\\infty}-algebras and Unitary Transformations
Gozzi, E.; Reuter, M.
2003-01-01
We investigate the algebraic properties of the quantum counterpart of the classical canonical transformations using the symbol-calculus approach to quantum mechanics. In this framework we construct a set of pseudo-differential operators which act on the symbols of operators, i.e., on functions defined over phase-space. They act as operatorial left- and right- multiplication and form a $W_{\\infty}\\times W_{\\infty}$- algebra which contracts to its diagonal subalgebra in the classical limit. We ...
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
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 thesi
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.
Ambiguities in second-order cosmological perturbations for non-canonical scalar fields
Appignani, Corrado; Shankaranarayanan, S
2010-01-01
Over the last few years, it was realised that non-canonical scalar fields can lead to the accelerated expansion in the early universe. The primordial spectrum in these scenarios not only shows near scale-invariance consistent with CMB observations,but also large primordial non-Gaussianity. Second-order perturbation theory is the primary theoretical tool to investigate such non-Gaussianity. However, it is still uncertain which quantities are gauge-invariant at second-order and their physical understanding therefore remains unclear. As an attempt to understand second order quantities, we consider a general non-canonical scalar field, minimally coupled to gravity, on the unperturbed FRW background where metric fluctuations are neglected a priori. In this simplified set-up, we show that there arise ambiguities in the expressions of physically relevant quantities, such as the effective speeds of the perturbations. Further, the stress tensor and energy density display a potential instability which is not present at...
Quantum cosmology with matter in scalar-tensor theory
Lee, S.; Lim, H.
2016-11-01
The cosmological application of the low energy effective action of string theory with perfect fluid type matter (satisfying p=γ ρ ) is reconsidered. First, its isotropic and anisotropic spacetime cosmological solutions are obtained for general γ . The scale factor duality is applied and checked for our model as well as in the presence of γ of which possible extension to nonvanishing γ is pioneered before. The asymptotic behavior of the solutions is investigated because of the complexity of the solutions. Second, as a quantization, we apply the canonical quantization and the corresponding Wheeler-De Witt equation is constructed for this scalar-tensor theory. By solving the Wheeler-De Witt equation the wave function is found for general value of γ . On the basis of its wave function, the tunneling rate turns out to be just the ratio of norms of the wave function for pre- and post-big-bang phases. This result shows that the rate grows as γ gets value close to a specific value. This resolves the undetermined value for the behavior of the scale factors.
Stable cosmological models driven by a free quantum scalar field
Energy Technology Data Exchange (ETDEWEB)
Dappiaggi, C.; Pinamonti, N. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik]|[Citta Univ., Roma (Italy). Istituto Nazionale di Alta Matematica ' ' F. Severi' ' - GNFM; Fredenhagen, K. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik
2008-01-15
In the mathematically rigorous analysis of semiclassical Einstein's equations, the renormalisation of the stress-energy tensor plays a crucial role. We address such a topic in the case of a scalar field with both arbitrary mass and coupling with gravity in the hypothesis that the underlying algebraic quantum state is of Hadamard type. Particularly, if we focus on highly symmetric solutions of the semiclassical Einstein's equations, the envisaged method displays a de Sitter type behaviour even without an a priori introduced cosmological constant. As a further novel result we shall show that these solutions turn out to be stable. (orig.)
Genericness of Big Bounce in isotropic loop quantum cosmology
Date, Ghanashyam; Hossain, Golam Mortuza
2004-01-01
The absence of isotropic singularity in loop quantum cosmology can be understood in an effective classical description as the universe exhibiting a Big Bounce. We show that with scalar matter field, the big bounce is generic in the sense that it is independent of quantization ambiguities and details of scalar field dynamics. The volume of the universe at the bounce point is parametrized by a single parameter. It provides a minimum length scale which serves as a cut-off for computations of den...
Ultraviolet cutoffs for quantum fields in cosmological spacetimes
Elías, Mauro
2015-01-01
We analyze critically the renormalization of quantum fields in cosmological spacetimes, using non covariant ultraviolet cutoffs. We compute explicitly the counterterms necessary to renormalize the semiclassical Einstein equations, using comoving and physical ultraviolet cutoffs. In the first case, the divergences renormalize bare conserved fluids, while in the second case it is necessary to break the covariance of the bare theory. We point out that, in general, the renormalized equations differ from those obtained with covariant methods, even after absorbing the infinities and choosing the renormalized parameters to force the consistency of the renormalized theory. We repeat the analysis for the evolution equation for the mean value of an interacting scalar field
One-loop quantum corrections to cosmological scalar field potentials
Arbey, A; Arbey, Alexandre; Mahmoudi, Farvah
2007-01-01
We study the loop corrections to potentials of complex or coupled real scalar fields used in cosmology to account for dark energy, dark matter or dark fluid. We show that the SUGRA quintessence and dark matter scalar field potentials are stable against the quantum fluctuations, and we propose solutions to the instability of the potentials of coupled quintessence and dark fluid scalar fields. We also find that a coupling to fermions is very restricted, unless this coupling has a structure which already exists in the scalar field potential or which can be compensated by higher order corrections. Finally, we study the influence of the curvature and kinetic term corrections.
Directory of Open Access Journals (Sweden)
Hal M. Haggard
2016-01-01
Full Text Available Prominent approaches to quantum gravity struggle when it comes to incorporating a positive cosmological constant in their models. Using quantization of a complex SL(2,C Chern–Simons theory we include a cosmological constant, of either sign, into a model of quantum gravity.
Calculation of Quantum Probability in O(2,2) String Cosmology with a Dilaton Potential
Institute of Scientific and Technical Information of China (English)
YAN Jun
2006-01-01
The quantum properties of O(2,2) string cosmology with a dilaton potential are studied in this paper. The cosmological solutions are obtained on three-dimensional space-time. Moreover, the quantum probability of transition between two duality universe is calculated through a Wheeler-De Witt approach.
Quantum cosmology in Ashtekar variables with non-minimally coupled scalar–tensor theory
Indian Academy of Sciences (India)
Subenoy Chakraborty
2002-01-01
Using non-minimally coupled scalar–tensor theory in homogeneous and isotropic cosmological model, quantum cosmology has been developed for Ashtekar variables. The wave function has been evaluated by solving the Wheeler–Dewitt (WD) equation and also using path integral formulation. Semi-classical limit using WKB approximation has also been discussed. Finally, the quantum Bohmian trajectories has been studied in detail.
Thermodynamic signatures of an underlying quantum phase transition: A grand canonical approach
Energy Technology Data Exchange (ETDEWEB)
Jimenez, Kevin, E-mail: kfjimenezfals@gmail.com; Reslen, Jose, E-mail: reslenjo@yahoo.com
2016-08-06
Highlights: • The grand-canonical statistics of a quantum phase transition is studied. • Thermodynamic quantities display features related to the quantum phase transition. • A mean field approach allows to obtain the partition function analytically. - Abstract: The grand canonical formalism is employed to study the thermodynamic structure of a model displaying a quantum phase transition when studied with respect to the canonical formalism. A numerical survey shows that the grand partition function diverges following a power law when the interaction parameter approaches a limiting constant. The power-law exponent takes a distinctive value when such limiting constant coincides with the critical point of the subjacent quantum phase transition. An approximated expression for the grand partition function is derived analytically implementing a mean field scheme and a number of thermodynamic observables are obtained. The system observables show signatures that can be used to track the critical point of the underlying transition. This result provides a simple fact that can be exploited to verify the existence of a quantum phase transition avoiding the zero temperature regime.
The Cosmological Constant Problem and Quantum Spacetime Reference Frame
Luo, M J
2015-01-01
This paper is a generalization of earlier papers [ Nucl. Phys. B 884, 344 (2014) (arXiv:1312.2759) and JHEP 6, 63 (2015) (arXiv:1401.2488) ]. Since space and time should be put on an equal footing, we generalize the idea of quantum clock time to a quantum spacetime reference frame via a physical realization of a reference system by quantum rulers and clocks. Omitting the internal degrees of freedoms (e.g. spin) of the physical rulers and clocks, only considering their metric properties, the spacetime reference frame is described by a bosonic non-linear sigma model. We study the quantum behavior of the system under given approximations, and obtain (1) a cosmological constant $(2/\\pi)\\rho_{c}$ ($\\rho_{c}$ the critical density) very close to current observational value; (2) an Einstein-Hilbert term in the quantum effective action; (3) the ratio of variance to mean-squared of spacetime distance tends to a universal constant $(2/\\pi)\\hbar^{2}$ in the infrared region. This effect is testable by observing the linear...
Classical and quantum cosmology of the little rip abrupt event
Albarran, Imanol; Bouhmadi-López, Mariam; Kiefer, Claus; Marto, João; Vargas Moniz, Paulo
2016-09-01
We analyze from a classical and quantum point of view the behavior of the Universe close to a little rip, which can be interpreted as a big rip sent towards the infinite future. Like a big rip singularity, a little rip implies the destruction of all bounded structures in the Universe and is thus an event where quantum effects could be important. We present here a new phantom scalar field model for the little rip. The quantum analysis is performed in quantum geometrodynamics, with the Wheeler-DeWitt equation as its central equation. We find that the little rip can be avoided in the sense of the DeWitt criterion, that is, by having a vanishing wave function at the place of the little rip. Therefore our analysis completes the answer to the question: can quantum cosmology smoothen or avoid the divergent behavior genuinely caused by phantom matter? We show that this can indeed happen for the little rip, similar to the avoidance of a big rip and a little sibling of the big rip.
Classical and quantum cosmology of the little rip abrupt event
Albarran, Imanol; Kiefer, Claus; Marto, João; Moniz, Paulo Vargas
2016-01-01
We analyze from a classical and quantum point of view the behavior of the universe close to a little rip, which can be interpreted as a big rip sent towards the infinite future. Like a big rip singularity, a little rip implies the destruction of all bounded structure in the Universe and is thus an event where quantum effects could be important. We present here a new phantom scalar field model for the little rip. The quantum analysis is performed in quantum geometrodynamics, with the Wheeler-DeWitt equation as its central equation. We find that the little rip can be avoided in the sense of the DeWitt criterion, that is, by having a vanishing wave function at the place of the little rip. Therefore our analysis completes the answer to the question: can quantum cosmology smoothen or avoid the divergent behavior genuinely caused by phantom matter? We show that this can indeed happen for the little rip, similar to the avoidance of a big rip and a little sibling of the big rip.
The perturbed universe in the deformed algebra approach of Loop Quantum Cosmology
Grain, J
2016-01-01
Loop quantum cosmology is a tentative approach to model the universe down to the Planck era where quantum gravity settings are needed. The quantization of the universe as a dynamical space-time is inspired by Loop Quantum Gravity ideas. In addition, loop quantum cosmology could bridge contact with astronomical observations, and thus potentially investigate quantum cosmology modellings in the light of observations. To do so however, modelling both the background evolution and its perturbations is needed. The latter describe cosmic inhomogeneities that are the main cosmological observables. In this context, we present the so-called deformed algebra approach implementing the quantum corrections to the perturbed universe at an effective level by taking great care of gauge issues. We particularly highlight that in this framework, the algebra of hypersurface deformation receives quantum corrections, and we discuss their meaning. The primordial power spectra of scalar and tensor inhomogeneities are then presented, a...
Primordial power spectra for scalar perturbations in loop quantum cosmology
de Blas, Daniel Martín
2016-01-01
We provide the power spectrum of small scalar perturbations propagating in an inflationary scenario within loop quantum cosmology. We consider the hybrid quantization approach applied to a Friedmann--Robertson--Walker spacetime with flat spatial sections coupled to a massive scalar field. We study the quantum dynamics of scalar perturbations on an effective background within this hybrid approach. We consider in our study adiabatic states of different orders. For them, we find that the hybrid quantization is in good agreement with the predictions of the dressed metric approach. We also propose an initial vacuum state for the perturbations, and compute the primordial and the anisotropy power spectrum in order to qualitatively compare with the current observations of Planck mission. We find that our vacuum state is in good agreement with them, showing a suppression of the power spectrum for large scale anisotropies. We compare with other choices already studied in the literature.
Comparative Quantum Cosmology: Causality, Singularity, and Boundary Conditions
Fellman, Philip V; Carmichael, Christine M; Post, Andrew Carmichael
2007-01-01
In this review article we compare the recent work of Peter Lynds, "On a finite universe with no beginning or end", with that of Stephen Hawking, primarily "Quantum Cosmology, M-Theory, and the Anthropic Principle", and two foundational works by Sean M. Carroll and Jennifer Chen, "Does Inflation Provide Natural Conditions for the Universe" and "Spontaneous Inflation and the Origin of the Arrow of Time", in order to evaluate their comparative treatments of the nature and role of causality, time ordering, thermodynamic reversibility, singularities and boundary conditions in the formation of the early universe. We briefly reference Smolin and Kauffman's recent arguments with respect to possible processes of "evolutionary selection" in early universe formation as an alternative explanation to key elements of Hawking's earlier "M-Theory", and its attendant anthropic principle. We also briefly excerpt a short section of Smolin's recent work on topology in quantum loop gravity, simply as an illustrative example of th...
Semi-classical States in Homogeneous Loop Quantum Cosmology
Tan, H; Ma, Yongge; Tan, Huahai
2006-01-01
Semi-classical states in homogeneous loop quantum cosmology (LQC) are constructed by two different ways. In the first approach, we firstly construct an exponentiated annihilation operator. Then a kind of semi-classical (coherent) state is obtained by solving the eigen-equation of that operator. Moreover, we use these coherent states to analyze the semi-classical limit of the quantum dynamics. It turns out that the Hamiltonian constraint operator employed currently in homogeneous LQC has correct classical limit with respect to the coherent states. In the second approach, the other kind of semi-classical state is derived from the mathematical construction of coherent states for compact Lie groups due to Hall.
Quantum cosmology: From hidden symmetries towards a new (supersymmetric) perspective
Jalalzadeh, S.; Rostami, T.; Moniz, P. V.
2016-02-01
We review pedagogically some of the basic essentials regarding recent results intertwining boundary conditions, the algebra of constraints and hidden symmetries in quantum cosmology. They were extensively published in Refs. [S. Jalalzadeh, S. M. M. Rasouli and P. V. Moniz, Phys. Rev. D 90 (2014) 023541, S. Jalalzadeh and P. V. Moniz, Phys. Rev. D 89 (2014), S. Jalalzadeh, T. Rostami and P. V. Moniz, Eur. Phys. J. C 75 (2015) 38, arXiv:gr-qc/1412.6439 and T. Rostami, S. Jalalzadeh and P. V. Moniz, Phys. Rev. D 92 (2015) 023526, arXiv:gr-qc/1507.04212], where complete discussions and full details can be found. More concretely, in Refs. [S. Jalalzadeh, S. M. M. Rasouli and P. V. Moniz, Phys. Rev. D 90 (2014) 023541, S. Jalalzadeh and P. V. Moniz, Phys. Rev. D 89 (2014) and S. Jalalzadeh, T. Rostami and P. V. Moniz, Eur. Phys. J. C 75 (2015) 38, arXiv:gr-qc/1412.6439] it has been shown that specific boundary conditions can be related to the algebra of Dirac observables. Moreover, a process afterwards associated to the algebra of existent hidden symmetries, from which the boundary conditions can be selected, was introduced. On the other hand, in Ref. [T. Rostami, S. Jalalzadeh and P. V. Moniz, Phys. Rev. D 92 (2015) 023526, arXiv:gr-qc/1507.04212] it was subsequently argued that some factor ordering choices can be extracted from the hidden symmetries structure of the minisuperspace model. In Refs. [S. Jalalzadeh, S. M. M. Rasouli and P. V. Moniz, Phys. Rev. D 90 (2014) 023541, S. Jalalzadeh and P. V. Moniz, Phys. Rev. D 89 (2014), S. Jalalzadeh, T. Rostami and P. V. Moniz, Eur. Phys. J. C 75 (2015) 38, arXiv:gr-qc/1412.6439 and T. Rostami, S. Jalalzadeh and P. V. Moniz, Phys. Rev. D 92 (2015) 023526, arXiv:gr-qc/1507.04212], we proceeded gradually towards less simple models, ranging from a FLRW model with a perfect fluid [S. Jalalzadeh, S. M. M. Rasouli and P. V. Moniz, Phys. Rev. D 90 (2014) 023541] up to a conformal scalar field content [T. Rostami, S. Jalalzadeh and
$\\psi$ = W e$^{\\pm\\phi}$ quantum cosmological solutions for Class A Bianchi models
Obregón, O
1995-01-01
We find solutions for quantum Class A Bianchi models of the form \\rm \\Psi=W\\, e^{\\pm \\Phi} generalizing the results obtained by Moncrief and Ryan in standard quantum cosmology. For the II and IX Bianchi models there are other solutions \\rm \\tilde\\Phi_2, \\rm \\tilde\\Phi_9 to the Hamilton-Jacobi equation for which \\rm \\Psi is necessarely zero, in contrast with solutions found in supersymmetric quantum cosmology.
Probing Gravitational Cat States in Canonical Quantum Theory vs Objective Collapse Theories
Derakhshani, Maaneli
2016-01-01
Using as a testbed the recently proposed "gravcat" experimental scheme in [1], we compare the properties of gravitational cat states in three descriptions: (1) canonical quantum theory (CQT) combined with the Newtonian limit of GR, (2) objective collapse theories (OCTs) extended to the regime of semiclassical Newtonian gravity, and (3) OCTs extended to incorporate quantized Newtonian gravity. For the CQT approach, we follow the treatment of Hu and Anastopoulos in [2]. For the OCTs, we conside...
Loop Quantum Gravity and the The Planck Regime of Cosmology
Ashtekar, Abhay
2013-01-01
The very early universe provides the best arena we currently have to test quantum gravity theories. The success of the inflationary paradigm in accounting for the observed inhomogeneities in the cosmic microwave background already illustrates this point to a certain extent because the paradigm is based on quantum field theory on the curved cosmological space-times. However, this analysis excludes the Planck era because the background space-time satisfies Einstein's equations all the way back to the big bang singularity. Using techniques from loop quantum gravity, the paradigm has now been extended to a self-consistent theory from the Planck regime to the onset of inflation, covering some 11 orders of magnitude in curvature. In addition, for a narrow window of initial conditions, there are departures from the standard paradigm, with novel effects, such as a modification of the consistency relation involving the scalar and tensor power spectra and a new source for non-Gaussianities. Thus, the genesis of the lar...
Quantized cosmological constant in 1+1 dimensional quantum gravity with coupled scalar matter
Energy Technology Data Exchange (ETDEWEB)
Govaerts, Jan; Zonetti, Simone, E-mail: Jan.Govaerts@uclouvain.be, E-mail: Simone.Zonetti@uclouvain.be [Centre for Cosmology, Particle Physics and Phenomenology (CP3), Institut de Recherche en Mathematique et Physique (IRMP), Universite catholique de Louvain, Chemin du Cyclotron 2, B-1348 Louvain-la Neuve (Belgium)
2011-09-21
A two-dimensional matter-coupled model of quantum gravity is studied in the Dirac approach to constrained dynamics in the presence of a cosmological constant. It is shown that after partial fixing to the conformal gauge, the requirement of a quantum realization of the conformal algebra for physical quantum states of the fields naturally constrains the cosmological constant to take values in a well-determined and mostly discrete spectrum. Furthermore, the contribution of the quantum fluctuations of the single dynamical degree of freedom in the gravitational sector, namely the conformal mode, to the cosmological constant is negative, in contrast to the positive contributions of the quantum fluctuations of the matter fields, possibly opening an avenue towards addressing the cosmological constant problem in a more general context.
Preon models, relativity, quantum mechanics and cosmology (I)
Gonzalez-Mestres, Luis
2009-01-01
Preons are hypothetic constituents of the standard particles. They were initially assumed to have basically similar properties to those of conventional matter. But this is not necessarily the case: the ultimate constituents of matter may feel a different space-time from that of special relativity and exhibit mechanical properties different from those predicted by standard quantum mechanics. They can also play an important cosmological role (inflation, dark matter, dark energy...). It is even not obvious that energy and momentum would have to be conserved in such a scenario. In this series of papers, we review the subject using the superbradyon model as an example, and suggest new ways to explore possible tests of the preon hypothesis.
Anisotropic models are unitary: A rejuvenation of standard quantum cosmology
Pal, Sridip
2016-01-01
The present work proves that the folk-lore of the pathology of non-conservation of probability in quantum anisotropic models is wrong. It is shown in full generality that all operator ordering can lead to a Hamiltonian with a self-adjoint extension as long as it is constructed to be a symmetric operator, thereby making the problem of non-unitarity in context of anisotropic homogeneous model a ghost. Moreover, it is indicated that the self-adjoint extension is not unique and this non-uniqueness is suspected not to be a feature of Anisotropic model only, in the sense that there exists operator orderings such that Hamiltonian for an isotropic homogeneous cosmological model does not have unique self-adjoint extension, albeit for isotropic model, there is a special unique extension associated with quadratic form of Hamiltonian i.e {\\it Friedrichs extension}. Details of calculations are carried out for a Bianchi III model.
Classical and quantum cosmology of Born-Infeld type models
Kamenshchik, Alexander; Kwidzinski, Nick
2016-01-01
We discuss Born-Infeld type fields (tachyon fields) in classical and quantum cosmology. We first partly review and partly extend the discussion of the classical solutions and focus in particular on the occurrence of singularities. For quantization, we employ geometrodynamics. In the case of constant potential, we discuss both Wheeler-DeWitt quantization and reduced quantization. We are able to give various solutions and discuss their asymptotics. For the case of general potential, we transform the Wheeler-DeWitt equation to a form where it leads to a difference equation. Such a difference equation was previously found in the quantization of black holes. We give explicit results for the cases of constant potential and inverse square potential and point out special features possessed by solutions of the difference equation.
Particle creation and non-adiabatic transitions in quantum cosmology
Massar, S
1998-01-01
The aim of this paper is to compute transitions amplitudes in quantum cosmology, and in particular pair creation amplitudes and radiative transitions. To this end, we apply a double adiabatic development to the solutions of the Wheeler-DeWitt equation restricted to mini-superspace wherein gravity is described by the scale factor $a$. The first development consists in working with instantaneous eigenstates, in $a$, of the matter Hamiltonian. The second development is applied to the gravitational part of the wave function and generalizes the usual WKB approximation. We then obtain an exact equation which replaces the Wheeler-DeWitt equation and determines the evolution, i.e. the dependence in $a$, of the coefficients of this double expansion. When working in the gravitational adiabatic approximation, the simplified equation delivers the unitary evolution of transition amplitudes occurring among instantaneous eigenstates. Upon abandoning this approximation, one finds that there is an additional coupling among ma...
Classical and quantum cosmology of Born-Infeld type models
Kamenshchik, Alexander; Kiefer, Claus; Kwidzinski, Nick
2016-04-01
We discuss Born-Infeld type fields (tachyon fields) in classical and quantum cosmology. We first partly review and partly extend the discussion of the classical solutions and focus in particular on the occurrence of singularities. For quantization, we employ geometrodynamics. In the case of constant potential, we discuss both Wheeler-DeWitt quantization and reduced quantization. We are able to give various solutions and discuss their asymptotics. For the case of general potential, we transform the Wheeler-DeWitt equation to a form where it leads to a difference equation. Such a difference equation was previously found in the quantization of black holes. We give explicit results for the cases of constant potential and inverse squared potential and point out special features possessed by solutions of the difference equation.
Condensates in Quantum Chromodynamics and the Cosmological Constant
Energy Technology Data Exchange (ETDEWEB)
Brodsky, Stanley J.; Shrock, Robert
2009-05-08
Casher and Susskind have noted that in the light-front description, spontaneous chiral symmetry breaking in quantum chromodynamics (QCD) 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 QCD condensates are associated with the internal dynamics of hadrons. We discuss condensates using condensed matter analogues, the AdS/CFT 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 et al., using the Bethe-Salpeter/Dyson-Schwinger formalism for QCD bound states. These results imply that QCD condensates give zero contribution to the cosmological constant, since all of the gravitational effects of the in-hadron condensates are already included in the normal contribution from hadron masses.
State refinements and coarse graining in a full theory embedding of loop quantum cosmology
Bodendorfer, N.
2017-07-01
Bridging between descriptions involving few large and many small quantum numbers is the main open problem in loop quantum gravity. In other words, one would like to be able to represent the same physical system in terms of a few ‘coarse’ quantum numbers, while the effective dynamics at the coarse level should agree with the one induced by a description involving many small quantum numbers. Efforts to understand this relationship face the problem of the enormous computational complexity involved in evolving a generic state containing many quanta. In a cosmological context however, certain symmetry assumptions on the quantum states allow one to simplify the problem. In this paper, we will show how quantum states describing a spatially flat homogeneous and isotropic universe can be refined and coarse grained. Invariance of the dynamics of the coarse observables is shown to require a certain scaling property (familiar from loop quantum cosmology) of the quantum states if no running of parameters is taken into account. The involved states are solutions to the Hamiltonian constraint when terms coming from spatial derivatives are neglected, i.e. one works in the approximation of non-interacting FRW patches. The technical means to arrive at this result are a version of loop quantum gravity based on variables inspired by loop quantum cosmology, as well as an exact solution to the quantum dynamics of loop quantum cosmology which extends to the full theory in the chosen approximation.
Quantum effects of massive modes in a cosmological quantum space-time
Tavakoli, Yaser
2015-01-01
The quantum theory of a massive, minimally coupled scalar field on an isotropic cosmological quantum space-time is revisited. The interplay between the quantum background and the massive modes of the field, when disregarding their back-reaction effects, gives rise to a theory of quantum field on an effective, dressed space-time whose isotropy may be broken in the direction of the field propagation. On the resulting dressed geometry, evolution of the massive modes, by analyzing the solutions to the corresponding Klein-Gordon equation, is investigated. In particular, by computing the leading order contributions in adiabatic series, an approximate solution for the mode function is obtained. By using the adiabatic regularization, to the fourth order in expansion series, the renormalization of the stress-energy and Hamiltonian of the quantized field is studied. The problem of particle production is studied here in the light of the classical theory of wave propagation on the effective anisotropic background. To the...
Socorro, J.; Nuñez, Omar E.
2017-04-01
The multi-scalar field cosmology of the anisotropic Bianchi type-I model is used in order to construct a family of potentials that are the best suited to model the inflation phenomenon. We employ the quantum potential approach to quantum mechanics due to Bohm in order to solve the corresponding Wheeler-DeWitt equation; which in turn enables us to restrict sensibly the aforementioned family of potentials. Supersymmetric Quantum Mechanics (SUSYQM) is also employed in order to constrain the superpotential function, at the same time the tools from SUSY Quantum Mechanics are used to test the family of potentials in order to infer which is the most convenient for the inflation epoch. For completeness solutions to the wave function of the universe are also presented.
From Big Crunch to Big Bang A Quantum String Cosmology Perspective
Maharana, J
2002-01-01
The scenario that the Universe contracts towards a big crunch and then undergoes a transition to expanding Universe in envisaged in the quantum string cosmology approach. The Wheeler-De Witt equation is solved exactly for an exponential dilaton potential. S-duality invariant cosmological effective action, for type IIB theory, is considered to derive classical solutions and solve WDW equations.
Anisotropic cosmology in S\\'aez-Ballester theory: classical and quantum solutions
Socorro, J; G., M A Sánchez; Palos, M G Frías
2010-01-01
We use the S\\'aez-Ballester theory on anisotropic Bianchi I cosmological model, with barotropic fluid and cosmological constant. We obtain the classical solution by using the Hamilton-Jacobi approach. Also the quantum regime is constructed and exact solutions to the Wheeler-DeWitt equation are found.
Quantum cosmology in Ho\\v{r}ava-Lifshitz gravity
Obregón, O
2013-01-01
Quantum cosmology is studied within the framework of the minimal quantum gravity theory proposed by Ho\\v{r}ava. For this purpose we choose the Kantowski-Sachs (KS) model and construct the corresponding Wheeler-DeWitt equation. We study the solution to this equation in the ultraviolet limit for different values of the running parameter {\\lambda} of the theory. It is observed that the wave packet for this Universe changes completely compared with the one observed in the infrared (general relativity) regime. We also look at the classical solutions by means of a WKB semiclassical approximation. It is observed that if {\\lambda} takes its relativistic value {\\lambda} = 1 a generalized KS metric is obtained which differs from the usual KS solution in general relativity by an additional term arising from the higher-order curvature terms in the action and which dominates the behavior of the solution for very small values of the time parameter. We discuss the physical properties of this solution by comparing it with th...
Loop quantum cosmology of Bianchi IX: Effective dynamics
Corichi, Alejandro
2015-01-01
We study numerically the solutions to the effective equations of Bianchi IX spacetimes within Loop Quantum Cosmology. We consider Bianchi IX models with and without inverse triad corrections whose matter content is a scalar field without mass. The solutions are classified using the classical observables. We show that both effective theories --with lapse N=V and N=1-- solve the big bang singularity and reproduce the classical dynamics far from the bounce. Moreover, due to the spatial compactness, there is an infinity number of bounces and recollapses. We study the limit of large volume 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, at the quantum nor effective level. W...
On the Green's function and iterative solutions of Loop Quantum Cosmology
Shojai, F.; Shojai, A.
2006-01-01
Here we shall find the Green’s function of the difference equation of loop quantum cosmology. To illustrate how to use it, we shall obtain an iterative solution for closed model and evaluate its corresponding Bohmian trajectory.
Engineering Stable Discrete-Time Quantum Dynamics via a Canonical QR Decomposition
Bolognani, Saverio
2009-01-01
We analyze the asymptotic behavior of discrete-time, Markovian quantum systems with respect to a subspace of interest. Global asymptotic stability of subspaces is relevant to quantum information processing, in particular for initializing the system in pure states or subspace codes. We provide a linear-algebraic characterization of the dynamical properties leading to invariance and attractivity of a given quantum subspace. We then construct a design algorithm for discrete-time feedback control that allows to stabilize a target subspace, proving that if the control problem is feasible, then the algorithm returns an effective control choice. In order to prove this result, a canonical QR matrix decomposition is derived, and also used to establish the control scheme potential for the simulation of open-system dynamics.
Canonical quantum gravity in the Vassiliev invariants arena; 1, Kinematical structure
Di Bartolo, C; Griego, J R; Pullin, J; Bartolo, Cayetano Di; Gambini, Rodolfo; Griego, Jorge; Pullin, Jorge
2000-01-01
We generalize the idea of Vassiliev invariants to the spin network context, with the aim of using these invariants as a kinematical arena for a canonical quantization of gravity. This paper presents a detailed construction of these invariants (both ambient and regular isotopic) requiring a significant elaboration based on the use of Chern-Simons perturbation theory which extends the work of Kauffman, Martin and Witten to four-valent networks. We show that this space of knot invariants has the crucial property -from the point of view of the quantization of gravity- of being loop differentiable in the sense of distributions. This allows the definition of diffeomorphism and Hamiltonian constraints. We show that the invariants are annihilated by the diffeomorphism constraint. In a companion paper we elaborate on the definition of a Hamiltonian constraint, discuss the constraint algebra, and show that the construction leads to a consistent theory of canonical quantum gravity.
Structure of multiphoton quantum optics. I. Canonical formalism and homodyne squeezed states
Dell'Anno, F; Illuminati, F; Anno, Fabio Dell'; Siena, Silvio De; 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 mixings 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 to vary at will the statist...
Yanai, Takeshi; Kurashige, Yuki; Neuscamman, Eric; Chan, Garnet Kin-Lic
2010-01-01
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 [Cu2O2]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 [Cu2O2]2+.
Gnutzmann, Sven; Waltner, Daniel
2016-12-01
We consider exact and asymptotic solutions of the stationary cubic nonlinear Schrödinger equation on metric graphs. We focus on some basic example graphs. The asymptotic solutions are obtained using the canonical perturbation formalism developed in our earlier paper [S. Gnutzmann and D. Waltner, Phys. Rev. E 93, 032204 (2016), 10.1103/PhysRevE.93.032204]. For closed example graphs (interval, ring, star graph, tadpole graph), we calculate spectral curves and show how the description of spectra reduces to known characteristic functions of linear quantum graphs in the low-intensity limit. Analogously for open examples, we show how nonlinear scattering of stationary waves arises and how it reduces to known linear scattering amplitudes at low intensities. In the short-wavelength asymptotics we discuss how genuine nonlinear effects may be described using the leading order of canonical perturbation theory: bifurcation of spectral curves (and the corresponding solutions) in closed graphs and multistability in open graphs.
Classical and quantum Big Brake cosmology for scalar field and tachyonic models
Kamenshchik, A
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.
Classical and Quantum Big Brake Cosmology for Scalar Field and Tachyonic Models
Kamenshchik, Alexander; Manti, Serena
2015-01-01
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.
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.
Directory of Open Access Journals (Sweden)
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.
Dupuy, John L
2016-01-01
The spatially closed Friedmann-Lemaitre-Robertson-Walker model in loop quantum cosmology admits two inequivalent consistent quantizations: one based on expressing field strength in terms of holonomies over closed loops, and, another using a connection operator and open holonomies. Using effective dynamics, we investigate the phenomenological differences between the two quantizations for single fluid and two fluid scenarios with various equations of state, including phantom matter. We show that a striking difference between the two quantizations is the existence of two distinct quantum turnarounds, either bounces or recollapses, in the connection quantization, in contrast to a single distinct quantum bounce or recollapse in the holonomy quantization. These results generalize an earlier result on two distinct quantum bounces for stiff matter by Corichi and Karami. However, we find that in certain situations two distinct quantum turnarounds can become virtually indistinguishable. And depending on initial conditi...
Di Bartolo, C; Griego, J R; Pullin, J; Bartolo, Cayetano Di; Gambini, Rodolfo; Griego, Jorge; Pullin, Jorge
2000-01-01
In a companion paper we introduced a kinematical arena for the discussion of the constraints of canonical quantum gravity in the spin network representation based on Vassiliev invariants. In this paper we introduce the Hamiltonian constraint, extend the space of states to non-diffeomorphism invariant ``habitats'' and check that the off-shell quantum constraint commutator algebra reproduces the classical Poisson algebra of constraints of general relativity without anomalies. One can therefore consider the resulting set of constraints and space of states as a consistent theory of canonical quantum gravity.
Rubakov, V A
2014-01-01
In these lectures we first concentrate on the cosmological problems which, hopefully, have to do with the new physics to be probed at the LHC: the nature and origin of dark matter and generation of matter-antimatter asymmetry. We give several examples showing the LHC cosmological potential. These are WIMPs as cold dark matter, gravitinos as warm dark matter, and electroweak baryogenesis as a mechanism for generating matter-antimatter asymmetry. In the remaining part of the lectures we discuss the cosmological perturbations as a tool for studying the epoch preceeding the conventional hot stage of the cosmological evolution.
Quantization ambiguities and bounds on geometric scalars in anisotropic loop quantum cosmology
Singh, Parampreet
2013-01-01
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-Lemaitre-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-Lemaitre-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.
Can Cosmological Constant be a Forbidden Zone (GAP) in Quantum Vacuum
Pankovic, Vladan; Ciganovic, Simo
2008-01-01
In this work we suggest, without detailed mathematical analysis, a hypothesis on the physical meaning of cosmological constant. It is primarily based on a conceptual analogy with energy characteristics of the crystal lattice structure, i.e. energy zones theory in solid state physics. Namely, according to some theories (holographic principle, emergent gravity etc.) it is supposed that empty space, i.e. quantum vacuum holds a structure like to crystal lattice. It implies a possibility of the existence of totally occupied zones consisting of many levels of the negative energies as well as at least one negative energy forbidden zone, i.e. negative energy gap without any (occupied or empty) level of the negative energy. We suppose that given negative energy forbidden zone in the quantum vacuum represents effectively a positive energy zone without quantum particles that corresponds to cosmological constant. Also we suggest some other (less extravagant) model of the cosmological constant. Here cosmological constant ...
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.
Teleparallel loop quantum cosmology in a system of intersecting branes
Sepehri, Alireza; Beesham, A; de Haro, Jaume
2016-01-01
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 the other 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 the D4 brane from one end and sticks to one of the anti-D8 branes from another one. In this system, there are three types of ?elds, corresponding to compacted D4 branes, intersecting branes and D3-branes. These ?elds interact with each other and make the angle between branes oscillate. By decreasing this angle and approaching the ...
Dupuy, John L.; Singh, Parampreet
2017-01-01
The spatially closed Friedmann-Lemaître-Robertson-Walker model in loop quantum cosmology admits two inequivalent consistent quantizations: one based on expressing the field strength in terms of the holonomies over closed loops and another using a connection operator and open holonomies. Using the effective dynamics, we investigate the phenomenological differences between the two quantizations for the single-fluid and the two-fluid scenarios with various equations of state, including the phantom matter. We show that a striking difference between the two quantizations is the existence of two distinct quantum turnarounds, either bounces or recollapses, in the connection quantization, in contrast to a single distinct quantum bounce or a recollapse in the holonomy quantization. These results generalize an earlier result on the existence of two distinct quantum bounces for stiff matter by Corichi and Karami. However, we find that in certain situations two distinct quantum turnarounds can become virtually indistinguishable. And depending on the initial conditions, a pure quantum cyclic universe can also exist undergoing a quantum bounce and a quantum recollapse. We show that for various equations of states, connection-based quantization leads to super-Planckian values of the energy density and the expansion scalar at quantum turnarounds. Interestingly, we find that very extreme energy densities can also occur for the holonomy quantization, breaching the maximum allowed density in the spatially flat loop quantized model. However, the expansion scalar in all these cases is bounded by a universal value.
Quantum Deformed Canonical Transformations, W_{infty}-algebras and Unitary Transformations
Gozzi, E
1994-01-01
We investigate the algebraic properties of the quantum counterpart of the classical canonical transformations using the symbol-calculus approach to quantum mechanics. In this framework we construct a set of pseudo-differential operators which act on the symbols of operators, i.e., on functions defined over phase-space. They act as operatorial left- and right- multiplication and form a $W_{infty}times W_{infty}$- algebra which contracts to its diagonal subalgebra in the classical limit. We also describe the Gel'fand-Naimark-Segal (GNS) construction in this language and show that the GNS representation-space (a doubled Hilbert space) is closely related to the algebra of functions over phase-space equipped with the star-product of the symbol-calculus.
Alvarenga, F G; Freitas, R C; Gonçalves, S V B
2015-01-01
In this paper we study the quantum Kantowski-Sachs model and we solve the Wheeler-DeWitt equation in minisuperspace to obtain the wave function of the corresponding universe. The perfect fluid is described by the Schutz's canonical formalism, which allows to attribute dynamical degrees of freedom to matter. The time is introduced phenomenologically using the fluid's degrees of freedom. In particular, we adopt a stiff matter fluid. The Kantowski-Sachs model is also presented with the introduction of so-called geometric time. Finally, the agreement between the results is analyzed and the possibility of equivalence between the two approaches is discussed.
Cosmology of the Planck Era from a Renormalization Group for Quantum Gravity
Bonanno, A
2002-01-01
Homogeneous and isotropic cosmologies of the Planck era before the classical Einstein equations become valid are studied taking quantum gravitational effects into account. The cosmological evolution equations are renormalization group improved by including the scale dependence of Newton's constant and of the cosmological constant as it is given by the flow equation of the effective average action for gravity. It is argued that the Planck regime can be treated reliably in this framework because gravity is found to become asymptotically free at short distances. The epoch immediately after the initial singularity of the Universe is described by an attractor solution of the improved equations which is a direct manifestation of an ultraviolet attractive renormalization group fixed point. It is shown that quantum gravity effects in the very early Universe might provide a resolution to the horizon and flatness problem of standard cosmology, and could generate a scale-free spectrum of primordial density fluctuations.
Teleparallel loop quantum cosmology in a system of intersecting branes
Directory of Open Access Journals (Sweden)
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
Sepehri, Alireza; Pradhan, Anirudh; Beesham, Aroonkumar; de Haro, Jaume
2016-09-01
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.
An Approach to Loop Quantum Cosmology Through Integrable Discrete Heisenberg Spin Chains
Dantas, Christine C
2012-01-01
The quantum evolution equation of Loop Quantum Cosmology (LQC) -- the quantum Hamiltonian constraint -- is a difference equation. We relate the LQC constraint equation in vacuum Bianchi I separable (locally rotationally symmetric) models with an integrable differential-difference nonlinear Schr\\"odinger type equation, which in turn is known to be associated with integrable, discrete Heisenberg spin chain models in condensed matter physics. We illustrate the similarity between both systems with a simple constraint in the linear regime.
The Causal Interpretation of Dust and Radiation Fluids Non-Singular Quantum Cosmologies
De Barros, J A; Sagioro-Leal, M A
1998-01-01
We apply the causal interpretation of quantum mechanics to homogeneous and isotropic quantum cosmology where the sources of the gravitational field are either dust or radiation perfect fluids. We find non-singular quantum trajectories which tends to the classical one when the scale factor becomes much larger then the Planck length. In this situation, the quantum potential becomes negligible. There are no horizons. As radiation is a good approximation for the matter content of the early universe, this result suggests that the universe can be eternal due to quantum effects.
Ward, B F L
2015-01-01
We argue that our recent success in using our resummed quantum gravity approach to Einstein's general theory of relativity, in the context of the Planck scale cosmology formulation of Bonanno and Reuter, to estimate the value of the cosmological constant \\Lambda supports the use of quantum mechanical consistency requirements to constrain the main uncertainty in that very promising result. This main uncertainty, which is due to the uncertainty in the value of the time t_{\\text{tr}} at which the transition from the Planck scale cosmology to the FRW model occurs, is shown to be reduced, by requiring consistency between the Heisenberg uncertainty principle and the known properties of the solutions of Einstein's equations, from four orders of magnitude to the level of a factor of {\\cal O}(10). This lends more credibility to the over-all resummed quantum gravity approach itself, in general, and to our estimate of $\\Lambda$ in particular.
Probing the small distance structure of canonical quantum gravity using the conformal group
Hooft, Gerard 't
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 expected to be conformally invariant and therefore finite. However, also the conformal integral itself diverges, and therefore the actual situation is more delicate. The effects of a renormalization counter term are considered, including the associated problem of unitarity violation, such as a Landau-like ghost. Adding (massive or massless) matter fields does not change the picture; to confirm this, detailed calculations were necessary, and they are presented. Some alternative ideas are offered, including a more daring speculation, which is that no counter term should be allowed for at all. This has far-reaching and important consequences, which we discuss. A surprising picture emerges of quantized elementary particles i...
A Langevin Canonical Approach to the Study of Quantum Stochastic Resonance in Chiral Molecules
Directory of Open Access Journals (Sweden)
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.
Homoclinic Chaos in Axisymmetric Bianchi-IX cosmological models with an "ad hoc" quantum potential
Corrêa, G. C.; Stuchi, T. J.; Jorás, S. E.
2010-01-01
In this work we study the dynamics of the axisymmetric Bianchi IX cosmological model with a term of quantum potential added. As it is well known this class of Bianchi IX models are homogeneous and anisotropic with two scale factors, $A(t)$ and $B(t)$, derived from the solution of Einstein's equation for General Relativity. The model we use in this work has a cosmological constant and the matter content is dust. To this model we add a quantum-inspired potential that is intended to represent sh...
Grishchuk, L P
1994-01-01
A theory of quantum-mechanical generation of cosmological perturbations is considered. The conclusion of this study is that if the large-angular-scale anisotropy in the cosmic microwave background radiation is caused by the long-wavelength cosmological perturbations of quantum mechanical origin, they are, most likely, gravitational waves, rather than density perturbations or rotational perturbations. Some disagreements with previous publications are clarified. This contribution to the Proceedings is based on Reference~[34]. NOTE: To generate an output, please extract and save the file crckapb.sty which appear at the beginning of the main file.
Vittorio, Nicola
2017-01-01
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.
Cosmology emerging as the gauge structure of a nonlinear quantum system
Kam, Chon-Fai
2016-01-01
Berry phases and gauge structures in parameter spaces of quantum systems are the foundation of a broad range of quantum effects such as quantum Hall effects and topological insulators. The gauge structures of interacting many-body systems, which often present exotic features, are particularly interesting. While quantum systems are intrinsically linear due to the superposition principle, nonlinear quantum mechanics can arise as an effective theory for interacting systems (such as condensates of interacting bosons). Here we show that gauge structures similar to curved spacetime can arise in nonlinear quantum systems where the superposition principle breaks down. In the canonical formalism of the nonlinear quantum mechanics, the geometric phases of quantum evolutions can be formulated as the classical geometric phases of a harmonic oscillator that represents the Bogoliubov excitations. We find that the classical geometric phase can be described by a de Sitter universe. The fundamental frequency of the harmonic o...
Cosmology with a Decaying Vacuum Energy Parametrization Derived from Quantum Mechanics
Szydlowski, Marek; Urbanowski, Krzysztof
2015-01-01
Within the quantum mechanical treatment of the decay problem one finds that at late times $t$ the 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: $\\Lambda - \\Lambda_{\\text{bare}}\\equiv \\Lambda(t) -\\Lambda_{\\text{bare}} \\sim 1/t^{2}$. 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 $\\Lambda(t)$ cosmologies (the $\\Lambda(t)$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 usin...
Big Crunch Avoidance in k = 1 Semi-Classical Loop Quantum Cosmology
Singh, P; Singh, Parampreet; Toporensky, Alexey
2004-01-01
It is well known that a closed universe with a minimally coupled massive scalar field always collapses to a singularity unless the initial conditions are extremely fine tuned. We show that the corrections to the equations of motion for the massive scalar field, given by loop quantum gravity in high curvature regime, always lead to a bounce independently of the initial conditions. In contrast to the previous works in loop quantum cosmology, we note that the singularity can be avoided even at the semi-classical level of effective dynamical equations with non-perturbative quantum gravity modifications, without using a discrete quantum evolution.
Thermalization and Canonical Typicality in Translation-Invariant Quantum Lattice Systems
Müller, Markus P.; Adlam, Emily; Masanes, Lluís; Wiebe, Nathan
2015-12-01
It has previously been suggested that small subsystems of closed quantum systems thermalize under some assumptions; however, this has been rigorously shown so far only for systems with very weak interaction between subsystems. In this work, we give rigorous analytic results on thermalization for translation-invariant quantum lattice systems with finite-range interaction of arbitrary strength, in all cases where there is a unique equilibrium state at the corresponding temperature. We clarify the physical picture by showing that subsystems relax towards the reduction of the global Gibbs state, not the local Gibbs state, if the initial state has close to maximal population entropy and certain non-degeneracy conditions on the spectrumare satisfied.Moreover,we showthat almost all pure states with support on a small energy window are locally thermal in the sense of canonical typicality. We derive our results from a statement on equivalence of ensembles, generalizing earlier results by Lima, and give numerical and analytic finite size bounds, relating the Ising model to the finite de Finetti theorem. Furthermore, we prove that global energy eigenstates are locally close to diagonal in the local energy eigenbasis, which constitutes a part of the eigenstate thermalization hypothesis that is valid regardless of the integrability of the model.
Localization of quantum objects in an expanding universe and cosmologically induced classicality
Herzenberg, C L
2010-01-01
Independent studies by different authors have proposed that classicality may be induced in quantum objects by cosmological constraints presented by an expanding universe of finite extent in space-time. Cosmological effects on a quantum system can be explored in one approach by considering an object at rest in space with a universal Hubble expansion taking place away from it, and developing a Schroedinger type governing differential equation incorporating an intrinsic expansion speed. Wave function solutions to this governing equation exhibit pronounced central localization. The extent of concentration of probability depends on mass; objects with small masses tend to behave in a delocalized manner as ordinary quantum objects do in a static space, while quantum objects with large masses are concentrated into much smaller regions. To develop a criterion for classicality, we consider that if the size of the localized region of concentrated probability density is larger than the size of the corresponding extended ...
Entangled States in Quantum Cosmology and the Interpretation of Λ
Directory of Open Access Journals (Sweden)
Orlando Luongo
2011-02-01
Full Text Available The cosmological constant Λ can be achieved as the result of entangled and statistically correlated minisuperspace cosmological states, built up by using a minimal choice of observable quantities, i.e., Ωm and Ωk, which assign the cosmic dynamics. In particular, we consider a cosmological model where two regions, corresponding to two correlated eras, are involved; the present universe description would be, in this way, given by a density matrix ˆρ, corresponding to an entangled final state. Starting from this assumption, it is possible to infer some considerations on the cosmic thermodynamics by evaluating the Von Neumann entropy. The correlation between different regions by the entanglement phenomenon results in the existence of Λ (in particular ΩΛ which could be interpreted in the framework of the recent astrophysical observations. As a byproduct, this approach could provide a natural way to solve the so called coincidence problem.
Wave packets and initial conditions in quantum cosmology
Gousheh, S S
2000-01-01
We discuss the construction of wave packets resulting from the solutions of a class of Wheeler-DeWitt equations in Robertson-Walker type cosmologies. We present an ansatz for the initial conditions which leads to a unique determination of the expansion coefficients in the construction of the wave packets with probability distributions which, in an interesting contrast to some of the earlier works, agree well with all possible classical paths. The possible relationship between these initial conditions and signature transition in the context of classical cosmology is also discussed.
Two-Loop Quantum Gravity Corrections to Cosmological Constant in Landau Gauge
Hamada, Ken-ji
2015-01-01
The anomalous dimensions of the Planck mass and the cosmological constant are calculated in a renormalizable quantum conformal gravity with a single dimensionless coupling, which is formulated using dimensional regularization on the basis of Hathrell's works for conformal anomalies. The dynamics of the traceless tensor field is handled by the Weyl action, while that of the conformal-factor field is described by the induced Wess-Zumino actions, including the Riegert action as the kinetic term. Loop calculations are carried out in Landau gauge in order to reduce the number of Feynman diagrams as well as to avoid some uncertainty. Especially, we calculate two-loop quantum gravity corrections to the cosmological constant. It suggests that there is a dynamical solution to the cosmological constant problem.
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 CMBR 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 the COBE-type observations.
Quantum Fluctuations in Cosmology and How They Lead to a Multiverse
Guth, Alan H
2013-01-01
This article discusses density perturbations in inflationary models, offering a pedagogical description of how these perturbations are generated by quantum fluctuations in the early universe. A key feature of inflation is that that rapid expansion can stretch microscopic fluctuations to cosmological proportions. I discuss also another important conseqence of quantum fluctuations: the fact that almost all inflationary models become eternal, so that once inflation starts, it never stops.
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.
Physical consequences of black holes in non-perturbative quantum gravity and inflationary cosmology
Reska, P.M.
2011-01-01
In this thesis the consequences of the presence of a Schwarzschild black hole in de Sitter space are studied in the setting of non-perturbative quantum gravity and in inflationary cosmology. We first review the formalism of Causal Dynamical Triangulations (CDT) which implements a lattice regularizat
Gravitation and cosmology with York time
Roser, Philipp
2016-01-01
[Shortened abstract:] In this thesis we investigate a solution to the `problem of time' in canonical quantum gravity by splitting spacetime into surfaces of constant mean curvature parameterised by York time. We argue that there are reasons to consider York time a viable candidate for a physically meaningful notion of time. We investigate a number York-time Hamiltonian-reduced cosmological models and explore some technical aspects, such as the non-canonical Poisson structure. We develop York-time Hamiltonian-reduced cosmological perturbation theory by solving the Hamiltonian constraint perturbatively around a homogeneous background for the physical (non-vanishing) Hamiltonian that is the momentum conjugate to the York time parameter. We proceed to canonically quantise the cosmological models and the perturbation theory and discuss a number of conceptual and technical points, such as volume eigenfunctions and the absence of a momentum representation due to the non-standard commutator structure. We propose an a...
Loop Quantum effects on Om-diagnostic and its Cosmological Implications
Rudra, Prabir
2014-01-01
In this paper we study the Loop quantum effects on the \\textit{Om} diagnostic and subsequently on the universe. We reconstruct the \\textit{Om} diagnostic in the background of Loop quantum gravity and then study the behaviour of various Chaplygin gas dark energy models using the modified diagnostic in a comparative scenario. The trajectories discriminate the various dark energy models from each other both in the Einstein gravity as well as Loop quantum gravity. The Loop quantum effects are also clearly noticeable from the trajectories in past, present and future universe. We see that the Loop quantum deviations are highly pronounced in the early universe, but alleviates as we tend towards the present universe and continue to decay in future. Thus it puts a big question on the effectiveness and consequently the suitability of loop quantum cosmology to explain the future universe.
State refinements and coarse graining in a full theory embedding of loop quantum cosmology
Bodendorfer, Norbert
2016-01-01
Bridging between descriptions involving few large and many small quantum numbers is the main open problem in loop quantum gravity. In other words, one would like to be able to represent the same physical system in terms of a few "coarse" quantum numbers, while the effective dynamics at the coarse level should agree with the one induced by a description involving many small quantum numbers. Efforts to understand this relationship face the problem of the enormous computational complexity involved in evolving a generic state containing many quanta. In a cosmological context however, certain symmetry assumptions on the quantum states allow to simplify the problem. In this paper, we will show how quantum states describing a spatially flat homogeneous and isotropic universe can be refined while the dynamics of the coarse observables is unchanged. The involved states are solutions to the Hamiltonian constraint when terms coming from spatial derivatives are neglected, i.e. one works in the approximation of non-intera...
Reconstructing the evolution of the Universe from loop quantum cosmology scalar fields
Oikonomou, V. K.
2016-08-01
We extend the scalar-tensor reconstruction techniques for classical cosmology frameworks, in the context of loop quantum cosmology. After presenting in some detail how the equations are generalized in the loop quantum cosmology case, we discuss which new features and limitations the quantum framework introduces, and we use various illustrative examples in order to demonstrate how the method works. As we show, the energy density has two different classes of solutions, and one of these yields the correct classical limit, while the second captures the quantum phenomena. We study in detail the scalar tensor reconstruction method for both of these solutions. We also discuss some scenarios for which the Hubble rate becomes unbounded at finite time, which corresponds for example to the case in which the big rip occurs. As we show, this issue is nontrivial and we discuss how this case should be treated in a consistent way. Finally, we investigate how the classical stability conditions for the scalar-tensor solutions are generalized in the loop quantum framework.
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.
Scalar and tensor perturbations in loop quantum cosmology: High-order corrections
Zhu, Tao; Cleaver, Gerald; Kirsten, Klaus; Sheng, Qin; Wu, Qiang
2015-01-01
Loop quantum cosmology (LQC) provides promising resolutions to the trans-Planckian issue and initial singularity arising in the inflationary models of general relativity. In general, due to different quantization approaches, LQC involves two types of quantum corrections, the holonomy and inverse-volume, to both of the cosmological background evolution and perturbations. In this paper, using {\\em the third-order uniform asymptotic approximations}, we derive explicitly the observational quantities of the slow-roll inflation in the framework of LQC with these quantum corrections. We calculate the power spectra, spectral indices, and running of the spectral indices for both scalar and tensor perturbations, whereby the tensor-to-scalar ratio is obtained. We expand all the observables at the time when the inflationary mode crosses the Hubble horizon. As the upper error bounds for the uniform asymptotic approximation at the third-order are $\\lesssim 0.15\\%$, these results represent the most accurate results obtained...
Emergence of product of constant curvature spaces in loop quantum cosmology
Dadhich, Naresh; 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 the 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 ...
Quantum de Sitter Spacetime and Energy Density Contributed from the Cosmological Constant
Institute of Scientific and Technical Information of China (English)
LIU Liao
2008-01-01
@@ Previously we introduce a new way to quantize the static Schwarzschild black hole (SSBH), there the SSBH was first treated as a single periodic Euclidean system and then the Bohr-Sommerfeld quantum condition of action was used to obtain a quantum theory of Schwarzschild black hole [Chin. Phys. Lett. (2004) 21 1887]. Here we try to extend the above method to quantize the static de Sitter (SDS) spacetime and establish a quantum theory of both SDS space and the energy density contributed from the cosmological constant.
Less Decoherence and More Coherence in Quantum Gravity, Inflationary Cosmology and Elsewhere
Okon, E
2015-01-01
In Crull (2015) it is argued that, in order to confront outstanding problems in cosmology and quantum gravity, interpretational aspects of quantum theory can by bypassed because decoherence is able to resolve them. As a result, Crull (2015) concludes that our focus on conceptual and interpretational issues, while dealing with such matters in Okon and Sudarsky (2014), is avoidable and even pernicious. Here we will defend our position by showing in detail why decoherence does not help in the resolution of foundational questions in quantum mechanics, such as the measurement problem or the emergence of classicality.
Quantum Cosmology in Bergmann-Wagoner Scalar-tensor Gravitational Theory
Pimentel, L O; Pimentel, Luis O.; Mora, Cesar
2000-01-01
The Wheeler-DeWitt equation is solved for the Bergmann-Wagoner scalar-tensor gravitational theory in the case of Friedmann-Robertson- Walker cosmological model. We present solutions for several cosmological functions: i) \\lambda(\\phi)=0, ii) \\lambda(\\phi)=3\\Lambda_0\\phi and iii) a more complex \\lambda(\\phi), that depends on the choice of the coupling function, considering closed, flat and hyperbolic Friedmann universes (k=1, 0, -1). In the first two cases we show particular quantum wormhole solutions. Also, classical solutions are considered for some scalar-tensor theories, and we study the third quantization of some minisuperspace models.
Unitary evolution for anisotropic quantum cosmologies: models with variable spatial curvature
Pandey, Sachin
2016-01-01
Contrary to the general belief, there has recently been quite a few examples of unitary evolution of quantum cosmological models. The present work gives more examples, namely Bianchi type VI and type II. These examples are important as they involve varying spatial curvature unlike the most talked about homogeneous but anisotropic cosmological models like Bianchi I, V and IX. We exhibit either explicit example of the unitary solutions of the Wheeler-DeWitt equation, or at least show that a self-adjoint extension is possible.
Unitary evolution for anisotropic quantum cosmologies: models with variable spatial curvature
Pandey, Sachin; Banerjee, Narayan
2016-11-01
Contrary to the general belief, there has recently been quite a few examples of unitary evolution of quantum cosmological models. The present work gives more examples, namely Bianchi type VI and type II. These examples are important as they involve varying spatial curvature unlike the most talked about homogeneous but anisotropic cosmological models like Bianchi I, V and IX. We exhibit either an explicit example of the unitary solutions of the Wheeler-DeWitt equation, or at least show that a self-adjoint extension is possible.
Propagator with Positive Cosmological Constant in the 3D Euclidian Quantum Gravity Toy Model
Bunting, William
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 Tuarev-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.
Unitary evolution for a quantum Kantowski-Sachs cosmology
Pal, Sridip
2015-01-01
It is shown that like Bianchi I, V and IX models, a Kantowski-Sachs cosmological model also allows a unitary evolution on quantization. It has also been shown that this unitarity is not at the expense of the anisotropy. Non-unitarity, if there is any, cannot escape notice in this as the evolution is studied against a properly oriented time parameter fixed by the evolution of the fluid. Furthermore, we have constructed a wave-packet by superposing different energy eigenstates, thereby establishing unitarity in a non-trivial way, which is a stronger result than an energy eigenstate trivially giving time independent probability density. For $\\alpha\
Background of relic gravitons in a perfect fluid in quantum cosmological models
Energy Technology Data Exchange (ETDEWEB)
Siffert, Beatriz B. [Centro Brasileiro de Pesquisas Fisicas (ICRA/CBPF), Rio de Janeiro, RJ (Brazil). Inst. de Cosmologia, Relatividade e Astrofisica; Bessada, Dennis [Instituto Nacional de Pesquisas Espaciais (INPE), SP (Brazil). Divisao de Astrofisica
2011-07-01
Full text: We studied the evolution of tensor cosmological perturbations of quantum origin in cosmological scenarios that predict a contracting phase prior to the present expansion phase. These bouncing models constitute a very plausible alternative to the current cosmological paradigm since they may be able to solve some of the cosmological puzzles present in the standard model, such as the horizon and flatness problems, without the requirement of an initial singularity or special initial conditions. While conventional inflationary models give rise to a relic background of gravitational waves that cannot be detected with present experiments, no such prediction had been made so far using quantum bouncing models. We have obtained analytically the graviton's energy density parameter as a function of time and frequency interval - which is the physical quantity to be confronted with observations - predicted by such models with a perfect fluid equation of state. To obtain the final spectrum, we numerically solved the expression for the density parameter for the time variable. The results can then be compared with the predictions from inflationary models and with the sensitivity curves of gravitational waves current detectors, such as the Virgo and Ligo interferometers, and upcoming detectors, like the LISA space mission, to determine the possibility of detection. (author)
Quantum Ho\\v{r}ava-Lifshitz cosmology and the quantum nature of coupling corrections of HL gravity
Martins, Laysa G
2015-01-01
In this work were studied quantum models of a Friedmann-Robertson-Walker (FRW) cosmology in the framework of the gravity's theory proposed by Ho\\v{r}ava, the so-called Ho\\v{r}ava-Lifshitz theory of the gravity. It was used the Ho\\v{r}ava theory for the projectable Ho\\v{r}ava-Lifshitz (HL) gravity without the detailed balance condition. Following the quantization of the model in the context of Wheeler-DeWitt approach and taking in account the ordering factor for operators were found the cosmological wave function. Solutions were studied and the results were discussed for some particular cases close of initial singularity. The resulting wave functions were used to investigate the possibility of to avoid the classical singularities due to quantum effects and for analyzing the entanglement entropy. In the ultraviolet phase were found the existence of cosmological wave function with a relation between the ordering factor and coupling constants showing their quantum nature, then it was possible to provide an explic...
Jalalzadeh, S; Sepangi, H R
2003-01-01
We study the classical and quantum cosmology of a $(4+d)$-dimensional spacetime minimally coupled to a scalar field and present exact solutions for the resulting field equations for the case where the universe is spatially flat. These solutions exhibit signature transition from a Euclidean to a Lorentzian domain and lead to stabilization of the internal space, in contrast to the solutions which do not undergo signature transition. The corresponding quantum cosmology is described by the Wheeler-DeWitt equation which has exact solutions in the mini-superspace, resulting in wavefunctions peaking around the classical paths. Such solutions admit parametrizations corresponding to metric solutions of the field equations that admit signature transition.
Zampeli, Adamantia; Terzis, Petros A; Christodoulakis, T
2015-01-01
In this paper, the classical and quantum solutions of some axisymmetric cosmologies coupled to a massless scalar field are studied in the context of minisuperspace approximation. In these models, the singular nature of the Lagrangians entails a search for possible conditional symmetries. These have been proven to be the simultaneous conformal symmetries of the supermetric and the superpotential. The quantization is performed by adopting the Dirac proposal for constrained systems, i.e. promoting the first-class constraints to operators annihilating the wave function. To further enrich the approach, we follow \\cite{Christodoulakis:2012eg} and impose the operators related to the classical conditional symmetries on the wave function. These additional equations select particular solutions of the Wheeler-DeWitt equation. In order to gain some physical insight from the quantization of these cosmological systems, we perform a semiclassical analysis following the Bohmian approach to quantum theory. The generic result ...
Dynamics of a perfect fluid through velocity potentials with aplication in quantum cosmology
Alvarenga, F G; Furtado, R G; Gonçalves, S V B
2016-01-01
We review the Eulerian description of hidrodynamics using Seliger-Whitham's formalism (in classical case) and Schutz's formalism (in relativistic case). In these formalisms, the velocity field of a perfect fluid is described by scalar potentials. With this we can obtain the evolution equations of the fluid and its Hamiltonian. In the scenario of quantum cosmology the Schutz's formalism makes it possible to introduce phenomenologically a time variable in minisuperspace models.
Equations of motion in Double Field Theory: from classical particles to quantum cosmology
Kan, Nahomi; Shiraishi, Kiyoshi
2012-01-01
The equation of motion for a point particle in the background field of double field theory is considered. We find that the motion is described by a geodesic flow in the doubled geometry. Inspired by analysis on the particle motion, we propose a modified model of quantum string cosmology, which includes two scale factors. The report is based on Phys. Rev. D84 (2011) 124049 [arXiv:1108.5795].
Barrau, Aurélien
2016-01-01
Within some approaches to loop quantum cosmology, the existence of an Euclidean phase at high density has been suggested. In this article, we try to explain clearly what are the observable consequences of this possible disappearance of time. Depending on whether it is a real fundamental effect or just an instability in the equation of motion, we show that very different conclusions should be drawn. We finally mention some possible consequences of this phenomenon in the black hole sector.
Dynamics of a Perfect Fluid Through Velocity Potentials with Application in Quantum Cosmology
Alvarenga, F. G.; Fracalossi, R.; Furtado, R. G.; Gonçalves, S. V. B.
2017-02-01
We review the Eulerian description of hydrodynamics using Seliger-Whitham's formalism (in classical case) and Schutz's formalism (in relativistic case). In these formalisms, the velocity field of a perfect fluid is described by scalar potentials. With this, we can obtain the evolution equations of the fluid and its Hamiltonian. In the scenario of quantum cosmology, the Schutz's formalism makes it possible to introduce phenomenologically a time variable in minisuperspace models.
Testing the Everett Interpretation of Quantum Mechanics with Cosmology
Barrau, Aurelien
2014-01-01
In this brief note, we argue that contrarily to what is still often stated, the Everett many-worlds interpretation of quantum mechanics is not in principle impossible to test. It is actually not more difficult (but not easier either) to test than most other kinds of multiverse theories. We also remind why multiverse scenarios can be falsified.
Goldstein, Sheldon; Lebowitz, Joel L.; Tumulka, Roderich; Zanghi, Nino
2005-01-01
It is well known that a system, S, weakly coupled to a heat bath, B, is described by the canonical ensemble when the composite, S+B, is described by the microcanonical ensemble corresponding to a suitable energy shell. This is true both for classical distributions on the phase space and for quantum density matrices. Here we show that a much stronger statement holds for quantum systems. Even if the state of the composite corresponds to a single wave function rather than a mixture, the reduced ...
Konkowski, D A; Helliwell, T M; Wieland, C
2004-01-01
Levi-Civita spacetimes have classical naked singularities. They also have quantum singularities. Quantum singularities in general relativistic spacetimes are determined by the behavior of quantum test particles. A static spacetime is said to be quantum mechanically singular if the spatial portion of the wave operator is not essentially self-adjoint on a $C_{0}^{\\infty}$ domain in $L^{2}$, a Hilbert space of square integrable functions. Here we summarize how Weyl's limit point-limit circle criterion can be used to determine whether a wave operator is essentially self-adjoint and how this test can then be applied to scalar wave packets in Levi-Civita spacetimes with and without a cosmological constant to help elucidate the physical properties of these spacetimes.
Modified FRW cosmologies arising from states of the hybrid quantum Gowdy model
Navascués, Beatriz Elizaga; Marugán, Guillermo A Mena
2015-01-01
We construct approximate solutions of the hybrid quantum Gowdy cosmology with three-torus topology, linear polarization, and local rotational symmetry, in the presence of a massless scalar field. More specifically, we determine some families of states for which the complicated inhomogeneous and anisotropic Hamiltonian constraint operator of the Gowdy model is approximated by a much simpler one. Our quantum states follow the dynamics governed by this simpler constraint, while being at the same time also approximate solutions of the full Gowdy model. This is so thanks to the quantum correlations that the considered states present between the isotropic and anisotropic sectors of the model. Remarkably, this simpler constraint can be regarded as that of a flat Friedmann-Robertson-Walker universe filled with different kinds of perfect fluids and geometrically corrected by homogeneous and isotropic curvature-like terms. Therefore, our quantum states, which are intrinsically inhomogeneous, admit approximate homogeneo...
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
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.
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.
Experimental quantum cosmology in time-dependent optical media
Westerberg, N; Belgiorno, F; Piazza, F Dalla; Faccio, D
2014-01-01
It is possible to construct artificial spacetime geometries for light by using intense laser pulses that modify the spatiotemporal properties of an optical medium. Here we theoretically investigate experimental possibilities for studying spacetime metrics of the form $\\textrm{d}s^2=c^2\\textrm{d}t^2-\\eta(t)^2\\textrm{d}x^2$. By tailoring the laser pulse shape and medium properties, it is possible to create a refractive index variation $n=n(t)$ that can be identified with $\\eta(t)$. Starting from a perturbative solution to a generalised Hopfield model for the medium described by an $n=n(t)$ we provide estimates for the number of photons generated by the time-dependent spacetime. The simplest example is that of a uniformly varying $\\eta(t)$ that therefore describes the Robertson-Walker metric, i.e. a cosmological expansion. The number of photon pairs generated in experimentally feasible conditions appears to be extremely small. However, large photon production can be obtained by periodically modulating the medium...
Cosmology from quantum potential in brane-anti-brane system
Sepehri, Alireza
2015-01-01
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 to each other, grow and and form a six-dimensional brane-antibrane system. This system is unstable, broken and present form of four dimensional universes , one anti-universe in additional to one wormhole are produced. Thus, there isn't any big-bang in cosmology and universe is a fundamental string at the beginning. Also, total age of universe contains two parts, one in related to initial age and second which is corresponded to present age of universe ($t_{tot}=t_{initial}+t_{present}$). On the other hand, initial age of universe includes two parts, the age of fundamental string and time of transition ($t_{initial}=t_{transition}+t_{f-string}$). We observe that only ...
Energy Technology Data Exchange (ETDEWEB)
Fewster, Christopher J [Department of Mathematics, University of York, Heslington, York YO10 5DD (United Kingdom); Sahlmann, Hanno [Spinoza Institute, Universiteit Utrecht (Netherlands)
2008-11-21
We give a definition for the Wigner function for quantum mechanics on the Bohr compactification of the real line and prove a number of simple consequences of this definition. We then discuss how this formalism can be applied to loop quantum cosmology. As an example, we use the Wigner function to give a new quantization of an important building block of the Hamiltonian constraint.
Fewster, C.J.; Sahlmann, H.
2008-01-01
We give a definition for the Wigner function for quantum mechanics on the Bohr compactification of the real line and prove a number of simple consequences of this definition. We then discuss how this formalism can be applied to loop quantum cosmology. As an example, we use the Wigner function to giv
Classical and quantum dynamics of a perfect fluid scalar-energy dependent metric cosmology
Khodadi, M.; Nozari, K.; Vakili, B.
2016-05-01
Inspired from the idea of minimally coupling of a real scalar field to geometry, we investigate the classical and quantum models of a flat energy-dependent FRW cosmology coupled to a perfect fluid in the framework of the scalar-rainbow metric gravity. We use the standard Schutz' representation for the perfect fluid and show that under a particular energy-dependent gauge fixing, it may lead to the identification of a time parameter for the corresponding dynamical system. It is shown that, under some circumstances on the minisuperspace prob energy, the classical evolution of the of the universe represents a late time expansion coming from a bounce instead of the big-bang singularity. Then we go forward by showing that this formalism gives rise to a Schrödinger-Wheeler-DeWitt 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 Bohmian interpretation of quantum cosmology.
SL(2,C) Chern-Simons Theory and Quantum Gravity with a Cosmological Constant
Haggard, Hal; Han, Muxin; Kaminski, Wojciech; Riello, Aldo
2015-04-01
We show a relation between 4-dimensional quantum gravity with a cosmological constant and SL(2,C) Chern-Simons theory in 3-dimensions with knotted graph defects. In particular, we study the expectation value of a non-planar Wilson graph operator in SL(2,C) Chern-Simons theory on S3. We analyze its asymptotic behavior in the double-scaling limit in which both the representation labels and the Chern-Simons coupling are taken to be large, but with fixed ratio. We find that a class of flat connections in the graph complement manifold are in correspondence with the geometries of constant curvature 4-simplices. We show that the asymptotic behavior of the amplitude contains an oscillatory part proportional to the Regge action for the single 4-simplex in the presence of a cosmological constant. In particular, the cosmological term contains the full-fledged curved volume of the 4-simplex. Interestingly, the volume term stems from the asymptotics of the Chern-Simons action. Another peculiarity of our approach is that the sign of the curvature of the reconstructed geometry, and hence of the cosmological constant in the Regge action, is not fixed a priori, but rather emerges semiclassically and dynamically from the solution of the equations of motion. This work was supported by the U.S. National Science Foundation, the European Marie Curie actions, and the Perimeter Institute.
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.
Impact of quantum entanglement on spectrum of cosmological fluctuations
Kanno, Sugumi
2014-01-01
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.
Perturbative instability of inflationary cosmology from quantum potentials
Tawfik, Abdel Nasser; Dahab, Eiman Abou El
2016-01-01
It was argued that the Raychaudhuri equation with a quantum correction term avoids the Big Bang singularity and proposes an everlasting Universe [PLB741,276(2015)]. Critical comments on both conclusions and on the correctness of the key expressions of this work are discussed in literature [1505.03070]. In the present work, we have analyses the stability conditions by means of a small perturbation and concluded that the quantum corrections and their additional parameters lead to an unstable Universe. We focused on perturbative instability in the inflationary era of the early Universe and found that both unstable and stable modes are incompatible with the corresponding ones obtained in the standard FLRW Universe. We have shown that in the evolutionary era, only unstable modes exist for a small (an)isotropic perturbation and with different equations of state. Inequalities for both unstable and stable solutions with the standard FLRW space are derived. They reveal that in the FLRW flat Universe both instability a...
Cosmological constraints on non-standard inflationary quantum collapse models
Landau, Susana J; Sudarsky, Daniel
2011-01-01
We briefly review an important shortcoming --unearthed in previous works-- of the standard version of the inflationary model for the emergence of the seeds of cosmic structure. We consider here some consequences emerging from a proposal inspired on ideas of Penrose and Di\\'osi about a quantum-gravity induced reduction of the wave function, which has been put forward to address the shortcomings, arguing that its effect on the inflaton field is what can lead to the emergence of the seeds of cosmic structure. The proposal leads to a deviation of the primordial spectrum from the scale-invariant Harrison-Zel'dovich one, and consequently, to a different CMB power spectrum. We perform statistical analyses to test two quantum collapse schemes with recent data from the CMB, including the 7-yr release of WMAP and the matter power spectrum measured using LRGs by the Sloan Digital Sky Survey. Results from the statistical analyses indicate that several collapse models are compatible with CMB and LRG data, and establish co...
Parvan, A S; Ploszajczak, M
2000-01-01
A quantum statistical model of nuclear multifragmentation is proposed. The recurrence equation method used within 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.
Singh, T P
2008-01-01
There ought to exist a reformulation of quantum mechanics which does not refer to an external classical spacetime manifold. Such a reformulation can be achieved using the language of noncommutative differential geometry. A consequence which follows is that the `weakly quantum, strongly gravitational' dynamics of a relativistic particle whose mass is much greater than Planck mass is dual to the `strongly quantum, weakly gravitational' dynamics of another particle whose mass is much less than Planck mass. The masses of the two particles are inversely related to each other, and the product of their masses is equal to the square of Planck mass. This duality explains the observed value of the cosmological constant, and also why this value is nonzero but extremely small in Planck units.
Classical and Quantum Dispersion in Robertson-Walker Cosmologies
Tomaschitz, R
1993-01-01
The instability of world lines in Robertson-Walker universes of negative spatial curvature is investigated. A probabilistic description of this instability, similar to the Liouville equation, is developed, but in a manifestly covariant, non-Hamiltonian form. To achieve this the concept of a horospherical geodesic flow of expanding bundles of parallel world lines is introduced. An invariant measure and a covariant evolution equation for the probability density on which this flow acts is constructed. The orthogonal surfaces to these bundles of trajectories are horospheres, closed surfaces in three-space, touching the boundary at infinity of hyperbolic space, where the flow lines emerge. These horospheres are just the wave fronts of spherical waves, which constitute a complete set of eigenfunctions of the Klein-Gordon equation. This fact suggests that the evolution of the quantum mechanical density with the classical one be compared, and asymptotic identity in the asymptotically flat region is found. This leads,...
Anisotropic loop quantum cosmology with self-dual variables
Wilson-Ewing, Edward
2015-01-01
A loop quantization of the diagonal class A Bianchi models starting from the complex-valued self-dual connection variables is presented in this paper. The basic operators in the quantum theory correspond to areas and generalized holonomies of the Ashtekar connection and the reality conditions are implemented via the choice of the inner product on the kinematical Hilbert space. The action of the Hamiltonian constraint operator is given explicitly for the case when the matter content is a massless scalar field (in which case the scalar field can be used as a relational clock), and it is shown that the big-bang and big-crunch singularities are resolved in the sense that singular and non-singular states decouple under the action of the Hamiltonian constraint operator.
Anisotropic loop quantum cosmology with self-dual variables
Wilson-Ewing, Edward
2016-04-01
A loop quantization of the diagonal class A Bianchi models starting from the complex-valued self-dual connection variables is presented in this paper. The basic operators in the quantum theory correspond to areas and generalized holonomies of the Ashtekar connection, and the reality conditions are implemented via the choice of the inner product on the kinematical Hilbert space. The action of the Hamiltonian constraint operator is given explicitly for the case when the matter content is a massless scalar field (in which case the scalar field can be used as a relational clock), and it is shown that the big bang and big crunch singularities are resolved in the sense that singular and nonsingular states decouple under the action of the Hamiltonian constraint operator.
Dark matter as the Bose-Einstein condensation in loop quantum cosmology
Energy Technology Data Exchange (ETDEWEB)
Atazadeh, K.; Mousavi, M. [Azarbaijan Shahid Madani University, Department of Physics, Tabriz (Iran, Islamic Republic of); Darabi, F. [Azarbaijan Shahid Madani University, Department of Physics, Tabriz (Iran, Islamic Republic of); Research Institute for Astronomy and Astrophysics of Maragha (RIAAM), Maragha (Iran, Islamic Republic of)
2016-06-15
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.)
Loop quantum cosmology of Bianchi IX: Inclusion of inverse triad corrections
Corichi, Alejandro; Karami, Asieh
2016-06-01
We consider the loop quantization of the (diagonal) Bianchi type IX cosmological model. We explore different quantization prescriptions that extend the work of Wilson-Ewing and Singh. In particular, we study two different ways of implementing the so-called inverse triad corrections. We construct the corresponding Hamiltonian constraint operators and show that the singularity is formally resolved. We find the effective equations associated with the different quantization prescriptions, and study the relation with the isotropic k = 1 model that, classically, is contained within the Bianchi IX model. Somewhat surprisingly, we find the most natural quantization does not reduce to the k = 1 model. We use geometrically defined scalar observables to explore the physical implications of each of these theories. This is the first part in a series of papers analyzing different aspects of the Bianchi IX model, with inverse corrections, within loop quantum cosmology (LQC).
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.
Loop quantum cosmology of Bianchi IX: Inclusion of inverse triad corrections
Corichi, Alejandro
2016-01-01
We consider the loop quantization of the (diagonal) Bianchi type IX cosmological model. We explore different quantization prescriptions that extend the work of Wilson-Ewing and Singh. In particular, we study two different ways of implementing the so-called inverse triad corrections. We construct the corresponding Hamiltonian constraint operators and show that the singularity is formally resolved. We find the effective equations associated with the different quantization prescriptions, and study the relation with the isotropic $k$=1 model that, classically, is contained within the Bianchi IX model. We use geometrically defined scalar observables to explore the physical implications of each of these theories. This is the first part in a series of papers analyzing different aspects of the Bianchi IX model, with inverse corrections, within loop quantum cosmology.
Quantum cosmology in (1 +1 )-dimensional Hořava-Lifshitz theory of gravity
Pitelli, J. P. M.
2016-05-01
In a recent paper [Phys. Rev. D 92, 084012 (2015)], the author studied the classical (1 +1 )-dimensional Friedmann-Robertson-Walker (FRW) universe filled with a perfect fluid in the Hořava-Lifshitz (HL) theory of gravity. This theory is dynamical due to the anisotropic scaling of space and time. It also resembles the Jackiw-Teitelboim model, in which a dilatonic degree of freedom is necessary for dynamics. In this paper, I will take one step further in the understanding of (1 +1 )-dimensional HL cosmology by means of the quantization of the FRW universe filled with a perfect fluid with the equation of state (EoS) p =w ρ . The fluid will be introduced in the model via Schutz formalism and Dirac's algorithm will be used for quantization. It will be shown that the Schrödinger equation for the wave function of the universe has the following properties: for w =1 (radiation fluid), the characteristic potential will be exponential, resembling Liouville quantum mechanics; for w ≠1 , a characteristic inverse square potential appears in addition to a regular polynomial that depends on the EoS. Explicit solutions for a few cases of interest will be found and the expectation value of the scale factor will be calculated. As in usual quantum cosmology, it will be shown that the quantum theory smooths out the big-bang singularity, but the classical behavior of the universe is recovered in the low-energy limit.
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....
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....
Quantum Exchange Algebra and Locality in Liouville Theory
Fujiwara, T; Takimoto, Y
1997-01-01
Exact operator solution for quantum Liouville theory is investigated based on the canonical free field. Locality, the field equation and the canonical commutation relations are examined based on the exchange algebra hidden in the theory. The exact solution proposed by Otto and Weigt is shown to be correct to all order in the cosmological constant.
Galilean quantum gravity with cosmological constant and the extended q-Heisenberg algebra
Papageorgiou, G; Schroers, B. J.
2010-01-01
We define a theory of Galilean gravity in 2+1 dimensions with cosmological constant as a Chern-Simons gauge theory of the doubly-extended Newton-Hooke group, extending our previous study of classical and quantum gravity in 2+1 dimensions in the Galilean limit. We exhibit an r-matrix which is compatible with our Chern-Simons action (in a sense to be defined) and show that the associated bi-algebra structure of the Newton-Hooke Lie algebra is that of the classical double of the extended Heisenb...
Das Mandal, Jyotirmay; Debnath, Ujjal
2016-08-01
We have studied the tachyon intermediate and logamediate warm inflation in loop quantum cosmological background by taking the dissipative co-efficient Γ = Γ0 (where Γ0 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.
The energy spectrum of gravitational waves in a loop quantum cosmological model
Morais, Joao; Henriques, Alfredo B
2014-01-01
We explore the consequences of loop quantum cosmology (inverse-volume corrections) in the spectrum of the gravitational waves using the method of the Bogoliubov coefficients. These corrections are taken into account at the background level of the theory as well as at the first order in the perturbations theory framework. We show that these corrections lead to an intense graviton production during the loop super-inflationary phase prior to the standard slow-roll era, which leave their imprints through new features on the energy spectrum of the gravitational waves as would be measured today, including a new maximum on the low frequency end of the spectrum.
Detailed analysis of the predictions of loop quantum cosmology for the primordial power spectra
Agullo, Ivan
2015-01-01
We provide an exhaustive numerical exploration of the predictions of loop quantum cosmology (LQC) with a post-bounce phase of inflation for the primordial power spectrum of scalar and tensor perturbations. We extend previous analysis by characterizing the phenomenologically relevant parameter space and by constraining it using observations. Furthermore, we characterize the shape of LQC-corrections to observable quantities across this parameter space. Our analysis provides a framework to contrast more accurately the theory with forthcoming polarization data, and it also paves the road for the computation of other observables beyond the power spectra, such as non-Gaussianity.
Quantum Cosmology of Quadratic f(R Theories with a FRW Metric
Directory of Open Access Journals (Sweden)
V. Vázquez-Báez
2017-01-01
Full Text Available We study the quantum cosmology of a quadratic fR theory with a FRW metric, via one of its equivalent Horndeski type actions, where the dynamic of the scalar field is induced. The classical equations of motion and the Wheeler-DeWitt equation, in their exact versions, are solved numerically. There is a free parameter in the action from which two cases follow: inflation + exit and inflation alone. The numerical solution of the Wheeler-DeWitt equation depends strongly on the boundary conditions, which can be chosen so that the resulting wave function of the universe is normalizable and consistent with Hermitian operators.
Cosmology from quantum potential in a system of oscillating branes
Sepehri, Alireza
2016-11-01
energy is produced and leads to an increase in the velocity of opening of M3. In these conditions, our universe, which is located on this brane, expands very fast and experiences an inflation epoch. Finally, by reducing the fields in 11-dimensional M-theory to the fields in four-dimensional universe, we show that our theory matches with quantum field theory prescriptions.
Canonical quantization of macroscopic electromagnetism
Energy Technology Data Exchange (ETDEWEB)
Philbin, T G, E-mail: tgp3@st-andrews.ac.u [School of Physics and Astronomy, University of St Andrews, North Haugh, St Andrews, Fife KY16 9SS (United Kingdom)
2010-12-15
Application of the standard canonical quantization rules of quantum field theory to macroscopic electromagnetism has encountered obstacles due to material dispersion and absorption. This has led to a phenomenological approach to macroscopic quantum electrodynamics where no canonical formulation is attempted. In this paper macroscopic electromagnetism is canonically quantized. The results apply to any linear, inhomogeneous, magnetodielectric medium with dielectric functions that obey the Kramers-Kronig relations. The prescriptions of the phenomenological approach are derived from the canonical theory.
Canonical quantization of macroscopic electromagnetism
Philbin, T G
2010-01-01
Application of the standard canonical quantization rules of quantum field theory to macroscopic electromagnetism has encountered obstacles due to material dispersion and absorption. This has led to a phenomenological approach to macroscopic quantum electrodynamics where no canonical formulation is attempted. In this paper macroscopic electromagnetism is canonically quantized. The results apply to any linear, inhomogeneous, magnetoelectric medium with dielectric functions that obey the Kramers-Kronig relations. The prescriptions of the phenomenological approach are derived from the canonical theory.
Inflationary spectra from a near Ω -deformed spacetime transition point in loop quantum cosmology
Chen, Long; Zhu, Jian-Yang
2016-09-01
Anomaly-free perturbations of loop quantum cosmology with holonomy corrections reveal an Ω -deformed spacetime structure, Ω ≔1 -2 ρ /ρc , where Ω 0 indicates a Lorentz-like space. It would be reasonable to give the initial value at the spacetime transition point, ρ =ρc/2 , but we find that it is impossible to define a Minkowski-like vacuum even for large k modes at that time. However, if we loosen the condition and give the initial value slightly after Ω =0 , e.g., Ω ≃0.2 , the vacuum state can be well defined and, furthermore, the slow roll approximation also works well in that region. Both scalar and tensor spectra are considered in the framework of loop quantum cosmology with holonomy corrections. We find that, if the energy density is not too small in relation to ρc/2 when the considered k mode crossing the horizon, effective theory can give a much smaller scalar power spectrum than classical theory and the spectrum of tensor perturbations could blueshift. However, when compared to other observations, since the energy densities when the modes crossed the horizon were significantly smaller than ρc, the results we get agree with previous work in the literature and with the classical inflation theory.
Zampeli, Adamantia; Pailas, Theodoros; Terzis, Petros A.; Christodoulakis, T.
2016-05-01
In this paper, the classical and quantum solutions of some axisymmetric cosmologies coupled to a massless scalar field are studied in the context of minisuperspace approximation. In these models, the singular nature of the Lagrangians entails a search for possible conditional symmetries. These have been proven to be the simultaneous conformal symmetries of the supermetric and the superpotential. The quantization is performed by adopting the Dirac proposal for constrained systems, i.e. promoting the first-class constraints to operators annihilating the wave function. To further enrich the approach, we follow [1] and impose the operators related to the classical conditional symmetries on the wave function. These additional equations select particular solutions of the Wheeler-DeWitt equation. In order to gain some physical insight from the quantization of these cosmological systems, we perform a semiclassical analysis following the Bohmian approach to quantum theory. The generic result is that, in all but one model, one can find appropriate ranges of the parameters, so that the emerging semiclassical geometries are non-singular. An attempt for physical interpretation involves the study of the effective energy-momentum tensor which corresponds to an imperfect fluid.
The Chern-Simons invariant as the natural time variable for classical and quantum cosmology
Smolin, L; Smolin, Lee; Soo, Chopin
1995-01-01
We propose that the Chern-Simons invariant of the Ashtekar-Sen connection is the natural internal time coordinate for classical and quantum cosmology. The reasons for this are a number of interesting properties of this functional, which we describe here. 1)It is a function on the gauge and diffeomorphism invariant configuration space, whose gradient is orthogonal to the two physical degrees of freedom, in the metric defined by the Ashtekar formulation of general relativity. 2)The imaginary part of the Chern-Simons form reduces in the limit of small cosmological constant, \\Lambda, and solutions close to DeSitter spacetime, to the York extrinsic time coordinate. 3)Small matter-field excitations of the Chern-Simons state satisfy, by virtue of the quantum constraints, a functional Schroedinger equation in which the matter fields evolve on a DeSitter background in the Chern-Simons time. We then n propose this is the natural vacuum state of the theory for \\Lambda \
Chen, Long
2016-01-01
Anomaly-free perturbations of loop quantum cosmology with holonomy corrections reveal a $\\Omega$ -deformed space-time structure, $\\Omega:=1-2\\rho/\\rho_c$, where $\\Omega0$ means a Lorentz-like space. It would be reasonable to give the initial value at the space-time transition point, $\\rho=\\rho_c/2$, but we find it is impossible to define a Minkowski-like vacuum even for large $k$-modes at that time. However if we loose the condition and give the initial value near after $\\Omega=0$, e.g. $\\Omega\\simeq 0.2$, the vacuum state can be well defined and furthermore the slow roll approximation also works well in that region. Both scalar and tensor spectra are considered in the framework of loop quantum cosmology with holonomy corrections. We find that if the energy density is not too small compared with $\\rho_c/2$ when the considered $k$-mode crossing the horizon, effective theory can give a much smaller scalar power spectrum than classical theory and the spectrum of tensor perturbations could blue shift. But when co...
圈量子宇宙学的新进展%Recent advances in loop quantum cosmology
Institute of Scientific and Technical Information of China (English)
马永革
2011-01-01
圈量子宇宙学在国际引力和宇宙学界日益成为一个热门的研究领域.本文将介绍圈量子引力理论的基本想法及其对称约化模型-圈量子宇宙学的基本结构与最新进展.新进展侧重于圈量子宇宙学的动力学构造及其有效理论的研究.%Loop quantum cosmology has become a rather hot topic recently in the fields of gravity and cosmology. In this paper, we will review the basic ideas of loop quantum gravity and the fundamental structure of its symmetry-reduced models known as loop quantum cosmology, as well as the recent advances of loop quantum cosmology. We will mainly focus on the progress in the quantum dynamics and effective theory.
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.
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...
Quesne, C.
2016-10-01
The quantum oscillator and Kepler-Coulomb problems in d-dimensional spaces with constant curvature are analyzed from several viewpoints. In a deformed supersymmetric framework, the corresponding nonlinear potentials are shown to exhibit a deformed shape invariance property. By using the point canonical transformation method, the two deformed Schrödinger equations are mapped onto conventional ones corresponding to some shape-invariant potentials, whose rational extensions are well known. The inverse point canonical transformations then provide some rational extensions of the oscillator and Kepler-Coulomb potentials in curved space. The oscillator on the sphere and the Kepler-Coulomb potential in a hyperbolic space are studied in detail and their extensions are proved to be consistent with already known ones in Euclidean space. The partnership between nonextended and extended potentials is interpreted in a deformed supersymmetric framework. Those extended potentials that are isospectral to some nonextended ones are shown to display deformed shape invariance, which in the Kepler-Coulomb case is enlarged by also translating the degree of the polynomial arising in the rational part denominator.
Achour, Jibril Ben; Grain, Julien; Marciano, Antonino
2016-01-01
Scalar cosmological perturbations in loop quantum cosmology (LQC) is revisited in a covariant manner, using self dual Ashtekar variables. For real-valued Ashtekar-Barbero variables, this `deformed algebra' approach has been shown to implement holonomy corrections from loop quantum gravity (LQG) in a consistent manner, albeit deforming the algebra of modified constraints in the process. This deformation has serious conceptual ramifications, not the least of them being an effective `signature-change' in the deep quantum regime. In this paper, we show that working with self dual variables lead to an undeformed algebra of hypersurface deformations, even after including holonomy corrections in the effective constraints. As a necessary consequence, the diffeomorphism constraint picks up non-perturbative quantum corrections thus hinting at a modification of the underlying space-time structure, a novel ingredient compared to the usual treatment of (spatial) diffeomorphisms in LQG. This work extends a similar result o...
Zhu, Tao; Kirsten, Klaus; Cleaver, Gerald; Sheng, Qin; Wu, Qiang
2015-01-01
We derive the primordial power spectra, spectral indices and runnings of both cosmological scalar perturbations and gravitational waves in the framework of loop quantum cosmology with the inverse-volume quantum corrections. This represents an extension of our previous treatment for $\\sigma$ being integers to the case with any given value of $\\sigma$. For this purpose, we adopt a new calculational strategy in the uniform asymptotic approximation, by expanding the involved integrals first in terms of the inverse-volume correction parameter to its first-order, a consistent requirement of the approximation of the inverse-volume corrections. In this way, we calculate explicitly the quantum gravitational corrections to the standard inflationary spectra and spectral indices to the second-order of the slow-roll parameters, and obtain the observational constraints on the inverse-volume corrections from Planck 2015 data for various values of $\\sigma$. Using these constraints we discuss whether these quantum gravitation...
Donoghue, John F
2014-01-01
We discuss cosmological effects of the quantum loops of massless particles, which lead to temporal non-localities in the equations of motion governing the scale factor a(t). For the effects discussed here, loops cause the evolution of a(t) to depend on the memory of the curvature in the past with a weight that scales initially as 1/(t-t'). As one of our primary examples we discuss the situation with a large number of light particles, such that these effects occur in a region where gravity may still be treated classically. However, we also describe the effect of quantum graviton loops and the full set of Standard Model particles. We show that these effects decrease with time in an expanding phase, leading to classical behavior at late time. In a contracting phase, within our approximations the quantum results can lead to a bounce-like behavior at scales below the Planck mass, avoiding the singularities required classically by the Hawking-Penrose theorems. For conformally invariant fields, such as the Standard ...
Quantum mechanics from Newton's second law and the canonical commutation relation [X, P] = i
Palenik, Mark C.
2014-07-01
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 [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.
(Non)-singular brane-world cosmology induced by quantum effects in d5 dilatonic gravity
Nojiri, S; Odintsov, S D; Nojiri, Shin'ichi; Obregon, Octavio; Odintsov, Sergei D.
2000-01-01
5d dilatonic gravity (bosonic sector of gauged supergravity) with non-trivial bulk potential and with surface terms (boundary cosmological constant and trace anomaly induced effective action for brane quantum matter) is considered. For constant bulk potential and maximally SUSY Yang-Mills theory (CFT living on the brane) the inflationary brane-world is constructed. There, bulk is singular asymptotically AdS space with non-constant dilaton and dilatonic de Sitter or hyperbolic brane is induced by quantum matter effects. On the same time, dilaton on the brane is determined dynamically. This all is natural realization of warped compactification in AdS/CFT correspondence. For fine-tuned toy example of non-constant bulk potential we found the non-singular dilatonic brane-world where bulk again represents asymptotically AdS space and de Sitter brane (inflationary phase of observable Universe) is induced exclusively by quantum effects. The radius of brane and dilaton are determined dynamically. The analytically solv...
Accelerated expansion in bosonic and fermionic 2D cosmologies with quantum effects
Samojeden, L L; Devecchi, F P
2009-01-01
In this work we analyze the effects produced by bosonic and fermionic constituents, including quantum corrections, in two-dimensional (2D) cosmological models. We focus on a gravitational theory related to the Callan-Giddings-Harvey-Strominger model, to simulate the dynamics of a young, spatially-lineal, universe. The cosmic substratum is formed by an {\\it inflaton} field plus a matter component, sources of the 2D gravitational field; the degrees of freedom also include the presence of a dilaton field. We show that this combination permits, among other scenarios, the simulation of a period of inflation, that would be followed by a (bosonic/fermionic) matter dominated era. We also analyse how quantum effects contribute to the destiny of the expansion, given the fact that in 2D we have a consistent (renormalizable) quantum theory of gravity. The dynamical behavior of the system follows from the solution of the gravitational field equations, the (Klein-Gordon and Dirac) equations for the sources and the dilaton ...
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.
Off-shell Dark Matter: A Cosmological relic of Quantum Gravity
Saravani, Mehdi
2016-01-01
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 (OfDM). However, their rate of production is suppressed by the scale of non-locality (e.g. Planck length). As a result, we show that OfDM 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 OfDM is indeed cold, and discuss potentially observable signatures on small scale matter power ...
Darabi, F
2009-01-01
We study a $(4+D)$-dimensional Kaluza-Klein cosmology with a Robertson-Walker type metric having two scale factors $a$ and $R$, corresponding to $D$-dimensional internal space and 4-dimensional universe, respectively. By introducing an exotic matter in the form of perfect fluid with an special equation of state, as the space-time part of the higher dimensional energy-momentum tensor, a four dimensional effective decaying cosmological term appears as $\\lambda \\sim R^{-m}$ with $0 \\leq m\\leq 2$, playing the role of an evolving dark energy in the universe. By taking $m=2$, which has some interesting implications in reconciling observations with inflationary models and is consistent with quantum tunneling, the resulting Einstein's field equations yield the exponential solutions for the scale factors $a$ and $R$. These exponential behaviors may account for the dynamical compactification of extra dimensions and the accelerating expansion of the 4-dimensional universe in terms of Hubble parameter, $H$. The accelerat...
Kirilyuk, A P
2006-01-01
The universal symmetry, or conservation, of complexity underlies any law or principle of system dynamics and describes the unceasing transformation of dynamic information into dynamic entropy as the unique way to conserve their sum, the total dynamic complexity. Here we describe the real world structure emergence and dynamics as manifestation of the universal symmetry of complexity of initially homogeneous interaction between two protofields. It provides the unified complex-dynamic, causally complete origin of physically real, 3D space, time, elementary particles, their properties (mass, charge, spin, etc.), quantum, relativistic, and classical behaviour, as well as fundamental interaction forces, including naturally quantized gravitation. The old and new cosmological problems (including "dark" mass and energy) are basically solved for this explicitly emerging, self-tuning world structure characterised by strictly positive (and large) energy-complexity. A general relation is obtained between the numbers of wo...
A scientometric study of General Relativity and Quantum Cosmology from 2000 to 2012
Fay, Stephane
2015-01-01
2015 is the centennial of Einstein General Relativity. On this occasion, we examine the General Relativity and Quantum Cosmology (GRQC) field of research by analysing 38291 papers uploaded on the electronic archives arXiv.org from 2000 to 2012. We establish a map of the countries contributing to GRQC in 2012. We determine the main journals publishing GRQC papers and which countries publish in which journals. We find that more and more papers are written by groups (instead of single) of authors with more and more international collaborations. There are huge differences between countries. Hence Russia is the country where most of papers are written by single authors whereas Canada is one of the countries where the most of papers are written with international collaborations. We also study mobility of researchers, determining how some groups of authors spread worldwide with time for different countries. The largest mobilities (as well as international collaborations) are between USA-UK and USA-Germany. Countries...
Chang, Zhe
2014-01-01
We propose the gravity's rainbow scenario as a possible alternative of the inflation paradigm to account for the flatness and horizon problems. We focus on studying the cosmological scalar perturbations which are seeded by the quantum fluctuations in the very early universe. The scalar power spectrum is expected to be nearly scale-invariant. We estimate the rainbow index $\\lambda$ and energy scale $M$ in the gravity's rainbow scenario by analyzing the Planck temperature and WMAP polarization datasets. The constraints on them are given by $\\lambda=2.933\\pm0.012$ and $\\ln (10^5M/M_p)= -0.401^{+0.457}_{-0.451}$ at the $68\\%$ confidence level.
Lorentzian Condition in Holographic Cosmology
Hertog, Thomas; Vreys, Yannick
2016-01-01
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.
Lorentzian condition in holographic cosmology
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.
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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.)
Nojiri, S; Odintsov, S D
1999-01-01
We review the anomaly induced effective action for dilaton coupled spinors and scalars in large N and s-wave approximation. It may be applied to study the following fundamental problems: construction of quantum corrected black holes (BHs), inducing of primordial wormholes in the early Universe (this effect is confirmed) and the solution of initial singularity problem. The recently discovered anti-evaporation of multiple horizon BHs is discussed. The existance of such primordial BHs may be interpreted as SUSY manifestation. Quantum corrections to BHs thermodynamics maybe also discussed within such scheme.
Revisiting Canonical Quantization
Klauder, John R
2012-01-01
Conventional canonical quantization procedures directly link various c-number and q-number quantities. Here, we advocate a different association of classical and quantum quantities that renders classical theory a natural subset of quantum theory with \\hbar>0. While keeping the good results of conventional procedures, some examples are noted where the new procedures offer better results than conventional ones.
Renormalization of 3d quantum gravity from matrix models
Ambjørn, Jan; Loll, R
2004-01-01
Lorentzian simplicial quantum gravity is a non-perturbatively defined theory of quantum gravity which predicts a positive cosmological constant. Since the approach is based on a sum over space-time histories, it is perturbatively non-renormalizable even in three dimensions. By mapping the three-dimensional theory to a two-matrix model with ABAB interaction we show that both the cosmological and the (perturbatively) non-renormalizable gravitational coupling constant undergo additive renormalizations consistent with canonical quantization.
Jorgensen, PET
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
Liu, Xiao; Zhu, Jian-Yang
2013-01-01
The dynamical behaviors of FRW Universe containing a posivive/negative potential scalar field in loop quantum cosmology scenario are discussed. The method of the phase-plane analysis is used to investigate the stability of the Universe. It is found that the stability properties in this situation are quite different from the classical cosmology case. For a positive potential scalar field coupled with a barotropic fluid, the cosmological autonomous system has five fixed points and one of them is stable if the adiabatic index $\\gamma$ satisfies $0<\\gamma<2$. This leads to the fact that the universe just have one bounce point instead of the singularity which lies in the quantum dominated area and it is caused by the quantum geometry effect. There are four fixed points if one considers a scalar field with a negative potential, but none of them is stable. Therefore, the universe has two kinds of bounce points, one is caused by the quantum geometry effect and the other is caused by the negative potential, the ...
Classical and quantum dynamics of a perfect fluid scalar-energy dependent metric cosmology
Khodadi, M; Vakili, B
2016-01-01
Inspired from the idea of minimally coupling of a real scalar field to geometry, we investigate the classical and quantum models of a flat energy-dependent FRW cosmology coupled to a perfect fluid in the framework of the scalar-rainbow metric gravity. We use the standard Schutz' representation for the perfect fluid and show that under a particular energy-dependent gauge fixing, it may lead to the identification of a time parameter for the corresponding dynamical system. It is shown that, under some circumstances on the minisuperspace prob energy, the classical evolution of the of the universe represents a late time expansion coming from a bounce instead of the big-bang singularity. Then we go forward by showing that this formalism gives rise to a Schr\\"{o}dinger-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 t...
The Problem of Time and Quantum Cosmology in the Relational Particle Mechanics Arena
Anderson, Edward
2011-01-01
Most readers' main interest in this article will be its reviews of the problem of time (POT) in quantum gravity (QG) in Secs 11, 16. Namely, that `time' in GR and in ordinary QM are mutually incompatible notions, which is problematic in trying to put these 2 theories together to form a theory of QG. I also establish relational particle models (RPM's) as useful for the study of the POT and of quantum cosmology (QC). I also unlock RPMs' configuration spaces, classical dynamics and QM in simple concrete examples. I use these to further our understanding of the histories, records, semiclassical, naive Schrodinger interpretation and hidden time strategies toward resolving the POT, alongside considering Halliwell's combination of the first 3. My relational whole-universe models are comparable to minisuperspace in amount of resemblance to full GR, but with a number of different resemblances including various midisuperspace-like ones which render RPM's appropriate as POT models. One point of view is that the best one...
Sesma, L Toledo; Loaiza, O
2015-01-01
In this work we construct an effective four-dimensional model by compactifying a ten-dimensional theory of gravity coupled with a real scalar dilaton field on a time-dependent torus. This approach is applied to anisotropic cosmological Bianchi type I model for which we study the classical coupling of the anisotropic scale factors with the two real scalar moduli produced by the compactification process. Under this approach, we present an isotropization mechanism for the Bianchi I cosmological model through the analysis of the ratio between the anisotropic parameters and the volume of the Universe which in general keeps constant or runs into zero for late times. Finally, we present some solutions to the corresponding Wheeler-DeWitt (WDW) equation in the context of Standard Quantum Cosmology.
Kauffmann, Steven Kenneth
2013-01-01
The quantum mechanics status of the probability vector current density has long seemed to be marginal. On one hand no systematic prescription for its construction is provided, and the special examples of it that are obtained for particular types of Hamiltonian operator could conceivably be attributed to happenstance. On the other hand this concept's key physical interpretation as local average particle flux, which flows from the equation of continuity that it is supposed to satisfy in conjunction with the probability scalar density, has been claimed to breach the uncertainty principle. Given the dispiriting impact of that claim, we straightaway point out that the subtle directional nature of the uncertainty principle makes it consistent with the measurement of local average particle flux. We next focus on the fact that the unique closed-form linear-superposition quantization of any classical Hamiltonian function yields in tandem the corresponding unique linear-superposition closed-form divergence of the proba...
Bolliet, B; Stahl, C; Linsefors, L; Barrau, A
2015-01-01
Loop quantum cosmology tries to capture the main ideas of loop quantum gravity and to apply them to the Universe as a whole. Two main approaches within this framework have been considered to date for the study of cosmological perturbations: the dressed metric approach and the deformed algebra approach. They both have advantages and drawbacks. In this article, we accurately compare their predictions. In particular, we compute the associated primordial tensor power spectra. We show -- numerically and analytically -- that the large scale behavior is similar for both approaches and compatible with the usual prediction of general relativity. The small scale behavior is, the other way round, drastically different. Most importantly, we show that in a range of wavenumbers explicitly calculated, both approaches do agree on predictions that, in addition, differ from standard general relativity and do not depend on unknown parameters. These features of the power spectrum at intermediate scales might constitute a univers...
Gomar, Laura Castelló; Blas, Daniel Martín-de; Marugán, Guillermo A Mena; Velhinho, José M
2012-01-01
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. Though the proof is generalizable to other compact spatial topologies in three or less dimensions, we focus on the case of the three-torus owing to its relevance in cosmology, paying a especial attention to the role played by the spatial isometries in the determination of the representatio...
Ryan, M.
1972-01-01
The study of cosmological models by means of equations of motion in Hamiltonian form is considered. Hamiltonian methods applied to gravity seem to go back to Rosenfeld (1930), who constructed a quantum-mechanical Hamiltonian for linearized general relativity theory. The first to notice that cosmologies provided a simple model in which to demonstrate features of Hamiltonian formulation was DeWitt (1967). Applications of the ADM formalism to homogeneous cosmologies are discussed together with applications of the Hamiltonian formulation, giving attention also to Bianchi-type universes. Problems involving the concept of superspace and techniques of quantization are investigated.
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Koivisto, Tomi S., E-mail: T.Koivisto@ThPhys.Uni-Heidelberg.d [Institute for Theoretical Physics, University of Heidelberg, 69120 (Germany); Nunes, Nelson J. [Institute for Theoretical Physics, University of Heidelberg, 69120 (Germany)
2010-03-01
Cosmology of self-interacting three-forms is investigated. The minimally coupled canonical theory can naturally generate a variety of isotropic background dynamics, including scaling, possibly transient acceleration and phantom crossing. An intuitive picture of the cosmological dynamics is presented employing an effective potential. Numerical solutions and analytical approximations are provided for scenarios which are potentially important for inflation or dark energy.
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Zuniga S, A. [Instituto Politecnico Nacional, Departamento de Fisica, Escuela Superior de Fisica y Matematicas, Edificio 9, Unidad Profesional Adolfo Lopez Mateos, 07738 Mexico D.F. (Mexico)
2003-07-01
Employing canonical transformations defined in the coherent-state representation of quantum mechanics, we introduce Schroedinger-Cat- Like-States. The squeezed displaced number states with real squeezing parameter are contained in these states. (Author)
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
Constraining Parameters of Generalized Cosmic Chaplygin Gas in Loop Quantum Cosmology
Ranjit, Chayan
2014-01-01
We have assumed the FRW universe in loop quantum cosmology (LQC) model filled with the dark matter and the Generalized Cosmic Chaplygin gas (GCCG) type dark energy where dark matter follows the linear equation of state. We present the Hubble parameter in terms of the observable parameters $\\Omega_{m0}$ and $H_{0}$ with the redshift $z$ and the other parameters like $A$, $B$, $w_{m}$, $ \\omega$ and $\\alpha$ which coming from our model. From Stern data set (12 points)\\& SNe Type Ia 292 data (from \\cite{Riess1,Riess2,Astier}) we have obtained the bounds of the arbitrary parameters by minimizing the $\\chi^{2}$ test. The best-fit values of the parameters are obtained by 66\\%, 90\\% and 99\\% confidence levels. Next due to joint analysis with Stern+BAO and Stern+BAO+CMB observations, we have also obtained the bounds of the parameters ($A,B$) by fixing some other parameters $\\alpha$, $w_{m}$ and $\\omega$. From the best fit values of the parameters, we have obtained the distance modulus $\\mu(z)$ for our theoretical...
Quantum Cosmology in $(1+1)$-dimensional Ho\\v{r}ava-Lifshitz theory of gravity
Pitelli, J P M
2016-01-01
In a recent paper [Phys. Rev. D 92:084012, 2015], the author studied the classical $(1+1)$-dimensional Friedmann-Robertson-Walker (FRW) universe filled with a perfect fluid in Ho\\v{r}ava-Lifshitz (HL) theory of gravity. This theory is dynamical due to the anisotropic scaling of space and time. It also resembles the Jackiw-Teitelboim model, in which a dilatonic degree of freedom is necessary for dynamics. In this paper, I will give one step further in the understanding of (1+1)-dimensional HL cosmology by means of the quantization of the FRW universe filled with a perfect fluid with equation of state (EoS) $p=w\\rho$. The fluid will be introduced in the model via Schutz formalism and Dirac's algorithm will be used for quantization. It will be shown that the Schr\\"odinger equation for the wave function of the universe has the following properties: for $w=1$ (radiation fluid), the characteristic potential will be exponential, resembling Liouville quantum mechanics; for $w\
Directory of Open Access Journals (Sweden)
Piero Chiarelli
2016-04-01
Full Text Available In the present work, it is shown that the problem of the cosmological constant (CC is practically the consequence of the inadequacy of general relativity to take into account the quantum property of the space. The equations show that the cosmological constant naturally emerges in the hydrodynamic formulation of quantum gravity and that it does not appear in the classical limit because the quantum energy-impulse tensor gives an equal contribution with opposite sign. The work shows that a very large local value of the CC comes from the space where the mass of a quasi-punctual particle is present but that it can be as small as measured on cosmological scale. The theory shows that the small dependence of the CC from the mean mass density of the universe is due to the null contribution coming from the empty space. This fact gives some hints for the explanation of the conundrum of the cosmic coincidence by making a high CC value of the initial instant of universe compatible with the very small one of the present era.
Canonical Form and Separability of PPT States in 2x2x2xN Composite Quantum Systems
Fei, S M; Wang, X H; Wang, Z X; Wu, K; Wu, Ke
2003-01-01
We give a canonical form of PPT states in ${\\cal C}^2 \\otimes {\\cal C}^2\\otimes {\\cal C}^2 \\otimes {\\cal C}^N$ with rank=$N$. From this canonical form a necessary separable condition for these states is presented.
Generalized BF state in quantum gravity
Yamashita, Shinji; Fukuda, Makoto
2014-01-01
The BF state is known as a simple wave function which satisfies three constraints in canonical quantum gravity without a cosmological constant. It is constructed from a product of the group delta functions. Applying the chiral asymmetric extension, the BF state is generalized to the state for the real values of the Barbero-Immirzi parameter.
Singh, Parampreet; Soni, S. K.
2016-06-01
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.
Hopfion canonical quantization
Acus, A; Norvaisas, E; Shnir, Ya
2012-01-01
We study the effect of the canonical quantization of the rotational mode of the charge Q=1 and Q=2 spinning Hopfions. The axially-symmetric solutions are constructed numerically, it is shown the quantum corrections to the mass of the configurations are relatively large.
Hopfion canonical quantization
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Acus, A. [Vilnius University, Institute of Theoretical Physics and Astronomy, Gostauto 12, Vilnius 01108 (Lithuania); Halavanau, A. [Department of Theoretical Physics and Astrophysics, BSU, Minsk (Belarus); Norvaisas, E. [Vilnius University, Institute of Theoretical Physics and Astronomy, Gostauto 12, Vilnius 01108 (Lithuania); Shnir, Ya., E-mail: shnir@maths.tcd.ie [Department of Theoretical Physics and Astrophysics, BSU, Minsk (Belarus); Institute of Physics, Carl von Ossietzky University Oldenburg (Germany)
2012-05-03
We study the effect of the canonical quantization of the rotational mode of the charge Q=1 and Q=2 spinning Hopfions. The axially-symmetric solutions are constructed numerically, it is shown the quantum corrections to the mass of the configurations are relatively large.
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
2017-07-04
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
Chiou, Dah-Wei
2014-01-01
This article presents an "in-a-nutshell" yet self-contained introductory review on loop quantum gravity (LQG) -- a background-independent, nonperturbative approach to a consistent quantum theory of gravity. Instead of rigorous and systematic derivations, it aims to provide a general picture of LQG, placing emphasis on the fundamental ideas and their significance. The canonical formulation of LQG, as the central topic of the article, is presented in a logically orderly fashion with moderate details, while the spin foam theory, black hole thermodynamics, and loop quantum cosmology are covered briefly. Current directions and open issues are also summarized.
Constraint algebra of general relativity from a formal continuum limit of canonical tensor model
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Sasakura, Naoki [Yukawa Institute for Theoretical Physics, Kyoto University,Oiwake-cho, Kitashirakawa, Sakyo-ku, Kyoto 606-8502 (Japan); Sato, Yuki [National Institute for Theoretical Physics, School of Physics andMandelstam Institute for Theoretical Physics, University of the Witwatersrand,Wits 2050 (South Africa)
2015-10-16
Canonical tensor model (CTM for short below) is a rank-three tensor model formulated as a totally constrained system in the canonical formalism. In the classical case, the constraints form a first-class constraint Poisson algebra with structures similar to that of the ADM formalism of general relativity, qualifying CTM as a possible discrete formalism for quantum gravity. In this paper, we show that, in a formal continuum limit, the constraint Poisson algebra of CTM with no cosmological constant exactly reproduces that of the ADM formalism. To this end, we obtain the expression of the metric tensor field in general relativity in terms of one of the dynamical rank-three tensors in CTM, and determine the correspondence between the constraints of CTM and those of the ADM formalism. On the other hand, the cosmological constant term of CTM seems to induce non-local dynamics, and is inconsistent with an assumption about locality of the continuum limit.
Negative Energy Cosmology and the Cosmological Constant
Prokopec, Tomislav
2011-01-01
It is well known that string theories naturally compactify on anti-de Sitter spaces, and yet cosmological observations show no evidence of a negative cosmological constant in the early Universe's evolution. In this letter we present two simple nonlocal modifications of the standard Friedmann cosmology that can lead to observationally viable cosmologies with an initial (negative) cosmological constant. The nonlocal operators we include are toy models for the quantum cosmological backreaction. In Model I an initial quasiperiodic oscillatory epoch is followed by inflation and a late time matter era, representing a dark matter candidate. The backreaction in Model II quickly compensates the negative cosmological term such that the Ricci curvature scalar rapidly approaches zero, and the Universe ends up in a late time radiation era.
Kiselev, V V
2012-01-01
A huge value of cosmological constant characteristic for the particle physics and the inflation of early Universe are inherently related to each other: one can construct a fine-tuned superpotential, which produces a flat potential of inflaton with a constant density of energy V=\\Lambda^4 after taking into account for leading effects due to the supergravity, so that an introduction of small quantum loop-corrections to parameters of this superpotential naturally results in the dynamical instability relaxing the primary cosmological constant by means of inflationary regime. The model phenomenologically agrees with observational data on the large scale structure of Universe at \\Lambda~10^{16} GeV.
Fabris, J C; Rodrigues, D C; Batista, C E M; Daouda, M H
2012-01-01
We review the difficulties of the generalized Chaplygin gas model to fit observational data, due to the tension between background and perturbative tests. We argue that such issues may be circumvented by means of a self-interacting scalar field representation of the model. However, this proposal seems to be successful only if the self-interacting scalar field has a non-canonical form. The latter can be implemented in Rastall's theory of gravity, which is based on a modification of the usual matter conservation law. We show that, besides its application to the generalized Chaplygin gas model, other cosmological models based on Rastall's theory have many interesting and unexpected new features.
Chaicherdsakul, Kanokkuan
2006-08-01
Quantum theory of cosmological fluctuations with other matters is studied to higher order to understand the origin of the universe during the time of inflation. This study also links gravitational and all matter fluctuations with the observed cosmic microwave background (CMB) anisotropy. It is important to keep in mind that what is tested observationally is the paradigm that the primordial spectrum of inhomogeneities was nearly scale invariant and predominantly adiabatic. Therefore, if other matters such as fermion and gauge fields which do not drive inflation predict the scale invariant spectrums, their existence during inflation cannot be ruled out. We therefore extend the calculation of quantum corrections to the cosmological correlation which has been done by Weinberg for a loop of minimally coupled scalars, to other types of matters loops and a general and realistic potential. This dissertation shows that departures from scale invariance are never large even when Dirac, vector, and conformal scalar fields are present during inflation and even when the two-loop spectrum is calculated. No fine tuning is needed, in the sense that effective masses can be arbitrary values. Although the loop power spectrum was generally expected to be smaller than the classical one by a factor of GH2, I find that the quantum effect could be in the order of the classical value at the two loop level. The momentum dependence of the quantum spectrum goes as q -3ln q for all massless matters at one-loop and goes as q-3 ln 2 q at two-loop. For massive matters, the momentum dependence goes as q-3+eta (m), where |eta| interactions between gravity and various matters during the time of Big Bang inflation.
Covariant canonical quantization
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Hippel, G.M. von [University of Regina, Department of Physics, Regina, Saskatchewan (Canada); Wohlfarth, M.N.R. [Universitaet Hamburg, Institut fuer Theoretische Physik, Hamburg (Germany)
2006-09-15
We present a manifestly covariant quantization procedure based on the de Donder-Weyl Hamiltonian formulation of classical field theory. This procedure agrees with conventional canonical quantization only if the parameter space is d=1 dimensional time. In d>1 quantization requires a fundamental length scale, and any bosonic field generates a spinorial wave function, leading to the purely quantum-theoretical emergence of spinors as a byproduct. We provide a probabilistic interpretation of the wave functions for the fields, and we apply the formalism to a number of simple examples. These show that covariant canonical quantization produces both the Klein-Gordon and the Dirac equation, while also predicting the existence of discrete towers of identically charged fermions with different masses. Covariant canonical quantization can thus be understood as a ''first'' or pre-quantization within the framework of conventional QFT. (orig.)
Covariant canonical quantization
Von Hippel, G M; Hippel, Georg M. von; Wohlfarth, Mattias N.R.
2006-01-01
We present a manifestly covariant quantization procedure based on the de Donder-Weyl Hamiltonian formulation of classical field theory. Covariant canonical quantization agrees with conventional canonical quantization only if the parameter space is d=1 dimensional time. In d>1 quantization requires a fundamental length scale, and any bosonic field generates a spinorial wave function, leading to the purely quantum-theoretical emergence of spinors as a byproduct. We provide a probabilistic interpretation of the wave functions for the fields, and apply the formalism to a number of simple examples. These show that covariant canonical quantization produces both the Klein-Gordon and the Dirac equation, while also predicting the existence of discrete towers of identically charged fermions with different masses.
Indian Academy of Sciences (India)
W. X. Zhong
2014-09-01
In this paper, we use the canonical ensemble model to discuss the radiation of a Schwarzschild–de Sitter black hole on the black hole horizon. Using this model, we calculate the probability distribution from function of the emission shell. And the statistical meaning which compare with the distribution function is used to investigate the black hole tunnelling radiation spectrum.We also discuss the mechanism of information flowing from the black hole.
The dark sector from interacting canonical and non-canonical scalar fields
Energy Technology Data Exchange (ETDEWEB)
De Souza, Rudinei C; Kremer, Gilberto M, E-mail: kremer@Fisica.ufpr.b [Departamento de Fisica, Universidade Federal do Parana, Curitiba (Brazil)
2010-09-07
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.
Dark Sector from Interacting Canonical and Non-Canonical Scalar Fields
de Souza, Rudinei C
2010-01-01
In this work it is investigated general models with interactions between two canonical scalar fields and between one non-canonical (tachyon-type) and one canonical scalar field. 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.
The infrared sector of quantum fields on cosmological space-times
Janssen, T.M.
2009-01-01
In this thesis the infrared properties of massless scalar fields, with a possible coupling to the Ricci scalar on a cosmological background are studied. Our background space-time is a homogeneous, flat FLRW space-time, with the additional constraint that the deceleration parameter is constant. It
The infrared sector of quantum fields on cosmological space-times
Janssen, T.M.
2009-01-01
In this thesis the infrared properties of massless scalar fields, with a possible coupling to the Ricci scalar on a cosmological background are studied. Our background space-time is a homogeneous, flat FLRW space-time, with the additional constraint that the deceleration parameter is constant. It ha
Neves, J C S
2015-01-01
In the Nietzschean philosophy, the concept of force from physics is important to build one of its main concepts: the will to power. The concept of force, which Nietzsche found out in the Classical Mechanics, almost disappears in the physics of the XX century with the Quantum Field Theory and General Relativity. Is the Nietzschean world as contending forces, a Dionysian cosmology, possible in the current science?
Alvarez, Enrique
1985-01-01
Some cosmological consequences of the assumption that superstrings are more fundamental objects than ordinary local quantum fields are examined. We study, in particular, the dependence of both the string tension and the temperature of the primordial string soup on cosmic time. A particular scenario is proposed in which the universe undergoes a contracting ``string phase'' before the ordinary ``big bang,'' which according to this picture is nothing but the outcome of the transition from nonlocal to local fundamental physics.
G., Leonardo Quintanar
2015-01-01
We study the cosmological implications of the Nambu-Jona-Lasinio (NJL model) when the coupling constant is field dependent. The NJL model has a four-fermion interaction describing two different phases due to quantum interaction effects and determined by the strength of the coupling constant g. It describes massless fermions for weak coupling and a massive fermions and strong coupling, where a fermion condensate is formed. In the original NJL model the coupling constant g is indeed constant, and in this work we consider a modified version of the NJL model by introducing a dynamical field dependent coupling motivated by string theory. The effective potential as a function of the varying coupling (aimed to implement a natural phase transition) is seen to develop a negative divergence, i.e. becomes a "bottomless well" in certain limit region. Although we explain how an lower unbounded potential is not necessarily unacceptable in a cosmological context, the divergence can be removed if we consider a mass term for ...
Kastrup, H A
1997-01-01
Many authors - beginning with Bekenstein - have suggested that the energy levels E_n of a quantized isolated Schwarzschild black hole have the form E_n = sigma sqrt{n} E_P, n=1,2,..., sigma =O(1), with degeneracies g^n. In the present paper properties of a system with such a spectrum, considered as a quantum canonical ensemble, are discussed: Its canonical partition function Z(g,beta=1/kT), defined as a series for g1 by means of an integral representation which reveals a cut of Z(g,beta) in the complex g-plane from g=1 to infinity. Approaching the cut from above yields a real and an imaginary part of Z. Very surprisingly, it is the (explicitly known) imaginary part which gives the expected thermodynamical properties of Schwarzschild black holes: Identifying the internal energy U with the rest energy Mc^2 requires beta to have the value (in natural units) beta = 2M(lng/sigma^2)[1+O(1/M^2)], (4pi sigma^2=lng gives Hawking's beta_H), and yields the entropy S=[lng/(4pi sigma^2)] A/4 + O(lnA), where A is the area ...
Energy Technology Data Exchange (ETDEWEB)
Wang, Sai, E-mail: wangsai@itp.ac.cn [State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, 100049, Beijing (China); Chang, Zhe [State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, 100049, Beijing (China); Institute of High Energy Physics, Chinese Academy of Sciences, 100049, Beijing (China)
2015-06-11
We propose the gravity’s rainbow scenario as a possible alternative of the inflation paradigm to account for the flatness and horizon problems. We focus on studying the cosmological scalar perturbations which are seeded by the quantum fluctuations in the very early universe. The scalar power spectrum is expected to be nearly scale-invariant. We estimate the rainbow index λ and energy scale M in the gravity’s rainbow scenario by analyzing the Planck temperature and WMAP polarization datasets. The constraints on them are given by λ=2.933±0.012 and ln(10{sup 5}M/M{sub p})=-0.401{sub -0.451}{sup +0.457} at the 68 % confidence level.
Energy Technology Data Exchange (ETDEWEB)
Wang, Sai [Chinese Academy of Sciences, State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Beijing (China); Chang, Zhe [Chinese Academy of Sciences, State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Beijing (China); Chinese Academy of Sciences, Institute of High Energy Physics, Beijing (China)
2015-06-15
We propose the gravity's rainbow scenario as a possible alternative of the inflation paradigm to account for the flatness and horizon problems. We focus on studying the cosmological scalar perturbations which are seeded by the quantum fluctuations in the very early universe. The scalar power spectrum is expected to be nearly scale-invariant. We estimate the rainbow index λ and energy scale M in the gravity's rainbow scenario by analyzing the Planck temperature and WMAP polarization datasets. The constraints on them are given by λ = 2.933 ± 0.012 and ln(10{sup 5}M/M{sub p}) = -0.401{sub -0.451}{sup +0.457} at the 68% confidence level. (orig.)
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.
Ostrogradski approach for the Regge-Teitelboim type cosmology
Cordero, Ruben; 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 {\\it 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 Wheeler equation agrees with previous results recently found. On these lines, we also comment upon the compatibili...
Pinto-Neto, N
2002-01-01
We consider quantum geometrodynamics and parametrized quantum field theories in the framework of the Bohm-de Broglie interpretation. In the first case, and following the lines of our previous work \\cite{must}, 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 a scalar field theory in Minkowski spacetime for any quantum potential, and we exhibit a concrete example where Lorentz invariance of individual events is broken.
When Canonical Quantization Fails, Here is How to Fix It
Klauder, John R.
2016-01-01
Following Dirac, the rules of canonical quantization include classical and quantum contact transformations of classical and quantum phase space variables. While arbitrary classical canonical coordinate transformations exist that is not the case for some analogous quantum canonical coordinate transformations. This failure is due to the rigid connection of quantum variables arising by promoting the corresponding classical variable from a $c$-number to a $q$-number. A different relationship of $...
Cosmological dark energy effects from entanglement
Energy Technology Data Exchange (ETDEWEB)
Capozziello, Salvatore, E-mail: capozziello@na.infn.it [Dipartimento di Fisica, Università di Napoli “Federico II”, Via Cinthia, 80126 Napoli (Italy); Istituto Nazionale di Fisica Nucleare (INFN), Sez. di Napoli, Via Cinthia, 80126 Napoli (Italy); Luongo, Orlando [Dipartimento di Fisica, Università di Napoli “Federico II”, Via Cinthia, 80126 Napoli (Italy); Istituto Nazionale di Fisica Nucleare (INFN), Sez. di Napoli, Via Cinthia, 80126 Napoli (Italy); Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de México (UNAM) (Mexico); Mancini, Stefano [Scuola di Scienze and Tecnologie, Università di Camerino, 62032 Camerino (Italy); Istituto Nazionale di Fisica Nucleare (INFN), Sez. di Perugia, Via Pascoli, 06123 Perugia (Italy)
2013-06-03
The thorny issue of relating information theory to cosmology is here addressed by assuming a possible connection between quantum entanglement measures and observable universe. In particular, we propose a cosmological toy model, where the equation of state of the cosmological fluid, which drives the today observed cosmic acceleration, can be inferred from quantum entanglement between different cosmological epochs. In such a way the dynamical dark energy results as byproduct of quantum entanglement.
Mashkevich, V S
1997-01-01
This paper is a continuation of the papers [gr-qc/9409010, gr-qc/9505034, gr-qc/9603022, gr-qc/9609035, gr-qc/9609046, gr-qc/9704033]. The aim of the paper is to incorporate singularities---both local (black hole and naked singularity) and global (big bang and big crunch)---into the dynamics of indeterministic quantum gravity and cosmology. The question is whether a singularity is dynamically passable, i.e., whether a dynamical process which ends with a singularity may be extended beyond the latter. The answer is yes. A local singularity is trivially passable, while the passableness for a global singularity may invoke CPT transformation. The passableness of the singularities implies pulsating black holes and the oscillating universe. For the local singularity, the escape effect takes place: In a vicinity of the singularity, quantum matter leaves the gravitational potential well. Keywords: tempered singularity, strong singularity, trivial passage, CPT passage, pulsating black hole, escape effect, oscillating u...
On classical and quantum dynamics of tachyon-like fields and their cosmological implications
Energy Technology Data Exchange (ETDEWEB)
Dimitrijević, Dragoljub D., E-mail: ddrag@pmf.ni.ac.rs; Djordjević, Goran S., E-mail: ddrag@pmf.ni.ac.rs; Milošević, Milan, E-mail: ddrag@pmf.ni.ac.rs [Department of Physics, Faculty of Science and Mathematics, University of Niš (Serbia); Vulcanov, Dumitru [Faculty of Physics, West University of Timisoara (Romania)
2014-11-24
We consider a class of tachyon-like potentials, motivated by string theory, D-brane dynamics and inflation theory in the context of classical and quantum mechanics. A formalism for describing dynamics of tachyon fields in spatially homogenous and one-dimensional - classical and quantum mechanical limit is proposed. A few models with concrete potentials are considered. Additionally, possibilities for p-adic and adelic generalization of these models are discussed. Classical actions and corresponding quantum propagators, in the Feynman path integral approach, are calculated in a form invariant on a change of the background number fields, i.e. on both archimedean and nonarchimedean spaces. Looking for a quantum origin of inflation, relevance of p-adic and adelic generalizations are briefly discussed.
Classical Universe emerging from quantum cosmology without horizon and flatness problems
Fathi, M; Moniz, P V
2016-01-01
We apply the complex de Broglie-Bohm formulation of quantum mechanics [1] to a spatially closed homogeneous and isotropic early Universe whose matter content 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.
Classical and quantum solutions in Brans-Dicke cosmology with a perfect fluid
Paliathanasis, Andronikos; Tsamparlis, Michael; Basilakos, Spyros; Barrow, John D.
2016-02-01
We consider the application of group invariant transformations in order to constrain a flat isotropic and homogeneous cosmological model, containing a Brans-Dicke scalar field and a perfect fluid with a constant equation of state parameter w , where the latter is not interacting with the scalar field in the gravitational action integral. The requirement that the Wheeler-DeWitt equation be invariant under one-parameter point transformations provides us with two families of power-law potentials for the Brans-Dicke field, in which the powers are functions of the Brans-Dicke parameter ωBD and the parameter w . The existence of the Lie symmetry in the Wheeler-DeWitt equation is equivalent to the existence of a conserved quantity in field equations and with oscillatory terms in the wave function of the Universe. This enables us to solve the field equations. For a specific value of the conserved quantity, we find a closed-form solution for the Hubble factor, which is equivalent to a cosmological model in general relativity containing two perfect fluids. This provides us with different models for specific values of the parameters ωBD , and w . Finally, the results hold for the specific case where the Brans-Dicke parameter ωBD is zero, that is, for the O'Hanlon massive dilaton theory and, consequently, for f (R ) gravity in the metric formalism.
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.)
Classical and Quantum Solutions in Brans-Dicke Cosmology with a Perfect Fluid
Paliathanasis, Andronikos; Basilakos, Spyros; Barrow, John D
2015-01-01
We consider the application of group invariant transformations in order to constrain a flat isotropic and homogeneous cosmological model, containing of a Brans-Dicke scalar field and a perfect fluid with a constant equation of state parameter $w$, where the latter is not interacting with the scalar field in the gravitational action integral. The requirement that the Wheeler-DeWitt equation be invariant under one-parameter point transformations provides us with two families of power-law potentials for the Brans-Dicke field, in which the powers are functions of the Brans-Dicke parameter $\\omega_{BD}$ and the parameter $w$. The existence of the Lie symmetry in the Wheeler-DeWitt equation is equivalent to the existence of a conserved quantity in field equations and with oscillatory terms in the wavefunction of the universe. This enables us to solve the field equations. For a specific value of the conserved quantity, we find a closed-form solution for the Hubble factor, which is equivalent to a cosmological model ...
Seshavatharam, U. V. S.; Lakshminarayana, S.
If one is willing to consider the current cosmic microwave back ground temperature as a quantum gravitational effect of the evolving primordial cosmic black hole (universe that constitutes dynamic space-time and exhibits quantum behavior) automatically general theory of relativity and quantum mechanics can be combined into a `scale independent' true unified model of quantum gravity. By considering the `Planck mass' as the initial mass of the baby Hubble volume, past and current physical and thermal parameters of the cosmic black hole can be understood. Current rate of cosmic black hole expansion is being stopped by the microscopic quantum mechanical lengths. In this new direction authors observed 5 important quantum mechanical methods for understanding the current cosmic deceleration. To understand the ground reality of current cosmic rate of expansion, sensitivity and accuracy of current methods of estimating the magnitudes of current CMBR temperature and current Hubble constant must be improved and alternative methods must be developed. If it is true that galaxy constitutes so many stars, each star constitutes so many hydrogen atoms and light is coming from the excited electron of galactic hydrogen atom, then considering redshift as an index of `whole galaxy' receding may not be reasonable. During cosmic evolution, at any time in the past, in hydrogen atom emitted photon energy was always inversely proportional to the CMBR temperature. Thus past light emitted from older galaxy's excited hydrogen atom will show redshift with reference to the current laboratory data. As cosmic time passes, in future, the absolute rate of cosmic expansion can be understood by observing the rate of increase in the magnitude of photon energy emitted from laboratory hydrogen atom. Aged super novae dimming may be due to the effect of high cosmic back ground temperature. Need of new mathematical methods & techniques, computer simulations, advanced engineering skills seem to be essential
Cherkas, S L
2015-01-01
It is shown, that initial conditions in the quasi-Heisenberg quantization scheme can be set at an initial cosmological singularity per se. This possibility is provided by finiteness of some quantities, namely momentums of the dynamical variables, at a singularity, in spite of infinity of the dynamical variables themselves. The uncertainty principle allows avoiding a necessity to set values of the dynamical variables at singularity, as a wave packet can be expressed through the finite momentums. The issue of a vacuum energy, arising during evolution when the gravitational waves appear, is addressed as well. It is shown that, in the certain gauge, the equations of motion contain a difference of kinetic and potential energies of the field oscillators. Thus, in this gauge, the leading divergent parts of the vacuum energy in the equations of motion cancel each other. It is conjectured that the UV cut-off allows physical interpretation of the weakly divergent part of the vacuum energy.
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.)
Classical and quantum cosmology with two perfect fluids: stiff matter and radiation
Alvarenga, F G; Freitas, R C; Gonçalves, S V B
2016-01-01
In this work the homogeneous and isotropic Universe of Friedmann-Robertson-Walker is studied in the presence of two fluids: stiff matter and radiation described by the Schutz's formalism. We obtain to the classic case the behaviour of the scale factor of the universe. For the quantum case the wave packets are constructed and the wave function of the universe is found.
Taming the cosmological constant in 2D causal quantum gravity with topology change
Loll, R.; Westra, W.; Zohren, S.
2006-01-01
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 dynamics o
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 dynamics o
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
Agarwal, Animesh
2015-01-01
Quantum effects due to the spatial delocalization of light atoms are treated in molecular simulation via the path integral technique. Among several methods, Path Integral (PI) Molecular Dynamics (MD) is nowadays a powerful tool to investigate properties induced by spatial delocalization of atoms; however computationally this technique is very demanding. The abovementioned limitation implies the restriction of PIMD applications to relatively small systems and short time scales. One possible solution to overcome size and time limitation is to introduce PIMD algorithms into the Adaptive Resolution Simulation Scheme (AdResS). AdResS requires a relatively small region treated at path integral level and embeds it into a large molecular reservoir consisting of generic spherical coarse grained molecules. It was previously shown that the realization of the idea above, at a simple level, produced reasonable results for toy systems or simple/test systems like liquid parahydrogen. Encouraged by previous results, in this ...
Shestakova, T P
2008-01-01
In "extended phase space" approach to quantum geometrodynamics numerical solutions to Schrodinger equation corresponding to various choice of gauge conditions are obtained for the simplest isotropic model. The "extended phase space" approach belongs to those appeared in the last decade in which, as a result of fixing a reference frame, the Wheeler - DeWitt static picture of the world is replaced by evolutionary quantum geometrodynamics. Some aspects of this approach were discussed at two previous PIRT meetings. We are interested in the part of the wave function depending on physical degrees of freedom. Three gauge conditions having a clear physical meaning are considered. They are the conformal time gauge, the gauge producing the appearance of Lambda-term in the Einstein equations, and the one covering the two previous cases as asymptotic limits. The interpretation and discussion of the obtained solutions is given.
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.
Quantum Oscillations Prevent the Big Bang Singularity in an Einstein-Dirac Cosmology
Finster, Felix
2008-01-01
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 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. We finally give 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.
A quantum cosmological model in Ho\\v{r}ava-Lifshitz gravity
Obregón, O
2013-01-01
A Wheeler-DeWitt equation for the Kantowski-Sachs model is derived within the framework of the minimal quantum gravity theory proposed by Ho\\v{r}ava. We study the solution to this equation in the ultraviolet limit for the specific case where the {\\lambda} parameter of the theory takes its relativistic value {\\lambda} = 1. It is observed that the minisuperspace variables switch their role compared with their usual infrared (General Relativity) behavior.
Quantum states of the bouncing universe
Gazeau, Jean Pierre; Piechocki, Wlodzimierz
2013-01-01
In this paper we study quantum dynamics of the bouncing cosmological model. We focus on the model of the flat Friedman-Robertson-Walker universe with a free scalar field. The bouncing behavior, which replaces classical singularity, appears due to the modification of general relativity along the methods of loop quantum cosmology. We show that there exist a unitary transformation that enables to describe the system as a free particle with Hamiltonian equal to canonical momentum. We examine properties of the various quantum states of the Universe: boxcar state, standard coherent state, and soliton-like state, as well as Schr{\\"o}dinger's cat states constructed from these states. Characteristics of the states such as quantum moments and Wigner functions are investigated. We show that each of these states have, for some range of parameters, a proper semiclassical limit fulfilling the correspondence principle. Decoherence of the superposition of two universes is described and possible interpretations in terms of tr...