Applications of Cosmological Perturbation Theory
Christopherson, Adam J
2011-01-01
Cosmological perturbation theory is crucial for our understanding of the universe. The linear theory has been well understood for some time, however developing and applying the theory beyond linear order is currently at the forefront of research in theoretical cosmology. This thesis studies the applications of perturbation theory to cosmology and, specifically, to the early universe. Starting with some background material introducing the well-tested 'standard model' of cosmology, we move on to develop the formalism for perturbation theory up to second order giving evolution equations for all types of scalar, vector and tensor perturbations, both in gauge dependent and gauge invariant form. We then move on to the main result of the thesis, showing that, at second order in perturbation theory, vorticity is sourced by a coupling term quadratic in energy density and entropy perturbations. This source term implies a qualitative difference to linear order. Thus, while at linear order vorticity decays with the expan...
Renormalized Cosmological Perturbation Theory
Crocce, M
2006-01-01
We develop a new formalism to study nonlinear evolution in the growth of large-scale structure, by following the dynamics of gravitational clustering as it builds up in time. This approach is conveniently represented by Feynman diagrams constructed in terms of three objects: the initial conditions (e.g. perturbation spectrum), the vertex (describing non-linearities) and the propagator (describing linear evolution). We show that loop corrections to the linear power spectrum organize themselves into two classes of diagrams: one corresponding to mode-coupling effects, the other to a renormalization of the propagator. Resummation of the latter gives rise to a quantity that measures the memory of perturbations to initial conditions as a function of scale. As a result of this, we show that a well-defined (renormalized) perturbation theory follows, in the sense that each term in the remaining mode-coupling series dominates at some characteristic scale and is subdominant otherwise. This is unlike standard perturbatio...
Gauge Invariant Cosmological Perturbation Theory
Durrer, R
1993-01-01
After an introduction to the problem of cosmological structure formation, we develop gauge invariant cosmological perturbation theory. We derive the first order perturbation equations of Einstein's equations and energy momentum ``conservation''. Furthermore, the perturbations of Liouville's equation for collisionless particles and Boltzmann's equation for Compton scattering are worked out. We fully discuss the propagation of photons in a perturbed Friedmann universe, calculating the Sachs--Wolfe effect and light deflection. The perturbation equations are extended to accommodate also perturbations induced by seeds. With these general results we discuss some of the main aspects of the texture model for the formation of large scale structure in the Universe (galaxies, clusters, sheets, voids). In this model, perturbations in the dark matter are induced by texture seeds. The gravitational effects of a spherically symmetric collapsing texture on dark matter, baryonic matter and photons are calculated in first orde...
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.
Effective Field Theory of Cosmological Perturbations
Piazza, Federico
2013-01-01
The effective field theory of cosmological perturbations stems from considering a cosmological background solution as a state displaying spontaneous breaking of time translations and (adiabatic) perturbations as the related Nambu-Goldstone modes. With this insight, one can systematically develop a theory for the cosmological perturbations during inflation and, with minor modifications, also describe in full generality the gravitational interactions of dark energy, which are relevant for late-time cosmology. The formalism displays a unique set of Lagrangian operators containing an increasing number of cosmological perturbations and derivatives. We give an introductory description of the unitary gauge formalism for theories with broken gauge symmetry---that allows to write down the most general Lagrangian---and of the Stueckelberg "trick"---that allows to recover gauge invariance and to make the scalar field explicit. We show how to apply this formalism to gravity and cosmology and we reproduce the detailed ana...
On counterterms in cosmological perturbation theory
Goswami, Gaurav
2014-01-01
Cosmological perturbation theory is the theory of fluctuations (scalar as well as tensor) around the inflationary cosmological background solution. It is important to understand the details of the process of renormalization in this theory. In more familiar applications of quantum field theory, the dependence on the external momenta of the dimensionally regulated expression of the one-loop contribution to a correlator determines the number of counter terms (and their forms) required to renormalize it. In this work, it is pointed out that in cosmological perturbation theory, though this still happens, it happens in a completely different way such that in the late time limit, the information about the number and forms of counter terms required gets erased. This is to be compared with what happens in spontaneous symmetry breaking where the use of fluctuation fields around a chosen vacuum seems to suggest that more counter terms shall be needed to renormalize the theory than are actually required. We also comment ...
A general theory of linear cosmological perturbations: bimetric theories
Lagos, Macarena
2016-01-01
We implement the method developed in [1] to construct the most general parametrised action for linear cosmological perturbations of bimetric theories of gravity. Specifically, we consider perturbations around a homogeneous and isotropic background, and identify the complete form of the action invariant under diffeomorphism transformations, as well as the number of free parameters characterising this cosmological class of theories. We discuss, in detail, the case without derivative interactions, and compare our results with those found in massive bigravity.
Perturbation Theory of the Cosmological Log-Density Field
DEFF Research Database (Denmark)
Wang, Xin; Neyrinck, Mark; Szapudi, István
2011-01-01
, motivating an analytic study of it. In this paper, we develop cosmological perturbation theory for the power spectrum of this field. Our formalism is developed in the context of renormalized perturbation theory, which helps to regulate the convergence behavior of the perturbation series, and of the Taylor...
Manifestly Covariant Gauge-invariant Cosmological Perturbation Theory
Miedema, P G
2010-01-01
It is shown that a first-order cosmological perturbation theory for the open, flat and closed Friedmann-Lemaitre-Robertson-Walker universes admits one, and only one, gauge-invariant variable which describes the perturbation to the energy density and which becomes equal to the usual Newtonian energy density in the non-relativistic limit. The same holds true for the perturbation to the particle number density. Using these two new variables, a new manifestly gauge-invariant cosmological perturbation theory has been developed. Density perturbations evolve diabatically. Perturbations in the total energy density are gravitationally coupled to perturbations in the particle number density, irrespective of the nature of the particles. There is, in first-order, no back-reaction of perturbations to the global expansion of the universe. Small-scale perturbations in the radiation-dominated era oscillate with an increasing amplitude, whereas in older, less precise treatments, oscillating perturbations are found with a decr...
Remarks on the Theory of Cosmological Perturbation
Institute of Scientific and Technical Information of China (English)
林文斌
2001-01-01
It is shown that the power spectrum defined in the synchronous gauge cannot be directly used to calculate the predictions of cosmological models on the large-scale structure of the Universe, which should be calculated directly by a suitable gauge-invariant power spectrum or the power spectrum defined in the Newtonian gauge.
Perturbation Theory of the Cosmological Log-Density Field
Wang, Xin; Szapudi, István; Szalay, Alex; Chen, Xuelei; Lesgourgues, Julien; Riotto, Antonio; Sloth, Martin; 10.1088/0004-637X/735/1/32
2011-01-01
The matter density field exhibits a nearly lognormal probability density distribution (PDF) after entering into the nonlinear regime. Recently, it has been shown that the shape of the power spectrum of a logarithmically transformed density field is very close to the linear density power spectrum, motivating an analytic study of it. In this paper, we develop cosmological perturbation theory for the power spectrum of this field. Our formalism is developed in the context of renormalized perturbation theory, which helps to regulate the convergence behavior of the perturbation series, and of the Taylor- series expansion we use of the logarithmic mapping. This approach allows us to handle the critical issue of density smoothing in a straightforward way. We also compare our perturbative results with simulation measurements.
On the non-linear scale of cosmological perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Blas, Diego [Theory Division, CERN, 1211 Geneva (Switzerland); Garny, Mathias; Konstandin, Thomas, E-mail: diego.blas@cern.ch, E-mail: mathias.garny@desy.de, E-mail: Thomas.Konstandin@desy.de [DESY, Notkestr. 85, 22607 Hamburg (Germany)
2013-09-01
We discuss the convergence of cosmological perturbation theory. We prove that the polynomial enhancement of the non-linear corrections expected from the effects of soft modes is absent in equal-time correlators like the power or bispectrum. We first show this at leading order by resumming the most important corrections of soft modes to an arbitrary skeleton of hard fluctuations. We derive the same result in the eikonal approximation, which also allows us to show the absence of enhancement at any order. We complement the proof by an explicit calculation of the power spectrum at two-loop order, and by further numerical checks at higher orders. Using these insights, we argue that the modification of the power spectrum from soft modes corresponds at most to logarithmic corrections at any order in perturbation theory. Finally, we discuss the asymptotic behavior in the large and small momentum regimes and identify the expansion parameter pertinent to non-linear corrections.
Efficient Cosmological Perturbation Theory with FAST-PT
Fang, Xiao; Blazek, Jonathan; McEwen, Joseph; Hirata, Christopher M.
2017-01-01
Cosmological perturbation theory is a powerful tool to model observations of large-scale structure in the weakly non-linear regime. However, even at next-to-leading order, it results in computationally expensive mode-coupling integrals. In this talk, I will focus on the physics behind our extremely efficient algorithm, FAST-PT. I will show how the algorithm can be applied to calculate 1-loop power spectra for several cosmological observables, including the matter density, galaxy bias, galaxy intrinsic alignments, the Ostriker-Vishniac effect, the secondary CMB polarization due to baryon flows, and redshift-space distortions. Our public code is written in Python and is easy to use and adapt to additional applications.
Effective gravitational couplings for cosmological perturbations in generalized Proca theories
De Felice, Antonio; Heisenberg, Lavinia; Kase, Ryotaro; Mukohyama, Shinji; Tsujikawa, Shinji; Zhang, Ying-li
2016-08-01
We consider the finite interactions of the generalized Proca theory including the sixth-order Lagrangian and derive the full linear perturbation equations of motion on the flat Friedmann-Lemaître-Robertson-Walker background in the presence of a matter perfect fluid. By construction, the propagating degrees of freedom (besides the matter perfect fluid) are two transverse vector perturbations, one longitudinal scalar, and two tensor polarizations. The Lagrangians associated with intrinsic vector modes neither affect the background equations of motion nor the second-order action of tensor perturbations, but they do give rise to nontrivial modifications to the no-ghost condition of vector perturbations and to the propagation speeds of vector and scalar perturbations. We derive the effective gravitational coupling Geff with matter density perturbations under a quasistatic approximation on scales deep inside the sound horizon. We find that the existence of intrinsic vector modes allows a possibility for reducing Geff. In fact, within the parameter space, Geff can be even smaller than the Newton gravitational constant G at the late cosmological epoch, with a peculiar phantom dark energy equation of state (without ghosts). The modifications to the slip parameter η and the evolution of the growth rate f σ8 are discussed as well. Thus, dark energy models in the framework of generalized Proca theories can be observationally distinguished from the Λ CDM model according to both cosmic growth and expansion history. Furthermore, we study the evolution of vector perturbations and show that outside the vector sound horizon the perturbations are nearly frozen and start to decay with oscillations after the horizon entry.
Adiabaticity and gravity theory independent conservation laws for cosmological perturbations
Romano, Antonio Enea; Sasaki, Misao
2015-01-01
We carefully study the implications of adiabaticity for the behavior of cosmological perturbations. There are essentially three similar but different definitions of non-adiabaticity: one is appropriate for a thermodynamic fluid $\\delta P_{nad}$, another is for a general matter field $\\delta P_{c,nad}$, and the last one is valid only on superhorizon scales. The first two definitions coincide if $c_s^2=c_w^2$ where $c_s$ is the propagation speed of the perturbation, while $c_w^2=\\dot P/\\dot\\rho$. Assuming the adiabaticity in the general sense, $\\delta P_{c,nad}=0$, we derive a relation between the lapse function in the comoving slicing $A_c$ and $\\delta P_{nad}$ valid for arbitrary matter field in any theory of gravity, by using only momentum conservation. The relation implies that as long as $c_s\
Cosmological perturbation theory in the synchronous and conformal newtonian gauges
Ma Chung Pei; Ma, Chung Pei; Bertschinger, Edmund
1995-01-01
This paper presents a systematic treatment of the linear theory of scalar gravitational perturbations in the synchronous gauge and the conformal Newtonian (or longitudinal) gauge. It differs from others in the literature in that we give, in both gauges, a complete discussion of all particle species that are relevant to any flat cold dark matter (CDM), hot dark matter (HDM), or CDM+HDM models (including a possible cosmological constant). The particles considered include CDM, baryons, photons, massless neutrinos, and massive neutrinos (an HDM candidate), where the CDM and baryons are treated as fluids while a detailed phase-space description is given to the photons and neutrinos. Particular care is applied to the massive neutrino component, which has been either ignored or approximated crudely in previous works. Isentropic initial conditions on super-horizon scales are derived. The coupled, linearized Boltzmann, Einstein and fluid equations that govern the evolution of the metric and density perturbations are t...
On the non-linear scale of cosmological perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Blas, Diego [European Organization for Nuclear Research (CERN), Geneva (Switzerland); Garny, Mathias; Konstandin, Thomas [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2013-04-15
We discuss the convergence of cosmological perturbation theory. We prove that the polynomial enhancement of the non-linear corrections expected from the effects of soft modes is absent in equal-time correlators like the power or bispectrum. We first show this at leading order by resumming the most important corrections of soft modes to an arbitrary skeleton of hard fluctuations. We derive the same result in the eikonal approximation, which also allows us to show the absence of enhancement at any order. We complement the proof by an explicit calculation of the power spectrum at two-loop order, and by further numerical checks at higher orders. Using these insights, we argue that the modification of the power spectrum from soft modes corresponds at most to logarithmic corrections. Finally, we discuss the asymptotic behavior in the large and small momentum regimes and identify the expansion parameter pertinent to non-linear corrections.
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.
Cosmological Perturbation Theory and the Evolution of Small-Scale Inhomogeneities
Miedema, P G
2011-01-01
It is shown that a first-order cosmological perturbation theory for the open, flat and closed Friedmann-Lemaitre-Robertson-Walker universes admits one, and only one, gauge-invariant variable which describes the perturbation to the energy density and which becomes equal to the usual Newtonian energy density in the non-relativistic limit. The same holds true for the perturbation to the particle number density. Using these two new variables, a new manifestly gauge-invariant cosmological perturbation theory based on the Lifshitz-Khalatnikov theory has been developed. Perturbations in the total energy density are gravitationally coupled to perturbations in the particle number density, irrespective of the nature of the particles. There is, in first-order, no back-reaction of perturbations to the global expansion of the universe. Small-scale perturbations in the radiation-dominated era oscillate with an increasing amplitude. Density perturbations do not evolve adiabatically, as is usually assumed, but diabatically, ...
Effective gravitational couplings for cosmological perturbations in generalized Proca theories
De Felice, Antonio; Kase, Ryotaro; Mukohyama, Shinji; Tsujikawa, Shinji; Zhang, Ying-li
2016-01-01
We consider the finite interactions of the generalized Proca theory including the sixth-order Lagrangian and derive the full linear perturbation equations of motion on the flat Friedmann-Lema\\^{i}tre-Robertson-Walker background in the presence of a matter perfect fluid. By construction, the propagating degrees of freedom (besides the matter perfect fluid) are two transverse vector perturbations, one longitudinal scalar, and two tensor polarizations. The Lagrangians associated with intrinsic vector modes neither affect the background equations of motion nor the second-order action of tensor perturbations, but they do give rise to non-trivial modifications to the no-ghost condition of vector perturbations and to the propagation speeds of vector and scalar perturbations. We derive the effective gravitational coupling $G_{\\rm eff}$ with matter density perturbations under a quasi-static approximation on scales deep inside the sound horizon. We find that the existence of intrinsic vector modes allows a possibility ...
Cosmological Perturbations in Antigravity
Oltean, Marius
2014-01-01
We compute the evolution of cosmological perturbations in a recently proposed Weyl-symmetric theory of two scalar fields with oppositely-signed conformal couplings to Einstein gravity. It is motivated from the minimal conformal extension of the Standard Model, such that one of these scalar fields is the Higgs while the other is a new particle, the dilaton, introduced to make the Higgs mass conformally symmetric. At the background level, the theory admits novel geodesically-complete cyclic cosmological solutions characterized by a brief period of repulsive gravity, or "antigravity", during each successive transition from a Big Crunch to a Big Bang. We show that despite the necessarily wrong-signed kinetic term of the dilaton in the full action, its cosmological solutions are stable at the perturbative level.
Cosmological perturbation theory at three-loop order
Energy Technology Data Exchange (ETDEWEB)
Blas, Diego [European Organization for Nuclear Research (CERN), Geneva (Switzerland); Garny, Mathias; Konstandin, Thomas [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2013-09-15
We analyze the dark matter power spectrum at three-loop order in standard perturbation theory of large scale structure. We observe that at late times the loop expansion does not converge even for large scales (small momenta) well within the linear regime, but exhibits properties compatible with an asymptotic series. We propose a technique to restore the convergence in the limit of small momentum, and use it to obtain a perturbative expansion with improved convergence for momenta in the range where baryonic acoustic oscillations are present. Our results are compared with data from N-body simulations at different redshifts, and we find good agreement within this range.
Cosmological perturbations in antigravity
Oltean, Marius; Brandenberger, Robert
2014-10-01
We compute the evolution of cosmological perturbations in a recently proposed Weyl-symmetric theory of two scalar fields with oppositely signed conformal couplings to Einstein gravity. It is motivated from the minimal conformal extension of the standard model, such that one of these scalar fields is the Higgs while the other is a new particle, the dilaton, introduced to make the Higgs mass conformally symmetric. At the background level, the theory admits novel geodesically complete cyclic cosmological solutions characterized by a brief period of repulsive gravity, or "antigravity," during each successive transition from a big crunch to a big bang. For simplicity, we consider scalar perturbations in the absence of anisotropies, with potential set to zero and without any radiation. We show that despite the necessarily wrong-signed kinetic term of the dilaton in the full action, these perturbations are neither ghostlike nor tachyonic in the limit of strongly repulsive gravity. On this basis, we argue—pending a future analysis of vector and tensor perturbations—that, with respect to perturbative stability, the cosmological solutions of this theory are viable.
Cosmological perturbations in massive bigravity
Energy Technology Data Exchange (ETDEWEB)
Lagos, Macarena; Ferreira, Pedro G., E-mail: m.lagos13@imperial.ac.uk, E-mail: p.ferreira1@physics.ox.ac.uk [Astrophysics, University of Oxford, DWB, Keble road, Oxford OX1 3RH (United Kingdom)
2014-12-01
We present a comprehensive analysis of classical scalar, vector and tensor cosmological perturbations in ghost-free massive bigravity. In particular, we find the full evolution equations and analytical solutions in a wide range of regimes. We show that there are viable cosmological backgrounds but, as has been found in the literature, these models generally have exponential instabilities in linear perturbation theory. However, it is possible to find stable scalar cosmological perturbations for a very particular choice of parameters. For this stable subclass of models we find that vector and tensor perturbations have growing solutions. We argue that special initial conditions are needed for tensor modes in order to have a viable model.
A general theory of linear cosmological perturbations: scalar-tensor and vector-tensor theories
Lagos, Macarena; Ferreira, Pedro G; Noller, Johannes
2016-01-01
We present a method for parametrizing linear cosmological perturbations of theories of gravity, around homogeneous and isotropic backgrounds. The method is sufficiently general and systematic that it can be applied to theories with any degrees of freedom (DoFs) and arbitrary gauge symmetries. In this paper, we focus on scalar-tensor and vector-tensor theories, invariant under linear coordinate transformations. In the case of scalar-tensor theories, we use our framework to recover the simple parametrizations of linearized Horndeski and "Beyond Horndeski" theories, and also find higher-derivative corrections. In the case of vector-tensor theories, we first construct the most general quadratic action for perturbations that leads to second-order equations of motion, which propagates two scalar DoFs. Then we specialize to the case in which the vector field is time-like (\\`a la Einstein-Aether gravity), where the theory only propagates one scalar DoF. As a result, we identify the complete forms of the quadratic act...
Cosmological Structure Formation with Augmented Lagrangian Perturbation Theory
Kitaura, Francisco-Shu
2012-01-01
We present a new fast and efficient approach to model structure formation with aug- mented Lagrangian perturbation theory (ALPT). Our method is based on splitting the dis- placement field into a long and a short range component. The long range component is computed by second order LPT (2LPT). This approximation contains a tidal nonlocal and nonlinear term. Unfortunately, 2LPT fails on small scales due to severe shell crossing and a crude quadratic behaviour in the low density regime. The spherical collapse (SC) approximation has been recently reported to correct for both effects by adding an ideal collapse truncation. However, this approach fails to reproduce the structures on large scales where it is significantly less correlated with the N-body result than 2LPT or linear LPT (the Zeldovich approximation). We propose to combine both approximations using for the short range displacement field the SC solution. A Gaussian filter with a smoothing radius r_S is used to separate between both regimes. We use the re...
Cosmological density perturbations from perturbed couplings
Tsujikawa, S
2003-01-01
The density perturbations generated when the inflaton decay rate is perturbed by a light scalar field $\\chi$ are studied. By explicitly solving the perturbation equations for the system of two scalar fields and radiation, we show that even in low energy-scale inflation nearly scale-invariant spectra of scalar perturbations with an amplitude set by observations are obtained through the conversion of $\\chi$ fluctuations into adiabatic density perturbations. We demonstrate that the spectra depend on the average decay rate of the inflaton & on the inflaton fluctuations. We then apply this new mechanism to string cosmologies & generalized Einstein theories and discuss the conditions under which scale-invariant spectra are possible.
FAST-PT: a novel algorithm to calculate convolution integrals in cosmological perturbation theory
McEwen, Joseph E.; Fang, Xiao; Hirata, Christopher M.; Blazek, Jonathan A.
2016-09-01
We present a novel algorithm, FAST-PT, for performing convolution or mode-coupling integrals that appear in nonlinear cosmological perturbation theory. The algorithm uses several properties of gravitational structure formation—the locality of the dark matter equations and the scale invariance of the problem—as well as Fast Fourier Transforms to describe the input power spectrum as a superposition of power laws. This yields extremely fast performance, enabling mode-coupling integral computations fast enough to embed in Monte Carlo Markov Chain parameter estimation. We describe the algorithm and demonstrate its application to calculating nonlinear corrections to the matter power spectrum, including one-loop standard perturbation theory and the renormalization group approach. We also describe our public code (in Python) to implement this algorithm. The code, along with a user manual and example implementations, is available at https://github.com/JoeMcEwen/FAST-PT.
FAST-PT: a novel algorithm to calculate convolution integrals in cosmological perturbation theory
McEwen, Joseph E; Hirata, Christopher M; Blazek, Jonathan A
2016-01-01
We present a novel algorithm, FAST-PT, for performing convolution or mode-coupling integrals that appear in nonlinear cosmological perturbation theory. The algorithm uses several properties of gravitational structure formation -- the locality of the dark matter equations and the scale invariance of the problem -- as well as Fast Fourier Transforms to describe the input power spectrum as a superposition of power laws. This yields extremely fast performance, enabling mode-coupling integral computations fast enough to embed in Monte Carlo Markov Chain parameter estimation. We describe the algorithm and demonstrate its application to calculating nonlinear corrections to the matter power spectrum, including one-loop standard perturbation theory and the renormalization group approach. We also describe our public code (in Python) to implement this algorithm, including the applications described here.
Disformal transformation of cosmological perturbations
Directory of Open Access Journals (Sweden)
Masato Minamitsuji
2014-10-01
Full Text Available We investigate the gauge-invariant cosmological perturbations in the gravity and matter frames in the general scalar–tensor theory where two frames are related by the disformal transformation. The gravity and matter frames are the extensions of the Einstein and Jordan frames in the scalar–tensor theory where two frames are related by the conformal transformation, respectively. First, it is shown that the curvature perturbation in the comoving gauge to the scalar field is disformally invariant as well as conformally invariant, which gives the predictions from the cosmological model where the scalar field is responsible both for inflation and cosmological perturbations. Second, in case that the disformally coupled matter sector also contributes to curvature perturbations, we derive the evolution equations of the curvature perturbation in the uniform matter energy density gauge from the energy (nonconservation in the matter sector, which are independent of the choice of the gravity sector. While in the matter frame the curvature perturbation in the uniform matter energy density gauge is conserved on superhorizon scales for the vanishing nonadiabatic pressure, in the gravity frame it is not conserved even if the nonadiabatic pressure vanishes. The formula relating two frames gives the amplitude of the curvature perturbation in the matter frame, once it is evaluated in the gravity frame.
Cosmological perturbations beyond linear order
CERN. Geneva
2013-01-01
Cosmological perturbation theory is the standard tool to understand the formation of the large scale structure in the Universe. However, its degree of applicability is limited by the growth of the amplitude of the matter perturbations with time. This problem can be tackled with by using N-body simulations or analytical techniques that go beyond the linear calculation. In my talk, I'll summarise some recent efforts in the latter that ameliorate the bad convergence of the standard perturbative expansion. The new techniques allow better analytical control on observables (as the matter power spectrum) over scales very relevant to understand the expansion history and formation of structure in the Universe.
Cosmological Perturbations and Quasi-Static Assumption in $f(R)$ Theories
Chiu, Mu-Chen; Shu, Chenggang; Tu, Hong
2015-01-01
$f(R)$ gravity is one of the simplest theories of modified gravity to explain the accelerated cosmic expansion. Although it is usually assumed that the quasi-Newtonian approach for cosmic perturbations is good enough to describe the evolution of large scale structure in $f(R)$ models, some studies have suggested that this method is not valid for all $f(R)$ models. Here, we show that in the matter-dominated era, the pressure and shear equations alone, which can be recast into four first-order equations to solve for cosmological perturbations exactly, are sufficient to solve for the Newtonian potential, $\\Psi$, and the curvature potential, $\\Phi$. Based on these two equations, we are able to clarify how the exact linear perturbations fit into different limits. We find that in the subhorizon limit, the so called quasi-static assumption plays no role in reducing the exact linear perturbations in any viable $f(R)$ gravity. Our findings also disagree with previous studies where we find little difference between our...
Cosmological Perturbations: Vorticity, Isocurvature and Magnetic Fields
Christopherson, Adam J
2014-01-01
In this paper I review some recent, interlinked, work undertaken using cosmological perturbation theory -- a powerful technique for modelling inhomogeneities in the Universe. The common theme which underpins these pieces of work is the presence of non-adiabatic pressure, or entropy, perturbations. After a brief introduction covering the standard techniques of describing inhomogeneities in both Newtonian and relativistic cosmology, I discuss the generation of vorticity. As in classical fluid mechanics, vorticity is not present in linearized perturbation theory (unless included as an initial condition). Allowing for entropy perturbations, and working to second order in perturbation theory, I show that vorticity is generated, even in the absence of vector perturbations, by purely scalar perturbations, the source term being quadratic in the gradients of first order energy density and isocurvature, or non-adiabatic pressure perturbations. This generalizes Crocco's theorem to a cosmological setting. I then introduc...
Perturbations in Massive Gravity Cosmology
Crisostomi, Marco; Pilo, Luigi
2012-01-01
We study cosmological perturbations for a ghost free massive gravity theory formulated with a dynamical extra metric that is needed to massive deform GR. In this formulation FRW background solutions fall in two branches. In the dynamics of perturbations around the first branch solutions, no extra degree of freedom with respect to GR ispresent at linearized level, likewise what is found in the Stuckelberg formulation of massive gravity where the extra metric isflat and non dynamical. In the first branch, perturbations are probably strongly coupled. On the contrary, for perturbations around the second branch solutions all expected degrees of freedom propagate. While tensor and vector perturbations of the physical metric that couples with matter follow closely the ones of GR, scalars develop an exponential Jeans-like instability on sub-horizon scales. On the other hand, around a de Sitter background there is no instability. We argue that one could get rid of the instabilities by introducing a mirror dark matter ...
BRST quantization of cosmological perturbations
Energy Technology Data Exchange (ETDEWEB)
Armendariz-Picon, Cristian [Physics Department, St. Lawrence University,Canton, NY 13617 (United States); Şengör, Gizem [Department of Physics, Syracuse University,Syracuse, NY 13244 (United States)
2016-11-08
BRST quantization is an elegant and powerful method to quantize theories with local symmetries. In this article we study the Hamiltonian BRST quantization of cosmological perturbations in a universe dominated by a scalar field, along with the closely related quantization method of Dirac. We describe how both formalisms apply to perturbations in a time-dependent background, and how expectation values of gauge-invariant operators can be calculated in the in-in formalism. Our analysis focuses mostly on the free theory. By appropriate canonical transformations we simplify and diagonalize the free Hamiltonian. BRST quantization in derivative gauges allows us to dramatically simplify the structure of the propagators, whereas Dirac quantization, which amounts to quantization in synchronous gauge, dispenses with the need to introduce ghosts and preserves the locality of the gauge-fixed action.
BRST Quantization of Cosmological Perturbations
Armendariz-Picon, Cristian
2016-01-01
BRST quantization is an elegant and powerful method to quantize theories with local symmetries. In this article we study the Hamiltonian BRST quantization of cosmological perturbations in a universe dominated by a scalar field, along with the closely related quantization method of Dirac. We describe how both formalisms apply to the perturbations in a time-dependent background, and how expectation values of gauge-invariant operators can be calculated in the in-in formalism. Our analysis focuses mostly on the free theory. By appropriate canonical transformations we simplify and diagonalize the free Hamiltonian. BRST quantization in derivative gauges allows us to dramatically simplify the structure of the propagators, whereas quantization in synchronous gauge, which amounts to Dirac quantization, dispenses with the need to introduce ghosts and preserves the locality of the gauge-fixed action.
Nakamura, Kouji
2008-01-01
Some formulae for the perturbations of the matter fields are summarized within the framework of the second-order gauge-invariant cosmological perturbation theory in a four dimensional homogeneous isotropic universe, which is developed in the papers [K. Nakamura, Prog. Theor. Phys. {\\bf 117} (2005), 17.]. We derive the formulae for the perturbations of the energy momentum tensors and equations of motion in the cases of a perfect fluid, an imperfect fluid, and a signle scalar field, and show that all equations are derived in terms of gauge-invariant variables without any gauge fixing.
Density Perturbation Growth in Teleparallel Cosmology
Geng, Chao-Qiang
2012-01-01
We study the cosmological perturbations in teleparallel dark energy models in which there is a dynamical scalar field with a non-minimal coupling to gravity. We find that the propagating degrees of freedom are the same as in quintessence cosmology despite that variables of the perturbed vierbein field are greater than those in metric theories. The resulting growth evolution shows that gravitational interactions are enhanced during the unique tracker evolution of teleparallel dark energy models.
Cosmological perturbations in theories with non-minimal coupling between curvature and matter
Bertolami, Orfeu; Páramos, Jorge
2013-01-01
In this work, one examines how the presence of a non-minimal coupling between the spacetime curvature and matter affects the evolution of cosmological perturbations around a homogeneous and isotropic Universe and hence the formation of large-scale structure. This framework places constraints on the terms which arise due to the coupling with matter and, in particular, on the modification in the growth of matter density perturbations. One obtains approximate analytical solutions for the evolution of matter overdensities during the matter dominated era and shows that these favor the presence of a coupling function that is compatible with the late-time cosmic acceleration.
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...
Density perturbation growth in teleparallel cosmology
Energy Technology Data Exchange (ETDEWEB)
Geng, Chao-Qiang [College of Mathematics and Physics, Chongqing University of Posts and Telecommunications, Chongqing, 400065 (China); Wu, Yi-Peng, E-mail: geng@phys.nthu.edu.tw, E-mail: s9822508@m98.nthu.edu.tw [Department of Physics, National Tsing Hua University, Hsinchu, 300 Taiwan (China)
2013-04-01
We study the cosmological perturbations in teleparallel dark energy models in which there is a dynamical scalar field with a non-minimal coupling to gravity. We find that the propagating degrees of freedom are the same as in quintessence cosmology despite that variables of the perturbed vierbein field are greater than those in metric theories. We numerically show some evident discrepancy from general relativity in the evolutions of the perturbations on all scales of the universe. We also demonstrate that the gravitational interactions are enhanced during the unique tracker evolutions in these models.
Back Reaction of Cosmological Perturbations
Brandenberger, R H
2000-01-01
The presence of cosmological perturbations affects the background metric and matter configuration in which the perturbations propagate. This effect, studied a long time ago for gravitational waves, also is operational for scalar gravitational fluctuations, inhomogeneities which are believed to be more important in inflationary cosmology. The back-reaction of fluctuations can be described by an effective energy-momentum tensor. The issue of coordinate invariance makes the analysis more complicated for scalar fluctuations than for gravitational waves. We show that the back-reaction of fluctuations can be described in a diffeomorphism-invariant way. In an inflationary cosmology, the back-reaction is dominated by infrared modes. We show that these modes give a contribution to the effective energy-momentum tensor of the form of a negative cosmological constant whose absolute value grows in time. We speculate that this may lead to a self-regulating dynamical relaxation mechanism for the cosmological constant. This ...
Initial conditions for cosmological perturbations
Ashtekar, Abhay
2016-01-01
Penrose proposed that the big bang singularity should be constrained by requiring that the Weyl curvature vanishes there. The idea behind this past hypothesis is attractive because it constrains the initial conditions for the universe in geometric terms and is not confined to a specific early universe paradigm. However, the precise statement of Penrose's hypothesis is tied to classical space-times and furthermore restricts only the gravitational degrees of freedom. These are encapsulated only in the tensor modes of the commonly used cosmological perturbation theory. Drawing inspiration from the underlying idea, we propose a quantum generalization of Penrose's hypothesis using the Planck regime in place of the big bang, and simultaneously incorporating tensor as well as scalar modes. Initial conditions selected by this generalization constrain the universe to be as homogeneous and isotropic in the Planck regime \\emph{as permitted by the Heisenberg uncertainty relations}.
Brane World Cosmological Perturbations
Casali, A G; Wang, B; Casali, Adenauer G.; Abdalla, Elcio; Wang, Bin
2004-01-01
We consider a brane world and its gravitational linear perturbations. We present a general solution of the perturbations in the bulk and find the complete perturbed junction conditions for generic brane dynamics. We also prove that (spin 2) gravitational waves in the great majority of cases can only arise in connection with a non-vanishing anisotropic stress. This has far reaching consequences for inflation in the brane world. Moreover, contrary to the case of the radion, perturbations are stable.
Cosmological Perturbations in Extended Massive Gravity
Gumrukcuoglu, A Emir; Lin, Chunshan; Mukohyama, Shinji; Trodden, Mark
2013-01-01
We study cosmological perturbations around self-accelerating solutions to two extensions of nonlinear massive gravity: the quasi-dilaton theory and the mass-varying theory. We examine stability of the cosmological solutions, and the extent to which the vanishing of the kinetic terms for scalar and vector perturbations of self-accelerating solutions in massive gravity is generic when the theory is extended. We find that these kinetic terms are in general non-vanishing in both extensions, though there are constraints on the parameters and background evolution from demanding that they have the correct sign. In particular, the self-accelerating solutions of the quasi-dilaton theory are always unstable to scalar perturbations with wavelength shorter than the Hubble length.
Frame independent cosmological perturbations
Energy Technology Data Exchange (ETDEWEB)
Prokopec, Tomislav; Weenink, Jan, E-mail: t.prokopec@uu.nl, E-mail: j.g.weenink@uu.nl [Institute for Theoretical Physics and Spinoza Institute, Utrecht University, Leuvenlaan 4, 3585 CE Utrecht (Netherlands)
2013-09-01
We compute the third order gauge invariant action for scalar-graviton interactions in the Jordan frame. We demonstrate that the gauge invariant action for scalar and tensor perturbations on one physical hypersurface only differs from that on another physical hypersurface via terms proportional to the equation of motion and boundary terms, such that the evolution of non-Gaussianity may be called unique. Moreover, we demonstrate that the gauge invariant curvature perturbation and graviton on uniform field hypersurfaces in the Jordan frame are equal to their counterparts in the Einstein frame. These frame independent perturbations are therefore particularly useful in relating results in different frames at the perturbative level. On the other hand, the field perturbation and graviton on uniform curvature hypersurfaces in the Jordan and Einstein frame are non-linearly related, as are their corresponding actions and n-point functions.
Scalar-Fluid theories: cosmological perturbations and large-scale structure
Koivisto, Tomi S; Tamanini, Nicola
2015-01-01
Recently a new Lagrangian framework was introduced to describe interactions between scalar fields and relativistic perfect fluids. This allows two consistent generalizations of coupled quintessence models: non-vanishing pressures and a new type of derivative interaction. Here the implications of these to the formation of cosmological large-scale structure are uncovered at the linear order. The full perturbation equations in the two cases are derived in a unified formalism and their Newtonian, quasi-static limit is studied analytically. Requiring the absence of an effective sound speed for the coupled dark matter fluid restricts the Lagrangian to be a linear function of the matter number density. This still leaves new potentially viable classes of both algebraically and derivatively interacting models wherein the coupling may impact the background expansion dynamics and imprint signatures into the large-scale structure.
Note on the semiclassicality of cosmological perturbations
Donà, Pietro; Marcianò, Antonino
2016-12-01
Moving from the consideration that matter fields must be treated in terms of their fundamental quantum counterparts, we show straightforward arguments, within the framework of ordinary quantum mechanics and quantum field theory, in order to convince readers that cosmological perturbations must be addressed in term of the semiclassical limit of the expectation value of quantum fields. We first take into account cosmological perturbations originated by a quantum scalar field, and then extend our treatment in order to account for the expectation values of bilinears of Dirac fermion fields. The latter can indeed transform as scalar quantities under diffeomorphisms, as well as all the other bilinear of the Dirac fields that belong to the Clifford algebra. This is the first of a series of works that is intended to prove that cosmological quantum perturbations can actually be accounted for in terms of Dirac fermion fields, which must be treated as fundamental quantum objects, and their dynamics.
Causal compensated perturbations in cosmology
Energy Technology Data Exchange (ETDEWEB)
Veeraraghavan, S.; Stebbins, A. (Harvard-Smithsonian Center for Astrophysics, Cambridge, MA (USA) California Univ., Berkeley (USA) Canadian Institute for Theoretical Astrophysics, Toronto (Canada))
1990-12-01
A theoretical framework is developed to calculate linear perturbations in the gravitational and matter fields which arise causally in response to the presence of stiff matter sources in a FRW cosmology. It is shown that, in order to satisfy energy and momentum conservation, the gravitational fields of the source must be compensated by perturbations in the matter and gravitational fields, and the role of such compensation in containing the initial inhomogeneities in their subsequent evolution is discussed. A complete formal solution is derived in terms of Green functions for the perturbations produced by an arbitrary source in a flat universe containing cold dark matter. Approximate Green function solutions are derived for the late-time density perturbations and late-time gravitational waves in a universe containing a radiation fluid. A cosmological energy-momentum pseudotensor is defined to clarify the nature of energy and momentum conservation in the expanding universe. 55 refs.
Junction conditions of cosmological perturbations
Tomita, K
2004-01-01
The behavior of perturbations is studied in cosmological models which consist of two different homogeneous regions connected in a spherical shell boundary. The junction conditions for the metric perturbations and the displacements of the shell boundary are analyzed and the surface densities of the perturbed energy and momentum in the shell are derived, using Mukohyama's gauge-invariant formalism and the Israel discontinuity condition. In both homogeneous regions the perturbations of scalar, vector and tensor types are expanded using the 3-dimensional harmonic functions, but the model coupling among them is caused in the shell by the inhomogeneity. By treating the perturbations with odd and even parities separately, it is found, however, that we can have consistent displacements and surface densities for given metric parturbations
Cosmological perturbations without inflation
Melia, Fulvio
2017-01-01
A particularly attractive feature of inflation is that quantum fluctuations in the inflaton field may have seeded inhomogeneities in the cosmic microwave background (CMB) and the formation of large-scale structure. In this paper, we demonstrate that a scalar field with zero active mass, i.e. with an equation of state ρ +3p=0 , where ρ and p are its energy density and pressure, respectively, could also have produced an essentially scale-free fluctuation spectrum, though without inflation. This alternative mechanism is based on the Hollands–Wald concept of a minimum wavelength for the emergence of quantum fluctuations into the semi-classical universe. A cosmology with zero active mass does not have a horizon problem, so it does not need inflation to solve this particular (non) issue. In this picture, the {{1}\\circ}{ {--}}{{10}\\circ} fluctuations in the CMB correspond almost exactly to the Planck length at the Planck time, firmly supporting the view that CMB observations may already be probing trans-Planckian physics.
Cosmological Perturbations without Inflation
Melia, Fulvio
2016-01-01
A particularly attractive feature of inflation is that quantum fluctuations in the inflaton field may have seeded inhomogeneities in the cosmic microwave background (CMB) and the formation of large-scale structure. In this paper, we demonstrate that a scalar field with zero active mass, i.e., with an equation of state rho+3p=0, where rho and p are its energy density and pressure, respectively, could also have produced an essentially scale-free fluctuation spectrum, though without inflation. This alternative mechanism is based on the Hollands-Wald concept of a minimum wavelength for the emergence of quantum fluctuations into the semi-classical universe. A cosmology with zero active mass does not have a horizon problem, so it does not need inflation to solve this particular (non) issue. In this picture, the 1-10 degree fluctuations in the CMB correspond almost exactly to the Planck length at the time these modes were produced, firmly supporting the view that CMB observations may already be probing trans-Plancki...
Fang, Xiao; Blazek, Jonathan A.; McEwen, Joseph E.; Hirata, Christopher M.
2017-02-01
Cosmological perturbation theory is a powerful tool to predict the statistics of large-scale structure in the weakly non-linear regime, but even at 1-loop order it results in computationally expensive mode-coupling integrals. Here we present a fast algorithm for computing 1-loop power spectra of quantities that depend on the observer's orientation, thereby generalizing the FAST-PT framework (McEwen et al., 2016) that was originally developed for scalars such as the matter density. This algorithm works for an arbitrary input power spectrum and substantially reduces the time required for numerical evaluation. We apply the algorithm to four examples: intrinsic alignments of galaxies in the tidal torque model; the Ostriker-Vishniac effect; the secondary CMB polarization due to baryon flows; and the 1-loop matter power spectrum in redshift space. Code implementing this algorithm and these applications is publicly available at https://github.com/JoeMcEwen/FAST-PT.
Fang, Xiao; McEwen, Joseph E; Hirata, Christopher M
2016-01-01
Cosmological perturbation theory is a powerful tool to predict the statistics of large-scale structure in the weakly non-linear regime, but even at 1-loop order it results in computationally expensive mode-coupling integrals. Here we present a fast algorithm for computing 1-loop power spectra of quantities that depend on the observer's orientation, thereby generalizing the FAST-PT framework (McEwen et al., 2016) that was originally developed for scalars such as the matter density. This algorithm works for an arbitrary input power spectrum and substantially reduces the time required for numerical evaluation. We apply the algorithm to four examples: intrinsic alignments of galaxies in the tidal torque model; the Ostriker-Vishniac effect; the secondary CMB polarization due to baryon flows; and the 1-loop matter power spectrum in redshift space. Code implementing this algorithm and these applications is publicly available at https://github.com/JoeMcEwen/FAST-PT.
Cosmological Perturbation Theory as a Tool for Estimating Box-Scale Effects in N-body Simulations
Orban, Chris
2013-01-01
In performing cosmological N-body simulations, it is widely appreciated that the growth of structure on the largest scales within a simulation box will be inhibited by the finite size of the simulation volume. Following ideas set forth in Seto 1999, this paper shows that standard (a.k.a. 1-loop) cosmological perturbation theory (SPT) can be used to predict at an order-of-magnitude level the deleterious effect of the box scale on the power spectrum of density fluctuations in simulation volumes. Alternatively, this approach can be used to quickly estimate post facto the effect of the box scale on power spectrum results from existing simulations. In this way SPT can help determine whether larger box sizes or other more-sophisticated methods are needed to achieve a particular level of precision for a given application (e.g. simulations to measure the non-linear evolution of baryon acoustic oscillations). I focus on SPT in this note and show that its predictions are order-of-magnitude accurate compared to N-body s...
Noncommutative Fluid and Cosmological Perturbations
Das, Praloy
2016-01-01
In the present paper we have developed a Non-Commutative (NC) generalization of perfect fluid model from first principles, in a Hamiltonian framework. The noncommutativity is introduced at the Lagrangian (particle) coordinate space brackets and the induced NC fluid bracket algebra for the Eulerian (fluid) field variables is derived. Together with a Hamiltonian this NC algebra generates the generalized fluid dynamics that satisfies exact local conservation laws for mass and energy thereby maintaining mass and energy conservation. However, nontrivial NC correction terms appear in charge and energy fluxes. Other non-relativistic spacetime symmetries of the NC fluid are also discussed in detail. This constitutes the NC fluid dynamics and kinematics. In the second part we construct an extension of Friedmann-Robertson-Walker (FRW) cosmological model based on the NC fluid dynamics presented here. We outline the way in which NC effects generate cosmological perturbations bringing in anisotropy and inhomogeneity in th...
FRW Cosmological Perturbations in Massive Bigravity
Comelli, D; Pilo, L
2014-01-01
Cosmological perturbations of FRW solutions in ghost free massive bigravity, including also a second matter sector, are studied in detail. At early time, we find that sub horizon exponential instabilities are unavoidable and they lead to a premature departure from the perturbative regime of cosmological perturbations.
Viable cosmology in bimetric theory
De Felice, Antonio; Mukohyama, Shinji; Tanahashi, Norihiro; Tanaka, Takahiro
2014-01-01
We study cosmological perturbations in bimetric theory with two fluids each of which is coupled to one of the two metrics. Focusing on a healthy branch of background solutions, we clarify the stability of the cosmological perturbations. For this purpose, we extend the condition for the absence of the so-called Higuchi ghost, and show that the condition is guaranteed to be satisfied on the healthy branch. We also calculate the squared propagation speeds of perturbations and derive the conditions for the absence of the gradient instability. To avoid the gradient instability, we find that the model parameters are weakly constrained.
Multi-field inflation and cosmological perturbations
Gong, Jinn-Ouk
2016-01-01
We provide a concise review on multi-field inflation and cosmological perturbations. We discuss convenient and physically meaningful bases in terms of which perturbations can be systematically studied. We give formal accounts on the gauge fixing conditions and present the perturbation action in two gauges. We also briefly review non-linear perturbations.
Inflationary Perturbations and Precision Cosmology
Habib, S; Heitmann, K; Jungman, G; Habib, Salman; Heinen, Andreas; Heitmann, Katrin; Jungman, Gerard
2005-01-01
Inflationary cosmology provides a natural mechanism for the generation of primordial perturbations which seed the formation of observed cosmic structure and lead to specific signals of anisotropy in the cosmic microwave background radiation. In order to test the broad inflationary paradigm as well as particular models against precision observations, it is crucial to be able to make accurate predictions for the power spectrum of both scalar and tensor fluctuations. We present detailed calculations of these quantities utilizing direct numerical approaches as well as error-controlled uniform approximations, comparing with the (uncontrolled) traditional slow-roll approach. A simple extension of the leading-order uniform approximation yields results for the power spectra amplitudes, the spectral indices, and the running of spectral indices, with accuracy of the order of 0.1% - approximately the same level at which the transfer functions are known. Several representative examples are used to demonstrate these resul...
Cosmological perturbations in massive gravity with doubly coupled matter
Gümrükçüoğlu, A Emir; Mukohyama, Shinji
2014-01-01
We investigate the cosmological perturbations around FLRW solutions to non- linear massive gravity with a new effective coupling to matter proposed recently. Unlike the case with minimal matter coupling, all five degrees of freedom in the gravity sector propagate on generic self-accelerating FLRW backgrounds. We study the stability of the cosmological solutions and put constraints on the parameters of the theory by demanding the correct sign for the kinetic terms for scalar, vector and tensor perturbations.
Cosmological perturbations in massive gravity with doubly coupled matter
Gümrükçüoğlu, A. Emir; Heisenberg, Lavinia; Mukohyama, Shinji
2015-02-01
We investigate the cosmological perturbations around FLRW solutions to non- linear massive gravity with a new effective coupling to matter proposed recently. Unlike the case with minimal matter coupling, all five degrees of freedom in the gravity sector propagate on generic self-accelerating FLRW backgrounds. We study the stability of the cosmological solutions and put constraints on the parameters of the theory by demanding the correct sign for the kinetic terms for scalar, vector and tensor perturbations.
Buchert, Thomas
2012-01-01
In this first paper we present a Lagrangian framework for the description of structure formation in general relativity, restricting attention to irrotational dust matter. As an application we present a self-contained derivation of a general-relativistic analogue of Zel'dovich's approximation for the description of structure formation in cosmology, and compare it with previous suggestions in the literature. This approximation is then investigated: paraphrasing the derivation in the Newtonian framework we provide general-relativistic analogues of the basic system of equations for a single dynamical field variable and recall the first-order perturbation solution of these equations. We then define a general-relativistic analogue of Zel'dovich's approximation and investigate consequences by functionally evaluating relevant variables. We so obtain a possibly powerful model that, although constructed through extrapolation of a perturbative solution, can be used to address non-perturbatively, e.g. problems of structu...
Cosmology Theory and Observations
Dolgov, A D
1998-01-01
The comparison of the Standard Cosmological Model (SCM) with astronomical observations, i.e. theory versus experiment, and with the Minimal Standard Model (MSM) in particle physics, i.e. theory versus theory, is discussed. The main issue of this talk is whether cosmology indicates new physics beyond the standard $SU(3)\\times SU(2)\\times U(1)$ model with minimal particle content. The answer to this question is strongly and definitely "YES". New, yet unknown, physics exists and cosmology presents very weighty arguments in its favor.
The Effective Field Theory of nonsingular cosmology
Cai, Yong; Li, Hai-Guang; Qiu, Taotao; Piao, Yun-Song
2016-01-01
In this paper, we explore the nonsingular cosmology within the framework of the Effective Field Theory(EFT) of cosmological perturbations. Due to the recently proved no-go theorem, any nonsingular cosmological models based on the cubic Galileon suffer from pathologies. We show how the EFT could help us clarify the origin of the no-go theorem, and offer us solutions to break the no-go. Particularly, we point out that the gradient instability can be removed by using some spatial derivative operators in EFT. Based on the EFT description, we obtain a realistic healthy nonsingular cosmological model, and show the perturbation spectrum can be consistent with the observations.
Newtonian Limits of the Relativistic Cosmological Perturbations
Hwang, J
1997-01-01
Relativistic cosmological perturbation analyses can be made based on several different fundamental gauge conditions. In the pressureless limit the variables in certain gauge conditions show the correct Newtonian behaviors. We consider the general curvature and the cosmological constant in the background medium. The perturbed density in the comoving gauge, and the perturbed velocity and the perturbed potential in the zero-shear gauge show the same behavior as the Newtonian ones in a general scale. Far inside horizon, except for the uniform-density gauge, density perturbations in all the fundamental gauge conditions show the correct Newtonian behavior. In this paper we elaborate these Newtonian correspondences. We also present the relativistic results considering general pressures in the background and perturbation.
Cosmological perturbations in a noncommutative braneworld inflation
Institute of Scientific and Technical Information of China (English)
Kourosh Nozari; Siamak Akhshabi
2012-01-01
We use the smeared,coherent state picture of noncommutativity to study evolution of perturbations in a noncommutative braneworld scenario.Within the standard procedure of studying braneworld cosmological perturbations,we study the evolution of the Bardeen metric potential and curvature perturbations in this model.We show that in this setup,the early stage of the universe's evolution has a transient phantom evolution with imaginary effective sound speed.
Hamilton-Jacobi formalism of tachyon inflation and cosmological perturbations
Directory of Open Access Journals (Sweden)
LIU Daojun
2014-08-01
Full Text Available We study the cosmological inflation models driven by the rolling tachyon field which has a Born-Infeld-type action.We drive the Hamilton-Jacobi equation for the cosmological dynamics of tachyon inflation and the mode equations for the scalar and tensor perturbations of tachyon field and spacetime, then a solution under the slow-roll condition is given. In the end,a realistic model from string theory is discussed.
Metric perturbations in Einstein-Cartan Cosmology
Garcia de Andrade, L C
2002-01-01
Metric perturbations the stability of solution of Einstein-Cartan cosmology (ECC) are given. The first addresses the stability of solutions of Einstein-Cartan (EC) cosmological model against Einstein static universe background. In this solution we show that the metric is stable against first-order perturbations and correspond to acoustic oscillations. The second example deals with the stability of de Sitter metric also against first-order perturbations. Torsion and shear are also computed in these cases. The resultant perturbed anisotropic spacetime with torsion is only de Sitter along one direction or is unperturbed along one direction and perturbed against the other two. Cartan torsion contributes to the frequency of oscillations in the model. Therefore gravitational waves could be triggered by the spin-torsion scalar density .
Axions : Theory and Cosmological Role
Kawasaki, Masahiro; Nakayama, Kazunori
2013-01-01
We review recent developments on axion cosmology. Topics include : axion cold dark matter, axions from topological defects, axion isocurvature perturbation and its non-Gaussianity and axino/saxion cosmology in supersymmetric axion model.
Energy Technology Data Exchange (ETDEWEB)
De Felice, Antonio, E-mail: antoniod@nu.ac.th [Department of Physics, Faculty of Science, Tokyo University of Science, 1-3, Kagurazaka, Shinjuku-ku, Tokyo 162-8601 (Japan); TPTP and NEP, The Institute for Fundamental Study, Naresuan University, Phitsanulok, 65000 (Thailand); Thailand Center of Excellence in Physics, Ministry of Education, Bangkok 10400 (Thailand); Kobayashi, Tsutomu [Hakubi Center, Kyoto University, Kyoto 606-8302 (Japan); Department of Physics, Kyoto University, Kyoto 606-8502 (Japan); Tsujikawa, Shinji [Department of Physics, Faculty of Science, Tokyo University of Science, 1-3, Kagurazaka, Shinjuku-ku, Tokyo 162-8601 (Japan)
2011-12-06
In the Horndeski's most general scalar-tensor theories the equations of scalar density perturbations are derived in the presence of non-relativistic matter minimally coupled to gravity. Under a quasi-static approximation on sub-horizon scales we obtain the effective gravitational coupling G{sub eff} associated with the growth rate of matter perturbations as well as the effective gravitational potential {Phi}{sub eff} relevant to the deviation of light rays. We then apply our formulas to a number of modified gravitational models of dark energy - such as those based on f(R) theories, Brans-Dicke theories, kinetic gravity braidings, covariant Galileons, and field derivative couplings with the Einstein tensor. Our results are useful to test the large-distance modification of gravity from the future high-precision observations of large-scale structure, weak lensing, and cosmic microwave background.
De Felice, Antonio; Tsujikawa, Shinji
2011-01-01
In the Horndeski's most general scalar-tensor theories the equations of scalar density perturbations are derived in the presence of non-relativistic matter minimally coupled to gravity. Under a quasi-static approximation on sub-horizon scales we obtain the effective gravitational coupling $G_{eff}$ associated with the growth rate of matter perturbations as well as the effective gravitational potential $\\Phi_{eff}$ relevant to the deviation of light rays. We then apply our formulas to a number of modified gravitational models of dark energy--such as those based on f(R) theories, Brans-Dicke theories, kinetic gravity braidings, covariant Galileons, and field derivative couplings with the Einstein tensor. Our results are useful to test the large-distance modification of gravity from the future high-precision observations of large-scale structure, weak lensing, and cosmic microwave background.
Cosmological perturbations from an inhomogeneous phase transition
Energy Technology Data Exchange (ETDEWEB)
Matsuda, Tomohiro, E-mail: matsuda@sit.ac.j [Laboratory of Physics, Saitama Institute of Technology, Fusaiji, Okabe-machi, Saitama 369-0293 (Japan)
2009-07-21
A mechanism for generating metric perturbations in inflationary models is considered. Long-wavelength inhomogeneities of light scalar fields in a decoupled sector may give rise to superhorizon fluctuations of couplings and masses in the low-energy effective action. Cosmological phase transitions may then occur that are not simultaneous in space, but occur with time lags in different Hubble patches that arise from the long-wavelength inhomogeneities. Here an interesting model in which cosmological perturbations may be created at the electroweak phase transition is considered. The results show that phase transitions may be a generic source of non-Gaussianity.
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.
Cosmological perturbations in mimetic matter model
Matsumoto, Jiro; Sushkov, Sergey V
2015-01-01
We investigate the cosmological evolution of mimetic matter model with arbitrary scalar potential. The cosmological reconstruction is explicitly done for different choices of potential. The cases that mimetic matter model shows the evolution as Cold Dark Matter(CDM), wCDM model, dark matter and dark energy with dynamical $Om(z)$ or phantom dark energy with phantom-non-phantom crossing are presented in detail. The cosmological perturbations for such evolution are studied in mimetic matter model. For instance, the evolution behavior of the matter density contrast which is different from usual one, i.e. $\\ddot \\delta + 2 H \\dot \\delta - \\kappa ^2 \\rho \\delta /2 = 0$ is investigated. The possibility of peculiar evolution of $\\delta$ in the model under consideration is shown. Special attention is paid to the behavior of matter density contrast near to future singularity where decay of perturbations may occur much earlier the singularity.
Dynamics of Cosmological Perturbations in Position Space
Bashinsky, S V; Bashinsky, Sergei; Bertschinger, Edmund
2002-01-01
We show that the linear dynamics of cosmological perturbations can be described by coupled wave equations, allowing their efficient numerical and, in certain limits, analytical integration directly in position space. The linear evolution of any perturbation can then be analyzed with the Green's function method. Prior to hydrogen recombination, assuming tight coupling between photons and baryons, neglecting neutrino perturbations, and taking isentropic (adiabatic) initial conditions, the obtained Green's functions for all metric, density, and velocity perturbations vanish beyond the acoustic horizon. At the acoustic wavefronts, a positive gravitational potential perturbation produces narrow photon-baryon density spikes, which provide one of the major contributions to the observed cosmic microwave background radiation anisotropy on all scales. The gravitational interaction between cold dark matter and baryons causes a dip in the observed temperature of the radiation at the center of the initial perturbation. We...
Classical and Quantum Theory of Perturbations in Inflationary Universe Models
Brandenberger, R H; Mukhanov, V
1993-01-01
A brief introduction to the gauge invariant classical and quantum theory of cosmological perturbations is given. The formalism is applied to inflationary Universe models and yields a consistent and unified description of the generation and evolution of fluctuations. A general formula for the amplitude of cosmological perturbations in inflationary cosmology is derived.
Cosmological perturbations through a simple bounce
Allen, L E
2004-01-01
We present a detailed study of a simple scalar field model that yields non-singular cosmological solutions. We study both the qualitative dynamics of the homogeneous and isotropic background and the evolution of inhomogeneous linear perturbations. We calculate the spectrum of perturbations generated on super-Hubble scales during the collapse phase from initial vacuum fluctuations on small scales and then evolve these numerically through the bounce. We show there is a gauge that remains well-defined throughout the bounce, even though other commonly used gauges break down. We show that the comoving curvature perturbation calculated during the collapse phase provides a good estimate of the resulting large scale adiabatic perturbation in the expanding phase while the Bardeen metric potential is dominated by what becomes a decaying mode after the bounce. We show that a power-law collapse phase with scale factor proportional $(-t)^{2/3}$ can yield a scale-invariant spectrum of adiabatic scalar perturbations in the ...
Automated Lattice Perturbation Theory
Energy Technology Data Exchange (ETDEWEB)
Monahan, Christopher
2014-11-01
I review recent developments in automated lattice perturbation theory. Starting with an overview of lattice perturbation theory, I focus on the three automation packages currently "on the market": HiPPy/HPsrc, Pastor and PhySyCAl. I highlight some recent applications of these methods, particularly in B physics. In the final section I briefly discuss the related, but distinct, approach of numerical stochastic perturbation theory.
Non-Gaussianity vs. non-linearity of cosmological perturbations
Verde, L
2001-01-01
Following the discovery of the CMB, the hot big-bang model has become the standard cosmological model. In this theory, small primordial fluctuations are subsequently amplified by gravity to form the large-scale structure seen today. Different theories for unified models of particle physics, lead to different predictions for the statistical properties of the primordial fluctuations, that can be divided in two classes: gaussian and non-gaussian. Convincing evidence against or for gaussian initial conditions would rule out many scenarios and point us towards a physical theory for the origin of structures. The statistical distribution of cosmological perturbations, as we observe them, can deviate from the gaussian distribution in several different ways. Even if perturbations start off gaussian, non-linear gravitational evolution can introduce non-gaussian features. Additionally, our knowledge of the Universe comes principally from the study of luminous material such as galaxies, but these might not be faithful tr...
Generalized Supersymmetric Perturbation Theory
Institute of Scientific and Technical Information of China (English)
B. G(o)n(ǖ)l
2004-01-01
@@ Using the basic ingredient of supersymmetry, a simple alternative approach is developed to perturbation theory in one-dimensional non-relativistic quantum mechanics. The formulae for the energy shifts and wavefunctions do not involve tedious calculations which appear in the available perturbation theories. The model applicable in the same form to both the ground state and excited bound states, unlike the recently introduced supersymmetric perturbation technique which, together with other approaches based on logarithmic perturbation theory, are involved within the more general framework of the present formalism.
Adiabatic perturbations in coupled scalar field cosmologies
Beyer, Joschka
2014-01-01
We present a comprehensive and gauge invariant treatment of perturbations around cosmological scaling solutions for two canonical scalar fields coupled through a common potential in the early universe, in the presence of neutrinos, photons and baryons, but excluding cold dark matter. This setup is relevant for analyzing cosmic perturbations in scalar field models of dark matter with a coupling to a quintessence field. We put strong restrictions on the shape of the common potential and adopt a matrix-eigensystem approach to determine the dominant perturbations modes in such models. Similar to recent results in scenarios where standard cold dark matter couples to quintessence, we show that the stability of the adiabatic perturbation mode can be an issue for this class of scalar field dark matter models, but only for specific choices of the common potential. For an exponential coupling potential, a rather common shape arising naturally in many instances, this problem can be avoided. We explicitly calculate the d...
Perturbative Topological Field Theory
Dijkgraaf, Robbert
We give a review of the application of perturbative techniques to topological quantum field theories, in particular three-dimensional Chern-Simons-Witten theory and its various generalizations. To this end we give an introduction to graph homology and homotopy algebras and the work of Vassiliev and Kontsevich on perturbative knot invariants.
Flowing with Time: a New Approach to Nonlinear Cosmological Perturbations
Pietroni, Massimo
2008-01-01
Nonlinear effects are crucial in order to compute the cosmological matter power spectrum to the accuracy required by future generation surveys. Here, a new approach is presented, in which the power spectrum and the bispectrum are obtained -at any redshift and for any momentum scale- by integrating a coupled system of differential equations. The solution of the equations corresponds, in perturbation theory, to the summation of an infinite class of corrections. Compared to other resummation frameworks, the scheme discussed here is particularly suited to cosmologies other than LambdaCDM, such as those based on modifications of gravity and those containing massive neutrinos. As a first application, we compute the Baryonic Acoustic Oscillation feature of the power spectrum, and compare the results with perturbation theory, the halo model, and N-body simulations. The density-velocity and velocity-velocity power spectra are also computed, showing that they are much less contaminated by nonlinearities than the densit...
Cosmological Perturbations with Multiple Fluids and Fields
Hwang, J
2002-01-01
We consider the evolution of perturbed cosmological spacetime with multiple fluid and field system in Einstein gravity. Equations are presented in gauge-ready forms, and are presented using the adiabatic and isocurvature perturbation variables. We present equations in the general background with $K$ and $\\Lambda$. We also clarify the conditions for conserved adiabatic and isocurvature perturbations in the large-scale limit. One interesting conclusion is that, for ideal fluid system, although the isocurvature modes can seed the adiabatic mode in the large-scale limit, the isocurvature modes decouple from the adiabatic one which is not the case for the field system. Useful sets of equations readily applicable to the quintessence models and the warm inflation scenario can be found in this work. An application to the scaling regime with an exponential field potential is made in the Appendix.
Density matrix perturbation theory.
Niklasson, Anders M N; Challacombe, Matt
2004-05-14
An orbital-free quantum perturbation theory is proposed. It gives the response of the density matrix upon variation of the Hamiltonian by quadratically convergent recursions based on perturbed projections. The technique allows treatment of embedded quantum subsystems with a computational cost scaling linearly with the size of the perturbed region, O(N(pert.)), and as O(1) with the total system size. The method allows efficient high order perturbation expansions, as demonstrated with an example involving a 10th order expansion. Density matrix analogs of Wigner's 2n+1 rule are also presented.
Double Field Theory Inspired Cosmology
Wu, Houwen
2014-01-01
Double field theory proposes a generalized spacetime action possessing manifest T-duality on the level of component fields. We calculate the cosmological solutions of double field theory with vanishing Kalb-Ramond field. It turns out that double field theory provides a more consistent way to construct cosmological solutions than the standard string cosmology. We find two sets of solutions in double field theory cosmology, respecting or violating the strong (weak) constraint. Both sets of solutions naturally contain the pre- and post-big bang evolutions in one single line element. This novel feature opens a window for possible resolution of the cosmic amnesia. We also demonstrate that the scale factor duality in the standard string cosmology is nothing but the T-duality in double field theory. The scale dual dilatons in the standard string cosmology is simply the usual diffeomorphic scalar dilaton $\\phi$ and dual diffeomorphic scalar dilaton $\\tilde\\phi$ in double field theory. Furthermore, we identify the "sh...
Brane Cosmology and Higher Derivative Theory
Naboulsi, R
2003-01-01
In this paper, we have considered a cosmological model with density perturbation and decreasing cosmological constant of the form Lambda = 3beta (frac{dot{R}^2}{R^2}) + delta (frac{ddot{R}}{R}), beta, gamma = const. Inspired from brane cosmology, we supposed the presence of exotic density related to the cosmological constant by the formula 2Lambda = 3m^2, where m is a constant having the dimension of Hubble constant. Their effects on the evolution of the spatially, flat FRW cosmoligical model of the Universe is analyzed in the framework of higher derivative theory. The Universe is found to be accelerating with time with no initial singularity for beta < frac{1}{3} and the cosmological constant is found to decrease as t^{-2} but smaller than 3H^2. The presence of interacting scalar field is also discussed.
Scalar cosmological perturbations from inflationary black holes
Energy Technology Data Exchange (ETDEWEB)
Prokopec, Tomislav; Reska, Paul, E-mail: t.prokopec@uu.nl, E-mail: p.m.reska@uu.nl [Spinoza Institute and Institute for Theoretical Physics, Utrecht University, Leuvenlaan 4, 3584 CE Utrecht (Netherlands)
2011-03-01
We study the correction to the scale invariant power spectrum of a scalar field on de Sitter space from small black holes that formed during a pre-inflationary matter dominated era. The formation probability of such black holes is estimated from primordial Gaussian density fluctuations. We determine the correction to the spectrum of scalar cosmological perturbations from the Keldysh propagator of a massless scalar field on Schwarzschild-de Sitter space. Our results suggest that the effect is strong enough to be tested — and possibly even ruled out — by observations.
Cosmological Perturbations in Restricted f(R)-Gravity
Chaichian, M; Kluson, J
2016-01-01
We investigate the metric perturbations of the restricted f(R) theory of gravity in the cosmological context and explore the phenomenological implications of this model. We show that it is possible to construct a restricted model of gravity, in which the background equations are the same as the equations of motion which are derived from the Einstein-Hilbert action with the cosmological constant term. We argue that the deviation from the Einstein-Hilbert model emerges in the perturbed equations, for which we have a non-vanishing anisotropic stress. Further, with the help of the results of Planck data for the modified gravity we obtain constraints on the parameters of the model.
One-particle-irreducible consistency relations for cosmological perturbations
Goldberger, Walter D; Nicolis, Alberto
2013-01-01
We derive consistency relations for correlators of scalar cosmological perturbations which hold in the "squeezed limit" in which one or more of the external momenta become soft. Our results are formulated as relations between suitably defined one-particle irreducible N-point and (N-1)-point functions that follow from residual spatial conformal diffeomorphisms of the unitary gauge Lagrangian. As such, some of these relations are exact to all orders in perturbation theory, and do not rely on approximate deSitter invariance or other dynamical assumptions (e.g., properties of the operator product expansion or the behavior of modes at horizon crossing). The consistency relations apply model-independently to cosmological scenarios where the time evolution is driven by a single scalar field. Besides reproducing the known results for single-field inflation in the slow roll limit, we verify that our consistency relations hold more generally, for instance in ghost condensate models in flat space. We comment on possible...
Cosmological perturbations on the phantom brane
Bag, Satadru; Viznyuk, Alexander; Shtanov, Yuri; Sahni, Varun
2016-07-01
We obtain a closed system of equations for scalar perturbations in a multi-component braneworld. Our braneworld possesses a phantom-like equation of state at late times, weff Consequently, the quasi-static approximation of Koyama and Maartens provides a good fit to the exact results during the matter-dominated epoch. We find that the late-time growth of density perturbations on the brane proceeds at a faster rate than in ΛCDM. Additionally, the gravitational potentials Φ and Ψ evolve differently on the brane than in ΛCDM, for which Φ = Ψ. On the brane, by contrast, the ratio Φ/Ψ exceeds unity during the late matter-dominated epoch (z lesssim 50). These features emerge as smoking gun tests of phantom brane cosmology and allow predictions of this scenario to be tested against observations of galaxy clustering and large-scale structure.
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...
Energy Technology Data Exchange (ETDEWEB)
Somogyi, Gabor [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Zurich Univ. (Switzerland). Inst. for Theoretical Physics; Smith, Robert E. [Zurich Univ. (Switzerland). Inst. for Theoretical Physics
2009-10-15
We generalize the ''renormalized'' perturbation theory (RPT) formalism of M. Crocce and R. Scoccimarro (2006) to deal with multiple fluids in the Universe and here we present the complete calculations up to the one-loop level in the RPT. We apply this approach to the problem of following the nonlinear evolution of baryon and cold dark matter (CDM) perturbations, evolving from the distinct sets of initial conditions, from the high redshift post-recombination Universe right through to the present day. In current theoretical and numerical models of structure formation, it is standard practice to treat baryons and CDM as an effective single matter fluid - the so called dark matter only modeling. In this approximation, one uses a weighed sum of late time baryon and CDM transfer functions to set initial mass fluctuations. In this paper we explore whether this approach can be employed for high precision modeling of structure formation. We show that, even if we only follow the linear evolution, there is a large-scale scale-dependent bias between baryons and CDM for the currently favored WMAP5 {lambda}CDM model. This time evolving bias is significant (> 1%) until the present day, when it is driven towards unity through gravitational relaxation processes. Using the RPT formalism we test this approximation in the non-linear regime. We show that the non-linear CDM power spectrum in the 2-component fluid differs from that obtained from an effective mean-mass 1-component fluid by {proportional_to} 3% on scales of order k {proportional_to} 0.05 h Mpc{sup -1} at z = 10, and by {proportional_to} 0.5% at z = 0. However, for the case of the non-linear evolution of the baryons the situation is worse and we find that the power spectrum is suppressed, relative to the total matter, by {proportional_to} 15% on scales k {proportional_to} 0.05 hMpc{sup -1} at z = 10, and by {proportional_to} 3 - 5% at z = 0. Importantly, besides the suppression of the spectrum, the
Instantaneous stochastic perturbation theory
Lüscher, Martin
2015-01-01
A form of stochastic perturbation theory is described, where the representative stochastic fields are generated instantaneously rather than through a Markov process. The correctness of the procedure is established to all orders of the expansion and for a wide class of field theories that includes all common formulations of lattice QCD.
Cosmological perturbations from the Standard Model Higgs
Energy Technology Data Exchange (ETDEWEB)
Simone, Andrea De [SISSA, Via Bonomea 265, I-34136 Trieste (Italy); Riotto, Antonio, E-mail: andrea.desimone@sissa.it, E-mail: antonio.riotto@unige.ch [Department of Theoretical Physics and Center for Astroparticle Physics (CAP), 24 quai E. Ansermet, CH-1211 Geneva 4 (Switzerland)
2013-02-01
We propose that the Standard Model (SM) Higgs is responsible for generating the cosmological perturbations of the universe by acting as an isocurvature mode during a de Sitter inflationary stage. In view of the recent ATLAS and CMS results for the Higgs mass, this can happen if the Hubble rate during inflation is in the range (10{sup 10}−10{sup 14}) GeV (depending on the SM parameters). Implications for the detection of primordial tensor perturbations through the B-mode of CMB polarization via the PLANCK satellite are discussed. For example, if the Higgs mass value is confirmed to be m{sub h} = 125.5 GeV and m{sub t},α{sub s} are at their central values, our mechanism predicts tensor perturbations too small to be detected in the near future. On the other hand, if tensor perturbations will be detected by PLANCK through the B-mode of CMB, then there is a definite relation between the Higgs and top masses, making the mechanism predictive and falsifiable.
Nonspherical Szekeres models in the language of cosmological perturbations
Sussman, Roberto A.; Hidalgo, Juan Carlos; Delgado Gaspar, Ismael; Germán, Gabriel
2017-03-01
We study the differences and equivalences between the nonperturbative description of the evolution of cosmic structure furnished by the Szekeres dust models (a nonspherical exact solution of Einstein's equations) and the dynamics of cosmological perturbation theory (C P T ) for dust sources in a Λ CDM background. We show how the dynamics of Szekeres models can be described by evolution equations given in terms of "exact fluctuations" that identically reduce (at all orders) to evolution equations of C P T in the comoving isochronous gauge. We explicitly show how Szekeres linearized exact fluctuations are specific (deterministic) realizations of standard linear perturbations of C P T given as random fields, but, as opposed to the latter perturbations, they can be evolved exactly into the full nonlinear regime. We prove two important results: (i) the conservation of the curvature perturbation (at all scales) also holds for the appropriate linear approximation of the exact Szekeres fluctuations in a Λ CDM background, and (ii) the different collapse morphologies of Szekeres models yields, at nonlinear order, different functional forms for the growth factor that follows from the study of redshift space distortions. The metric-based potentials used in linear C P T are computed in terms of the parameters of the linearized Szekeres models, thus allowing us to relate our results to linear C P T results in other gauges. We believe that these results provide a solid starting stage to examine the role of non-perturbative general relativity in current cosmological research.
Nakamura, Kouji
2010-01-01
We derived the second-order perturbations of the Einstein equations and the Klein-Gordon equation for a generic situation in terms of gauge-invariant variables. The consistency of all the equations is confirmed. This confirmation implies that all the derived equations of the second order are self-consistent and these equations are correct in this sense. We also discuss the physical implication of these equations.
Cosmological perturbations in mimetic Horndeski gravity
Arroja, Frederico; Karmakar, Purnendu; Matarrese, Sabino
2016-01-01
We study linear scalar perturbations around a flat FLRW background in mimetic Horndeski gravity. In the absence of matter, we show that the Newtonian potential satisfies a second-order differential equation with no spatial derivatives. This implies that the sound speed for scalar perturbations is exactly zero on this background. We also show that in mimetic $G^3$ theories the sound speed is equally zero. We obtain the equation of motion for the comoving curvature perturbation (first order differential equation) and solve it to find that the comoving curvature perturbation is constant on all scales in mimetic Horndeski gravity. We find solutions for the Newtonian potential evolution equation in two simple models. Finally we show that the sound speed is zero on all backgrounds and therefore the system does not have any wave-like scalar degrees of freedom.
Cosmology in generalized Proca theories
De Felice, Antonio; Heisenberg, Lavinia; Kase, Ryotaro; Mukohyama, Shinji; Tsujikawa, Shinji; Zhang, Ying-li
2016-06-01
We consider a massive vector field with derivative interactions that propagates only the 3 desired polarizations (besides two tensor polarizations from gravity) with second-order equations of motion in curved space-time. The cosmological implications of such generalized Proca theories are investigated for both the background and the linear perturbation by taking into account the Lagrangian up to quintic order. In the presence of a matter fluid with a temporal component of the vector field, we derive the background equations of motion and show the existence of de Sitter solutions relevant to the late-time cosmic acceleration. We also obtain conditions for the absence of ghosts and Laplacian instabilities of tensor, vector, and scalar perturbations in the small-scale limit. Our results are applied to concrete examples of the general functions in the theory, which encompass vector Galileons as a specific case. In such examples, we show that the de Sitter fixed point is always a stable attractor and study viable parameter spaces in which the no-ghost and stability conditions are satisfied during the cosmic expansion history.
Cosmology in generalized Proca theories
De Felice, Antonio; Kase, Ryotaro; Mukohyama, Shinji; Tsujikawa, Shinji; Zhang, Ying-li
2016-01-01
We consider a massive vector field with derivative interactions that propagates only the 3 desired polarizations (besides two tensor polarizations from gravity) with second-order equations of motion in curved space-time. The cosmological implications of such generalized Proca theories are investigated for both the background and the linear perturbation by taking into account the Lagrangian up to quintic order. In the presence of a matter fluid with a temporal component of the vector field, we derive the background equations of motion and show the existence of de Sitter solutions relevant to the late-time cosmic acceleration. We also obtain conditions for the absence of ghosts and Laplacian instabilities of tensor, vector, and scalar perturbations in the small-scale limit. Our results are applied to concrete examples of the general functions in the theory, which encompass vector Galileons as a specific case. In such examples, we show that the de Sitter fixed point is always a stable attractor and study viable ...
Large Spin Perturbation Theory
Alday, Luis F
2016-01-01
We consider conformal field theories around points of large twist degeneracy. Examples of this are theories with weakly broken higher spin symmetry and perturbations around generalised free fields. At the degenerate point we introduce twist conformal blocks. These are eigenfunctions of certain quartic operators and encode the contribution, to a given four-point correlator, of the whole tower of intermediate operators with a given twist. As we perturb around the degenerate point, the twist degeneracy is lifted. In many situations this breaking is controlled by inverse powers of the spin. In such cases the twist conformal blocks can be decomposed into a sequence of functions which we systematically construct. Decomposing the four-point correlator in this basis turns crossing symmetry into an algebraic problem. Our method can be applied to a wide spectrum of conformal field theories in any number of dimensions and at any order in the breaking parameter. As an example, we compute the spectrum of various theories ...
Ooguri, H; Ooguri, Hirosi; Yin, Zheng
1996-01-01
These lecture notes are based on a course on string theories given by Hirosi Ooguri in the first week of TASI 96 Summer School at Boulder, Colorado. It is an introductory course designed to provide students with minimum knowledge before they attend more advanced courses on non-perturbative aspects of string theories in the School. The course consists of five lectures: 1. Bosonic String, 2. Toroidal Compactifications, 3. Superstrings, 4. Heterotic Strings, and 5. Orbifold Compactifications.
Running vacuum cosmological models: linear scalar perturbations
Perico, E. L. D.; Tamayo, D. A.
2017-08-01
In cosmology, phenomenologically motivated expressions for running vacuum are commonly parameterized as linear functions typically denoted by Λ(H2) or Λ(R). Such models assume an equation of state for the vacuum given by bar PΛ = - bar rhoΛ, relating its background pressure bar PΛ with its mean energy density bar rhoΛ ≡ Λ/8πG. This equation of state suggests that the vacuum dynamics is due to an interaction with the matter content of the universe. Most of the approaches studying the observational impact of these models only consider the interaction between the vacuum and the transient dominant matter component of the universe. We extend such models by assuming that the running vacuum is the sum of independent contributions, namely bar rhoΛ = Σibar rhoΛi. Each Λ i vacuum component is associated and interacting with one of the i matter components in both the background and perturbation levels. We derive the evolution equations for the linear scalar vacuum and matter perturbations in those two scenarios, and identify the running vacuum imprints on the cosmic microwave background anisotropies as well as on the matter power spectrum. In the Λ(H2) scenario the vacuum is coupled with every matter component, whereas the Λ(R) description only leads to a coupling between vacuum and non-relativistic matter, producing different effects on the matter power spectrum.
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).
Uniqueness of the gauge invariant action for cosmological perturbations
Energy Technology Data Exchange (ETDEWEB)
Prokopec, Tomislav; Weenink, Jan, E-mail: t.prokopec@uu.nl, E-mail: j.g.weenink@uu.nl [Institute for Theoretical Physics and Spinoza Institute, Utrecht University, Leuvenlaan 4, 3585 CE Utrecht (Netherlands)
2012-12-01
In second order perturbation theory different definitions are known of gauge invariant perturbations in single field inflationary models. Consequently the corresponding gauge invariant cubic actions do not have the same form. Here we show that the cubic action for one choice of gauge invariant variables is unique in the following sense: the action for any other, non-linearly related variable can be brought to the same bulk action, plus additional boundary terms. These boundary terms correspond to the choice of hypersurface and generate extra, disconnected contributions to the bispectrum. We also discuss uniqueness of the action with respect to conformal frames. When expressed in terms of the gauge invariant curvature perturbation on uniform field hypersurfaces the action for cosmological perturbations has a unique form, independent of the original Einstein or Jordan frame. Crucial is that the gauge invariant comoving curvature perturbation is frame independent, which makes it extremely helpful in showing the quantum equivalence of the two frames, and therefore in calculating quantum effects in nonminimally coupled theories such as Higgs inflation.
Cosmology in beyond-generalized Proca theories
Nakamura, Shintaro; Kase, Ryotaro; Tsujikawa, Shinji
2017-05-01
The beyond-generalized Proca theories are the extension of second-order massive vector-tensor theories (dubbed generalized Proca theories) with two transverse vector modes and one longitudinal scalar besides two tensor polarizations. Even with this extension, the propagating degrees of freedom remain unchanged on the isotropic cosmological background without an Ostrogradski instability. We study the cosmology in beyond-generalized Proca theories by paying particular attention to the dynamics of late-time cosmic acceleration and resulting observational consequences. We derive conditions for avoiding ghosts and instabilities of tensor, vector, and scalar perturbations and discuss viable parameter spaces in concrete models allowing the dark energy equation of state smaller than -1 . The propagation speeds of those perturbations are subject to modifications beyond the domain of generalized Proca theories. There is a mixing between scalar and matter sound speeds, but such a mixing is suppressed during most of the cosmic expansion history without causing a new instability. On the other hand, we find that derivative interactions arising in beyond-generalized Proca theories give rise to important modifications to the cosmic growth history. The growth rate of matter perturbations can be compatible with the redshift-space distortion data due to the realization of gravitational interaction weaker than that in generalized Proca theories. Thus, it is possible to distinguish the dark energy model in beyond-generalized Proca theories from the counterpart in generalized Proca theories as well as from the Λ CDM model.
Energy Technology Data Exchange (ETDEWEB)
Shafi, Qaisar [Univ. of Delaware, Newark, DE (United States); Barr, Steven [Univ. of Delaware, Newark, DE (United States); Gaisser, Thomas [Univ. of Delaware, Newark, DE (United States); Stanev, Todor [Univ. of Delaware, Newark, DE (United States)
2015-03-31
1. Executive Summary (April 1, 2012 - March 31, 2015) Title: Particle Theory, Particle Astrophysics and Cosmology Qaisar Shafi University of Delaware (Principal Investigator) Stephen M. Barr, University of Delaware (Co-Principal Investigator) Thomas K. Gaisser, University of Delaware (Co-Principal Investigator) Todor Stanev, University of Delaware (Co-Principal Investigator) The proposed research was carried out at the Bartol Research included Professors Qaisar Shafi Stephen Barr, Thomas K. Gaisser, and Todor Stanev, two postdoctoral fellows (Ilia Gogoladze and Liucheng Wang), and several graduate students. Five students of Qaisar Shafi completed their PhD during the period August 2011 - August 2014. Measures of the group’s high caliber performance during the 2012-2015 funding cycle included pub- lications in excellent refereed journals, contributions to working groups as well as white papers, and conference activities, which together provide an exceptional record of both individual performance as well as overall strength. Another important indicator of success is the outstanding quality of the past and current cohort of graduate students. The PhD students under our supervision regularly win the top departmental and university awards, and their publications records show excellence both in terms of quality and quantity. The topics covered under this grant cover the frontline research areas in today’s High Energy Theory & Phenomenology. For Professors Shafi and Barr they include LHC related topics including supersymmetry, collider physics, fl vor physics, dark matter physics, Higgs boson and seesaw physics, grand unifi and neutrino physics. The LHC two years ago discovered the Standard Model Higgs boson, thereby at least partially unlocking the secrets behind electroweak symmetry breaking. We remain optimistic that new and exciting physics will be found at LHC 14, which explain our focus on physics beyond the Standard Model. Professors Shafi continued his
Asymptotic analysis of perturbed dust cosmologies to second order
Uggla, Claes; Wainwright, John
2013-08-01
Nonlinear perturbations of Friedmann-Lemaitre cosmologies with dust and a cosmological constant Λ >0 have recently attracted considerable attention. In this paper our first goal is to compare the evolution of the first and second order perturbations by determining their asymptotic behaviour at late times in ever-expanding models. We show that in the presence of spatial curvature K or a cosmological constant, the density perturbation approaches a finite limit both to first and second order, but the rate of approach depends on the model, being power law in the scale factor if Λ >0 but logarithmic if Λ =0 and K0 the decaying mode does not die away, i.e. it contributes on an equal footing as the growing mode to the asymptotic expression for the density perturbation. On the other hand, the future asymptotic regime of the Einstein-de Sitter universe (K=Λ =0) is completely different, as exemplified by the density perturbation which diverges; moreover, the second order perturbation diverges faster than the first order perturbation, which suggests that the Einstein-de Sitter universe is unstable to perturbations, and that the perturbation series do not converge towards the future. We conclude that the presence of spatial curvature or a cosmological constant stabilizes the perturbations. Our second goal is to derive an explicit expression for the second order density perturbation that can be used to study the effects of including a cosmological constant and spatial curvature.
Degenerate Density Perturbation Theory
Palenik, Mark C
2016-01-01
Fractional occupation numbers can be used in density functional theory to create a symmetric Kohn-Sham potential, resulting in orbitals with degenerate eigenvalues. We develop the corresponding perturbation theory and apply it to a system of $N_d$ degenerate electrons in a harmonic oscillator potential. The order-by-order expansions of both the fractional occupation numbers and unitary transformations within the degenerate subspace are determined by the requirement that a differentiable map exists connecting the initial and perturbed states. Using the X$\\alpha$ exchange-correlation (XC) functional, we find an analytic solution for the first-order density and first through third-order energies as a function of $\\alpha$, with and without a self-interaction correction. The fact that the XC Hessian is not positive definite plays an important role in the behavior of the occupation numbers.
Degenerate density perturbation theory
Palenik, Mark C.; Dunlap, Brett I.
2016-09-01
Fractional occupation numbers can be used in density functional theory to create a symmetric Kohn-Sham potential, resulting in orbitals with degenerate eigenvalues. We develop the corresponding perturbation theory and apply it to a system of Nd degenerate electrons in a harmonic oscillator potential. The order-by-order expansions of both the fractional occupation numbers and unitary transformations within the degenerate subspace are determined by the requirement that a differentiable map exists connecting the initial and perturbed states. Using the X α exchange-correlation (XC) functional, we find an analytic solution for the first-order density and first- through third-order energies as a function of α , with and without a self-interaction correction. The fact that the XC Hessian is not positive definite plays an important role in the behavior of the occupation numbers.
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.
Cosmological perturbations in SFT inspired non-local scalar field models
Energy Technology Data Exchange (ETDEWEB)
Koshelev, Alexey S. [Vrije Universiteit Brussel and The International Solvay Institutes, Theoretische Natuurkunde, Brussels (Belgium); Vernov, Sergey Yu. [Instituto de Ciencias del Espacio (ICE/CSIC) and Institut d' Estudis Espacials de Catalunya (IEEC), Bellaterra, Barcelona (Spain); Lomonosov Moscow State University, Theoretical High Energy Physics Division, Skobeltsyn Institute of Nuclear Physics, Moscow (Russian Federation)
2012-10-15
We study cosmological perturbations in models with a single non-local scalar field originating from the string field theory description of the rolling tachyon dynamics. We construct the equation for the energy density perturbations of the non-local scalar field and explicitly prove that for the free field it is identical to a system of local cosmological perturbation equations in a particular model with multiple (maybe infinitely many) local free scalar fields. We also show that vector and tensor perturbations are absent in this set-up. (orig.)
Cosmological history in York time: inflation and perturbations
Roser, Philipp
2016-01-01
The constant mean extrinsic curvature on a spacelike slice may constitute a physically preferred time coordinate, `York time'. One line of enquiry to probe this idea is to understand processes in our cosmological history in terms of York time. Following a review of the theoretical motivations, we focus on slow-roll inflation and the freezing and Hubble re-entry of cosmological perturbations. We show how the mathematical account of these processes is distinct from the conventional account in terms of standard cosmological or conformal time. We also consider the cosmological York-timeline more broadly and contrast it with the conventional cosmological timeline.
Cosmological history in York time: inflation and perturbations
Roser, Philipp; Valentini, Antony
2017-02-01
The constant mean extrinsic curvature on a spacelike slice may constitute a physically preferred time coordinate, `York time'. One line of enquiry to probe this idea is to understand processes in our cosmological history in terms of York time. Following a review of the theoretical motivations, we focus on slow-roll inflation and the freezing and Hubble re-entry of cosmological perturbations. While the physics is, of course, observationally equivalent, we show how the mathematical account of these processes is distinct from the conventional account in terms of standard cosmological or conformal time. We also consider the cosmological York-timeline more broadly and contrast it with the conventional cosmological timeline.
Matter Density Perturbations in Modified Teleparallel Theories
Wu, Yi-Peng
2012-01-01
We study the matter density perturbations in modified teleparallel gravity theories, where extra degrees of freedom arise from the local Lorentz violation in the tangent space. We formulate a vierbein perturbation with variables addressing all the 16 components of the vierbein field. By assuming the perfect fluid matter source, we examine the cosmological implication of the 6 unfamiliar new degrees of freedom in modified $f(T)$ gravity theories. We find that despite the new modes in the vierbein scenario provide no explicit significant effect in the small-scale regime, they exhibit some deviation from the standard general relativity results in super-horizon scales.
Patwardhan, Ajay; Kumar, M S R
2008-01-01
The second order perturbation calculations for gravity wave and Einstein equation for space time and matter are presented for the FRW metric cosmological model. While exact equations are found, suitable approximations are made to obtain definite results. In the gravity wave case the small wavelength case allows nearly locally flat background for obtaining a fit to the WMAP data. In the density and curvature case the FRW background is retained for the length scale of WMAP. Clustering and inhomogeneity are understood. The gravity wave ripples from Big Bang couple nonlinearly and redistribute the modes to higher values of 'l' giving consistency with the WMAP results. The order by order consistency of Einstein equations relate the second order perturbations in the curvature and density and the wrinkles in spacetime caused by the gravity wave modes reorganize these distributions. The radiation data of WMAP gives the picture of a FRW spacetime deformed and wrinkled consistent with matter distribution to one hundred...
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.
One-particle-irreducible consistency relations for cosmological perturbations
Goldberger, Walter D.; Hui, Lam; Nicolis, Alberto
2013-05-01
We derive consistency relations for correlators of scalar cosmological perturbations that hold in the “squeezed limit” in which one or more of the external momenta become soft. Our results are formulated as relations between suitably defined one-particle-irreducible N-point and (N-1)-point functions that follow from residual spatial conformal diffeomorphisms of the unitary gauge Lagrangian. As such, some of these relations are exact to all orders in perturbation theory and do not rely on approximate de Sitter invariance or other dynamical assumptions (e.g., properties of the operator product expansion or the behavior of modes at the horizon crossing). The consistency relations apply model-independently to cosmological scenarios in which the time evolution is driven by a single scalar field. Besides reproducing the known results for single-field inflation in the slow-roll limit, we verify that our consistency relations hold more generally, for instance, in ghost condensate models in flat space. We comment on possible extensions of our results to multifield models.
Cosmological perturbations in coherent oscillating scalar field models
Energy Technology Data Exchange (ETDEWEB)
Cembranos, J.A.R.; Maroto, A.L.; Jareño, S.J. Núñez [Departamento de Física Teórica I, Universidad Complutense de Madrid,Avenida Complutense s/n, Madrid (Spain)
2016-03-03
The fact that fast oscillating homogeneous scalar fields behave as perfect fluids in average and their intrinsic isotropy have made these models very fruitful in cosmology. In this work we will analyse the perturbations dynamics in these theories assuming general power law potentials V(ϕ)=λ|ϕ|{sup n}/n. At leading order in the wavenumber expansion, a simple expression for the effective sound speed of perturbations is obtained c{sub eff}{sup 2}=ω=(n−2)/(n+2) with ω the effective equation of state. We also obtain the first order correction in k{sup 2}/ω{sub eff}{sup 2}, when the wavenumber k of the perturbations is much smaller than the background oscillation frequency, ω{sub eff}. For the standard massive case we have also analysed general anharmonic contributions to the effective sound speed. These results are reached through a perturbed version of the generalized virial theorem and also studying the exact system both in the super-Hubble limit, deriving the natural ansatz for δϕ; and for sub-Hubble modes, exploiting Floquet’s theorem.
Cosmological perturbations in coherent oscillating scalar field models
Cembranos, J A R; Jareño, S J Núñez
2015-01-01
The fact that fast oscillating homogeneous scalar fields behave as perfect fluids in average and their intrinsic isotropy have made these models very fruitful in cosmology. In this work we will analyse the perturbations dynamics in these theories assuming general power law potentials $V(\\phi)=\\lambda \\vert\\phi\\vert^{n}/n$. At leading order in the wavenumber expansion, a simple expression for the effective sound speed of perturbations is obtained $c_{\\text{eff}}^2 = \\omega=(n-2)/(n+2)$ with $\\omega$ the effective equation of state. We also obtain the first order correction in $k^2/\\omega_{\\text{eff}}^2$, when the wavenumber $k$ of the perturbations is much smaller than the background oscillation frequency, $\\omega_{\\text{eff}}$. For the standard massive case we have also analysed general anharmonic contributions to the effective sound speed. These results are reached through a perturbed version of the generalized virial theorem and also studying the exact system both in the super-Hubble limit, deriving the nat...
Cosmological perturbations in coherent oscillating scalar field models
Cembranos, J. A. R.; Maroto, A. L.; Jareño, S. J. Núñez
2016-03-01
The fact that fast oscillating homogeneous scalar fields behave as perfect fluids in average and their intrinsic isotropy have made these models very fruitful in cosmology. In this work we will analyse the perturbations dynamics in these theories assuming general power law potentials V( ϕ) = λ| ϕ| n /n. At leading order in the wavenumber expansion, a simple expression for the effective sound speed of perturbations is obtained c eff 2 = ω = ( n - 2)/( n + 2) with ω the effective equation of state. We also obtain the first order correction in k 2/ ω eff 2 , when the wavenumber k of the perturbations is much smaller than the background oscillation frequency, ω eff. For the standard massive case we have also analysed general anharmonic contributions to the effective sound speed. These results are reached through a perturbed version of the generalized virial theorem and also studying the exact system both in the super-Hubble limit, deriving the natural ansatz for δϕ; and for sub-Hubble modes, exploiting Floquet's theorem.
Applications Of Chiral Perturbation Theory
Mohta, V
2005-01-01
Effective field theory techniques are used to describe the spectrum and interactions of hadrons. The mathematics of classical field theory and perturbative quantum field theory are reviewed. The physics of effective field theory and, in particular, of chiral perturbation theory and heavy baryon chiral perturbation theory are also reviewed. The geometry underlying heavy baryon chiral perturbation theory is described in detail. Results by Coleman et. al. in the physics literature are stated precisely and proven. A chiral perturbation theory is developed for a multiplet containing the recently- observed exotic baryons. A small coupling expansion is identified that allows the calculation of self-energy corrections to the exotic baryon masses. Opportunities in lattice calculations are discussed. Chiral perturbation theory is used to study the possibility of two multiplets of exotic baryons mixed by quark masses. A new symmetry constraint on reduced partial widths is identified. Predictions in the literature based ...
Double field theory inspired cosmology
Wu, Houwen; Yang, Haitang
2014-07-01
Double field theory proposes a generalized spacetime action possessing manifest T-duality on the level of component fields. We calculate the cosmological solutions of double field theory with vanishing Kalb-Ramond field. It turns out that double field theory provides a more consistent way to construct cosmological solutions than the standard string cosmology. We construct solutions for vanishing and non-vanishing symmetry preserving dilaton potentials. The solutions assemble the pre- and post-big bang evolutions in one single line element. Our results show a smooth evolution from an anisotropic early stage to an isotropic phase without any special initial conditions in contrast to previous models. In addition, we demonstrate that the contraction of the dual space automatically leads to both an inflation phase and a decelerated expansion of the ordinary space during different evolution stages.
The Energy-Momentum Tensor for Cosmological Perturbations
Abramo, L R W; Mukhanov, V M
1997-01-01
We study the effective energy-momentum tensor (EMT) for cosmological perturbations and formulate the gravitational back-reaction problem in a gauge invariant manner. We analyze the explicit expressions for the EMT in the cases of scalar metric fluctuations and of gravitational waves and derive the resulting equations of state. The formalism is applied to investigate the back-reaction effects in chaotic inflation. We find that for long wavelength scalar and tensor perturbations, the effective energy density is negative and thus counteracts any pre-existing cosmological constant. For scalar perturbations during an epoch of inflation, the equation of state is de Sitter-like.
Approach to exact solutions of cosmological perturbations: Tachyon field inflation
Herrera, Ramón; Pérez, Roberto G.
2016-03-01
An inflationary universe scenario in the context of a tachyon field is studied. This study is carried out using an ansatz for the effective potential of cosmological perturbations U (η ). We describe in great detail the analytical solutions of the scalar and tensor perturbations for two different Ansätze for the effective potential of cosmological perturbations: Easther's model and an effective potential similar to power-law inflation. Also, we find from the background equations that the effective tachyonic potentials V (φ ) in both models satisfy the properties of a tachyonic potential. We consider the recent data from the Planck to constrain the parameters in our effective potential generating the cosmological perturbations.
Asymptotic analysis of perturbed dust cosmologies to second order
Uggla, Claes
2013-01-01
Nonlinear perturbations of Friedmann-Lemaitre cosmologies with dust and a positive cosmological constant have recently attracted considerable attention. In this paper our first goal is to compare the evolution of the first and second order perturbations by determining their asymptotic behaviour at late times in ever-expanding models. We show that in the presence of spatial curvature K or a positive cosmological constant, the density perturbation approaches a finite limit both to first and second order, but the rate of approach depends on the model, being power law in the scale factor if the cosmological constant is positive but logarithmic if it is zero and and K<0. Scalar perturbations in general contain a growing and a decaying mode. We find, somewhat surprisingly, that if the cosmological constant is positive the decaying mode does not die away, i.e. it contributes on an equal footing as the growing mode to the asymptotic expression for the density perturbation. On the other hand, the future asymptotic ...
Cosmological N -body simulations including radiation perturbations
DEFF Research Database (Denmark)
Brandbyge, Jacob; Rampf, Cornelius; Tram, Thomas
2017-01-01
Cosmological $N$-body simulations are the standard tool to study the emergence of the observed large-scale structure of the Universe. Such simulations usually solve for the gravitational dynamics of matter within the Newtonian approximation, thus discarding general relativistic effects such as th......Cosmological $N$-body simulations are the standard tool to study the emergence of the observed large-scale structure of the Universe. Such simulations usually solve for the gravitational dynamics of matter within the Newtonian approximation, thus discarding general relativistic effects...
xPand: An algorithm for perturbing homogeneous cosmologies
Pitrou, Cyril; Umeh, Obinna
2013-01-01
In the present paper, we develop in detail a fully geometrical method for deriving perturbation equations about a spatially homogeneous background. This method relies on the 3+1 splitting of the background space-time and does not use any particular set of coordinates: it is implemented in terms of geometrical quantities only, using the tensor algebra package xTensor in the xAct distribution along with the extension for perturbations xPert. Our algorithm allows one to obtain the perturbation equations for all types of homogeneous cosmologies, up to any order and in all possible gauges. As applications, we recover the well-known perturbed Einstein equations for Friedmann--Lema\\^itre--Robertson--Walker cosmologies up to second order and for Bianchi I cosmologies at first order. This work opens the door to the study of these models at higher order and to that of any other perturbed Bianchi cosmologies, by circumventing the usually too cumbersome derivation of the perturbed equations.
Exactly solvable model for cosmological perturbations in dilatonic brane worlds
Koyama, K; Koyama, Kazuya; Takahashi, Keitaro
2003-01-01
We construct a model where cosmological perturbations are analytically solved based on dilatonic brane worlds. A bulk scalar field has an exponential potential in the bulk and an exponential coupling to the brane tension. The bulk scalar field yields a power-law inflation on the brane. The exact background metric can be found including the back-reaction of the scalar field. Then exact solutions for cosmological perturbations which properly satisfy the junction conditions on the brane are derived. These solutions provide us an interesting model to understand the connection between the behavior of cosmological perturbations on the brane and the geometry of the bulk. Using these solutions, the behavior of an anisotropic stress induced on the inflationary brane by bulk gravitational fields is investigated.
Perturbation Theory of Embedded Eigenvalues
DEFF Research Database (Denmark)
Engelmann, Matthias
We study problems connected to perturbation theory of embedded eigenvalues in two different setups. The first part deals with second order perturbation theory of mass shells in massive translation invariant Nelson type models. To this end an expansion of the eigenvalues w.r.t. fiber parameter up...... project gives a general and systematic approach to analytic perturbation theory of embedded eigenvalues. The spectral deformation technique originally developed in the theory of dilation analytic potentials in the context of Schrödinger operators is systematized by the use of Mourre theory. The group...
Scale invariant density perturbations from cyclic cosmology
Frampton, Paul Howard
2016-04-01
It is shown how quantum fluctuations of the radiation during the contraction era of a comes back empty (CBE) cyclic cosmology can provide density fluctuations which re-enter the horizon during the subsequent expansion era and at lowest order are scale invariant, in a Harrison-Zel’dovich-Peebles sense. It is necessary to be consistent with observations of large scale structure.
Cosmological applications in Kaluza-Klein theory
Institute of Scientific and Technical Information of China (English)
M. I. Wanas; Gamal G. L. Nashed; A. A. Nowaya
2012-01-01
The field equations of Kaluza-Klein (KK) theory have been applied in the domain of cosmology.These equations are solved for a flat universe by taking the gravitational and the cosmological constants as a function of time t.We use Taylor's expansion of cosmological function,△(t),up to the first order of the time t.The cosmological parameters are calculated and some cosmological problems are discussed.
Cosmological applications in Kaluza-Klein theory
Wanas, M I; Nowaya, A A
2011-01-01
The field equations of Kaluza-Klein (KK) theory have been applied in the domain of cosmology. These equations are solved for a flat universe by taking the gravitational and the cosmological constants as a function of time t. We use Taylor's expansion of cosmological function, $\\Lambda(t)$, up to the first order of the time $t$. The cosmological parameters are calculated and some cosmological problems are discussed.
Producing a scale-invariant spectrum of perturbations in a Hagedorn phase of string cosmology.
Nayeri, Ali; Brandenberger, Robert H; Vafa, Cumrun
2006-07-14
We study the generation of cosmological perturbations during the Hagedorn phase of string gas cosmology. Using tools of string thermodynamics we provide indications that it may be possible to obtain a nearly scale-invariant spectrum of cosmological fluctuations on scales which are of cosmological interest today. In our cosmological scenario, the early Hagedorn phase of string gas cosmology goes over smoothly into the radiation-dominated phase of standard cosmology, without having a period of cosmological inflation.
Cosmological scalar field perturbations can grow
Alcubierre, Miguel; Diez-Tejedor, Alberto; Torres, José M
2015-01-01
It has been argued that the small perturbations in the energy density to the homogeneous and isotropic configurations of a canonical scalar field in an expanding universe do not grow. We show that this is not true in general, and clarify the root of the misunderstanding. We revisit a simple model in which the linear perturbations grow like those in the standard cold dark matter scenario, but with the Jeans length at the scale of the Compton wavelength of the scalar particle.
A decoupled system of hyperbolic equations for linearized cosmological perturbations
Ramírez, J
2002-01-01
A decoupled system of hyperbolic partial differential equations for linear perturbations around spatially flat FRW universes is obtained for the first time. The two key ingredients in obtaining this system are i) the explicit decomposition of the perturbing energy momentum tensor into two pieces: intrinsic and free, which have definite and distinct mathematical properties and physical interpretation, and ii) the introduction of a new gauge which plays a similar role as harmonic gauge does for perturbations around Minkowski space-time. The proposed formalism could be highly relevant for physical cosmology, since our universe is most likely flat. We deal with classical perturbations, but our treatment, being covariant, is also very appropriate for the description of linearized quantum gravity around cosmological backgrounds.
Perturbations of Kantowski-Sachs models with a cosmological constant
Keresztes, Zoltán; Bradley, Michael; Dunsby, Peter K S; Gergely, László Á
2013-01-01
We investigate perturbations of Kantowski-Sachs models with a positive cosmological constant, using the gauge invariant 1+3 and 1+1+2 covariant splits of spacetime together with a harmonic decomposition. The perturbations are assumed to be vorticity-free and of perfect fluid type, but otherwise include general scalar, vector and tensor modes. In this case the set of equations can be reduced to six evolution equations for six harmonic coefficients.
Cosmological perturbation effects on gravitational-wave luminosity distance estimates
Bertacca, Daniele; Raccanelli, Alvise; Bartolo, Nicola; Matarrese, Sabino
2017-01-01
Waveforms of gravitational waves provide information about a variety of parameters for the binary system merging. However, standard calculations have been performed assuming a FLRW universe with no perturbations. In reality this assumption should be dropped: we show that the inclusion of cosmological perturbations translates into corrections to the estimate of astrophysical parameters derived for the merging binary systems. We compute corrections to the estimate of the luminosity distance due...
Cosmological Inflation: Theory and Observations
Baumann, Daniel
2008-01-01
In this article we review the theory of cosmological inflation with a particular focus on the beautiful connection it provides between the physics of the very small and observations of the very large. We explain how quantum mechanical fluctuations during the inflationary era become macroscopic density fluctuations which leave distinct imprints in the cosmic microwave background (CMB). We describe the physics of anisotropies in the CMB temperature and polarization and discuss how CMB observations can be used to probe the primordial universe.
Cosmological perturbations on the Phantom brane
Bag, Satadru; Shtanov, Yuri; Sahni, Varun
2016-01-01
We obtain a closed system of equations for scalar perturbations in a multi-component braneworld. Our braneworld possesses a phantom-like equation of state at late times, $w_{\\rm eff} < -1$, but no big-rip future singularity. In addition to matter and radiation, the braneworld possesses a new effective degree of freedom - the 'Weyl fluid' or 'dark radiation'. Setting initial conditions on super-Hubble spatial scales at the epoch of radiation domination, we evolve perturbations of radiation, pressureless matter and the Weyl fluid until the present epoch. We observe a gradual decrease in the amplitude of the Weyl-fluid perturbations after Hubble-radius crossing, which results in a negligible effect of the Weyl fluid on the evolution of matter perturbations on spatial scales relevant for structure formation. Consequently, the quasi-static approximation of Koyama and Maartens provides a good fit to the exact results during the matter-dominated epoch. We find that the late-time growth of density perturbations on...
Fractality in a Perturbed Einstein-de Sitter Cosmology
Abdalla, Elcio; Ribeiro, M B; Abdalla, Elcio; Mohayaee, Roya; Ribeiro, Marcelo B.
1999-01-01
This work presents the first step of an attempt to check the validity of a hypothesis known as the ``apparent fractal conjecture'' (Ribeiro 1999), according to which the observed fractal structure of large-scale distribution of galaxies arises when observational quantities are calculated along the past light cone. Inasmuch as general relativity states that astronomical observations are carried out in this spacetime hypersurface, observational quantities relevant for direct comparison with astronomical data must be calculated along it. Implementing this condition profoundly changes the behaviour of many observables in the standard cosmological models. In particular, the observed average density, becomes inhomogeneous, even in the spatially homogeneous spacetime of standard cosmology. Such a change in the observational quantities has already been fully analysed in previous works by Ribeiro (1992b, 1993, 1994, 1995) for a non-perturbed cosmological model. Here we derive observational relations in a perturbed Ein...
Gauge invariant cosmological perturbations for the nonminimally coupled inflaton field
Weenink, J.; Prokopec, T.
2010-01-01
We construct the gauge invariant free action for cosmological perturbations for the nonminimally coupled inflaton field in the Jordan frame. For this the phase space formalism is used, which keeps track of all the dynamical and constraint fields. We perform explicit conformal transformations to demo
Review of chiral perturbation theory
Indian Academy of Sciences (India)
B Ananthanarayan
2003-11-01
A review of chiral perturbation theory and recent developments on the comparison of its predictions with experiment is presented. Some interesting topics with scope for further elaboration are touched upon.
Cosmological perturbations in transient phantom inflation scenarios
Energy Technology Data Exchange (ETDEWEB)
Richarte, Martin G. [Universidade Federal do Parana, Departamento de Fisica, Caixa Postal 19044, Curitiba (Brazil); Universidad de Buenos Aires, Ciudad Universitaria 1428, Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Buenos Aires (Argentina); Kremer, Gilberto M. [Universidade Federal do Parana, Departamento de Fisica, Caixa Postal 19044, Curitiba (Brazil)
2017-01-15
We present a model of inflation where the inflaton is accommodated as a phantom field which exhibits an initial transient pole behavior and then decays into a quintessence field which is responsible for a radiation era. We must stress that the present unified model only deals with a single field and that the transition between the two eras is achieved in a smooth way, so the model does not suffer from the eternal inflation issue. We explore the conditions for the crossing of the phantom divide line within the inflationary era along with the structural stability of several critical points. We study the behavior of the phantom field within the slow-climb approximation along with the necessary conditions to have sufficient inflation. We also examine the model at the level of classical perturbations within the Newtonian gauge and determine the behavior of the gravitational potential, contrast density and perturbed field near the inflation stage and the subsequent radiation era. (orig.)
Cosmological scalar field perturbations can grow
Alcubierre, Miguel; de la Macorra, Axel; Diez-Tejedor, Alberto; Torres, José M.
2015-09-01
It has been argued that the small perturbations to the homogeneous and isotropic configurations of a canonical scalar field in an expanding universe do not grow. We show that this is not true in general, and clarify the root of the misunderstanding. We revisit a simple model in which the zero mode of a free scalar field oscillates with high frequency around the minimum of the potential. Under this assumption the linear perturbations grow like those in the standard cold dark matter scenario, but with a Jeans length at the scale of the Compton wavelength of the scalar particle. Contrary to previous analyses in the literature our results do not rely on time averages and/or fluid identifications, and instead we solve both analytically (in terms of a well-defined series expansion) and numerically the linearized Einstein-Klein-Gordon system. Also, we use gauge-invariant fields, which makes the physical analysis more transparent and simplifies the comparison with previous works carried out in different gauges. As a byproduct of this study we identify a time-dependent modulation of the different physical quantities associated to the background as well as the perturbations with potential observational consequences in dark matter models.
Amplification of curvature perturbations in cyclic cosmology
Zhang, Jun; Liu, Zhi-Guo; Piao, Yun-Song
2010-12-01
We analytically and numerically show that through the cycles with nonsingular bounce, the amplitude of curvature perturbation on a large scale will be amplified and the power spectrum will redden. In some sense, this amplification will eventually destroy the homogeneity of the background, which will lead to the ultimate end of cycles of the global universe. We argue that for the model with increasing cycles, it might be possible that a fissiparous multiverse will emerge after one or several cycles, in which the cycles will continue only at corresponding local regions.
Basics of QCD perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Soper, D.E. [Univ. of Oregon, Eugene, OR (United States). Inst. of Theoretical Science
1997-06-01
This is an introduction to the use of QCD perturbation theory, emphasizing generic features of the theory that enable one to separate short-time and long-time effects. The author also covers some important classes of applications: electron-positron annihilation to hadrons, deeply inelastic scattering, and hard processes in hadron-hadron collisions. 31 refs., 38 figs.
Enea Romano, Antonio; Sanes Negrete, Sergio; Sasaki, Misao; Starobinsky, Alexei A.
2014-06-01
We study effects on the luminosity distance of a local inhomogeneity seeded by primordial curvature perturbations of the type predicted by the inflationary scenario and constrained by the cosmic microwave background radiation. We find that a local underdensity originated from a one, two or three standard deviations peaks of the primordial curvature perturbations field can induce corrections to the value of a cosmological constant of the order of 0.6{%},1{%},1.5{%} , respectively. These effects cannot be neglected in the precision cosmology era in which we are entering. Our results can be considered an upper bound for the effect of the monopole component of the local non-linear structure which can arise from primordial curvature perturbations and requires a fully non-perturbative relativistic treatment.
Dynamical Systems Approach to Magnetised Cosmological Perturbations
Hobbs, S; Hobbs, Stacey; Dunsby, Peter K. S.
2000-01-01
Assuming a large-scale homogeneous magnetic field, we follow the covariant and gauge-invariant approach used by Tsagas and Barrow to describe the evolution of density and magnetic field inhomogeneities and curvature perturbations in a matter-radiation universe. We use a two parameter approximation scheme to linearize their exact non-linear general-relativistic equations for magneto-hydrodynamic evolution. Using a two-fluid approach we set up the governing equations as a fourth order autonomous dynamical system. Analysis of the equilibrium points for the radiation dominated era lead to solutions similar to the super-horizon modes found analytically by Tsagas and Maartens. We find that a study of the dynamical system in the dust-dominated era leads naturally to a magnetic critical length scale closely related to the Jeans Length. Depending on the size of wavelengths relative to this scale, these solutions show three distinct behaviours: large-scale stable growing modes, intermediate decaying modes, and small-sc...
The theory of singular perturbations
De Jager, E M
1996-01-01
The subject of this textbook is the mathematical theory of singular perturbations, which despite its respectable history is still in a state of vigorous development. Singular perturbations of cumulative and of boundary layer type are presented. Attention has been given to composite expansions of solutions of initial and boundary value problems for ordinary and partial differential equations, linear as well as quasilinear; also turning points are discussed. The main emphasis lies on several methods of approximation for solutions of singularly perturbed differential equations and on the mathemat
Stable cosmology in ghost-free quasidilaton theory
Gümrükçüoǧlu, A. Emir; Koyama, Kazuya; Mukohyama, Shinji
2017-08-01
We present a novel cosmological solution in the framework of extended quasidilaton theory which underwent scrutiny recently. We only consider terms that do not generate the Boulware-Deser degree of freedom, hence the ghost-free quasidilaton theory, and show three new branches of cosmological evolution therein. One of the solutions passes the perturbative stability tests. This new solution exhibits a late time self-acceleration and all graviton polarizations acquire masses that converge to a constant in the asymptotic future. Moreover, all modes propagate at the speed of light. We propose that this solution can be used as a benchmark model for future phenomenological studies.
de Sitter limit of inflation and nonlinear perturbation theory
Jarnhus, Philip R
2007-01-01
We study the fourth order action of comoving curvature perturbations in an inflationary universe in order to understand more systematically the de Sitter limit in nonlinear cosmological perturbation theory. We derive the action of the curvature perturbations to fourth order in the comoving gauge, and show that it vanishes sufficiently fast in the de Sitter limit. By studying the de Sitter limit, we then extrapolate to the n'th order action of comoving curvature perturbations and discuss the slow-roll order of the n-point correlation function.
Noether Identities and Gauge-Fixing the Action for Cosmological Perturbations
Lagos, Macarena; Ferreira, Pedro G; García-Sáenz, Sebastián
2014-01-01
We propose and develop a general algorithm for finding the action for cosmological perturbations which rivals the conventional, gauge-invariant approach and can be applied to theories with more than one metric. We then apply it to a particular case of bigravity, focusing on the Eddington- inspired Born-Infeld theory, and show that we can obtain a nearly scale-invariant power spectrum for both scalar and tensor primordial quantum perturbations. Unfortunately, in the case of the minimal Eddington-inspired Born-Infeld theory, we find that the tensor-to-scalar ratio of perturbations is unacceptably large. We discuss the applicability of our general method and the possibility of resurrecting the specific theory we have looked at.
Basics of thermal field theory - a tutorial on perturbative computations
Laine, Mikko; Vuorinen, Aleksi
2017-01-01
These lecture notes, suitable for a two-semester introductory course or self-study, offer an elementary and self-contained exposition of the basic tools and concepts that are encountered in practical computations in perturbative thermal field theory. Selected applications to heavy ion collision physics and cosmology are outlined in the last chapter.
Perturbations of cosmological and black hole solutions in massive gravity and bi-gravity
Kobayashi, Tsutomu; Siino, Masaru; Yamaguchi, Masahide; Yoshida, Daisuke
2016-10-01
We investigate perturbations of a class of spherically symmetric solutions in massive gravity and bi-gravity. The background equations of motion for the particular class of solutions we are interested in reduce to a set of the Einstein equations with a cosmological constant. Thus, the solutions in this class include all the spherically symmetric solutions in general relativity, such as the Friedmann-Lemaître-Robertson-Walker solution and the Schwarzschild (-de Sitter) solution, though the one-parameter family of two parameters of the theory admits such a class of solutions. We find that the equations of motion for the perturbations of this class of solutions also reduce to the perturbed Einstein equations at first and second order. Therefore, the perturbative stability of the solutions coincides with that of the corresponding solutions in general relativity at least up to the second-order perturbations.
Chiral Perturbation Theory and Unitarization
Ruiz-Arriola, E; Nieves, J; Peláez, J R
2000-01-01
We review our recent work on unitarization and chiral perturbation theory both in the $\\pi\\pi$ and the $\\pi N$ sectors. We pay particular attention to the Bethe-Salpeter and Inverse Amplitude unitarization methods and their recent applications to $\\pi\\pi$ and $\\pi N$ scattering.
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.
Early time perturbations behaviour in scalar field cosmologies
Perrotta, F; Perrotta, Francesca; Baccigalupi, Carlo
1999-01-01
We consider the problem of the initial conditions and behaviour of the perturbations in scalar field cosmology with general potential. We use the general definition of adiabatic and isocurvature conditions to set the appropriate initial values for the perturbation in the scalar field and in the ordinary matter and radiation components. In both the cases of initial adiabaticity and isocurvature, we solve the Einstein and fluid equation at early times and on superhorizon scales to find the initial behaviour of the relevant quantities. In particular, in the isocurvature case, we consider models in which the initial perturbation arises from the matter as well as from the scalar field itself, provided that the initial value of the gauge invariant curvature is zero. We extend the standard code to include all these cases, and we show some results concerning the power spectrum of the cosmic microwave background temperature anisotropies. In particular, it turns out that the acoustic peaks follow opposite behaviours in...
Scalar perturbations in two-temperature cosmological plasmas
Moortgat, J.B.; Marklund, M.
2006-01-01
We study the properties of density perturbations of a two-component plasma with a temperature difference on a homogeneous and isotropic background. For this purpose, we extend the general relativistic gauge-invariant and covariant (GIC) perturbation theory to include a multifluid with a particular e
Holographic curvature perturbations in a cosmology with a space-like singularity
Energy Technology Data Exchange (ETDEWEB)
Ferreira, Elisa G.M. [Department of Physics, McGill University,3600 University St., Montréal, QC, H3A 2T8 (Canada); Brandenberger, Robert [Department of Physics, McGill University,3600 University St., Montréal, QC, H3A 2T8 (Canada); Institute for Theoretical Studies, ETH Zürich,Clausiusstr. 47, Zürich, CH-8092 (Switzerland)
2016-07-19
We study the evolution of cosmological perturbations in an anti-de-Sitter (AdS) bulk through a cosmological singularity by mapping the dynamics onto the boundary conformal fields theory by means of the AdS/CFT correspondence. We consider a deformed AdS space-time obtained by considering a time-dependent dilaton which induces a curvature singularity in the bulk at a time which we call t=0, and which asymptotically approaches AdS both for large positive and negative times. The boundary field theory becomes free when the bulk curvature goes to infinity. Hence, the evolution of the fluctuations is under better controle on the boundary than in the bulk. To avoid unbounded particle production across the bounce it is necessary to smooth out the curvature singularity at very high curvatures. We show how the bulk cosmological perturbations can be mapped onto boundary gauge field fluctuations. We evolve the latter and compare the spectrum of fluctuations on the infrared scales relevant for cosmological observations before and after the bounce point. We find that the index of the power spectrum of fluctuations is the same before and after the bounce.
Can superhorizon cosmological perturbations explain the acceleration of the universe?
Hirata, C M; Hirata, Christopher M.; Seljak, Uros
2005-01-01
We investigate the recent suggestions by Barausse et al. (astro-ph/0501152) and Kolb et al. (hep-th/0503117) that the acceleration of the universe could be explained by large superhorizon fluctuations generated by inflation. We show that no acceleration can be produced by this mechanism. We begin by showing how the application of Raychaudhuri equation to inhomogeneous cosmologies results in several ``no go'' theorems for accelerated expansion. Next we derive an exact solution for a specific case of initial perturbations, for which application of the Kolb et al. expressions leads to an acceleration, while the exact solution reveals that no acceleration is present. We show that the discrepancy can be traced to higher order terms that were dropped in the Kolb et al. analysis. We proceed with the analysis of initial value formulation of general relativity to argue that causality severely limits what observable effects can be derived from superhorizon perturbations. By constructing a Riemann normal coordinate syst...
Shortcomings in the Understanding of Why Cosmological Perturbations Look Classical
Sudarsky, Daniel
2009-01-01
There is a persistent state of confusion regarding the account of the quantum origin of the seeds of cosmological structure during inflation. In fact, a recent article (C. Kiefer & D. Polarski, ArXiv: 0810.0087 [astro-ph]) addresses the question "Why do the Cosmological Perturbations look Classical?" and offers an answer based on unitary quantum mechanics (i.e., without reference to the projection postulate) relying on the decoherence type of analysis. The argument is, thus, implicitly assuming that decoherence offers a satisfactory solution to the measurement problem in quantum mechanics. We will review here, why do we, together with various other researchers in the field, consider that this is not the case, in general, and particularly not at all in the situation at hand. In fact, as has been previously discussed (A. Perez, H. Sahlmann, and D. Sudarsky, CQG 23, 2317, (2006);[arXiv: gr-qc/0508100]), we will argue that the cosmological situation is one where the measurement problem of quantum mechanics ap...
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.
Testing gauge-invariant perturbation theory
Törek, Pascal
2016-01-01
Gauge-invariant perturbation theory for theories with a Brout-Englert-Higgs effect, as developed by Fr\\"ohlich, Morchio and Strocchi, starts out from physical, exactly gauge-invariant quantities as initial and final states. These are composite operators, and can thus be considered as bound states. In case of the standard model, this reduces almost entirely to conventional perturbation theory. This explains the success of conventional perturbation theory for the standard model. However, this is due to the special structure of the standard model, and it is not guaranteed to be the case for other theories. Here, we review gauge-invariant perturbation theory. Especially, we show how it can be applied and that it is little more complicated than conventional perturbation theory, and that it is often possible to utilize existing results of conventional perturbation theory. Finally, we present tests of the predictions of gauge-invariant perturbation theory, using lattice gauge theory, in three different settings. In ...
Kurtosis, skewness, and non-Gaussian cosmological density perturbations
Luo, Xiaochun; Schramm, David N.
1993-01-01
Cosmological topological defects as well as some nonstandard inflation models can give rise to non-Gaussian density perturbations. Skewness and kurtosis are the third and fourth moments that measure the deviation of a distribution from a Gaussian. Measurement of these moments for the cosmological density field and for the microwave background temperature anisotropy can provide a test of the Gaussian nature of the primordial fluctuation spectrum. In the case of the density field, the importance of measuring the kurtosis is stressed since it will be preserved through the weakly nonlinear gravitational evolution epoch. Current constraints on skewness and kurtosis of primeval perturbations are obtained from the observed density contrast on small scales and from recent COBE observations of temperature anisotropies on large scales. It is also shown how, in principle, future microwave anisotropy experiments might be able to reveal the initial skewness and kurtosis. It is shown that present data argue that if the initial spectrum is adiabatic, then it is probably Gaussian, but non-Gaussian isocurvature fluctuations are still allowed, and these are what topological defects provide.
New Cosmological Solutions in Massive Gravity Theory
Pinho, S. S. A.; Pereira, S. H.; Mendonça, E. L.
2017-04-01
In this paper we present some new cosmological solutions in massive gravity theory. Some homogeneous and isotropic solutions correctly describe accelerated evolutions for the universe. The study was realized considering a specific form to the fiducial metric and found different functions and constant parameters of the theory that guarantee the conservation of the energy momentum tensor. Several accelerating cosmologies were found, all of them reproducing a cosmological constant term proportional to the graviton mass, with a de Sitter type solution for the scale factor. We have also verified that when the fiducial metric is close to the physical metric the solutions are absent, except for some specific open cases.
Inflaton perturbations in brane-world cosmology with induced gravity
Koyama, K; Koyama, Kazuya; Mizuno, Shuntaro
2006-01-01
We study cosmological perturbations in the brane models with an induced Einstein-Hilbert term on a brane. We consider an inflaton confined to a de Sitter brane in a five-dimensional Minkowski spacetime. Inflaton fluctuations excite Kaluza-Klein modes of bulk metric perturbations with mass $m^2 = -2(2\\ell-1) (\\ell +1) H^2$ and $m^2 = -2\\ell(2\\ell+3) H^2$ where $\\ell$ is an integer. There are two branches ($\\pm$ branches) of solutions for the background spacetime. In the $+$ branch, which includes the self-accelerating universe, a resonance appears for a mode with $m^2 = 2 H^2$ due to a spin-0 perturbation with $m^2 = 2H^2$. The self-accelerating universe has a distinct feature because there is also a helicity-0 mode of spin-2 perturbations with $m^2 = 2H^2$. In the $-$ branch, which can be thought as the Randall-Sundrum type brane-world with the high energy quantum corrections, there is no resonance. At high energies, we analytically confirm that four-dimensional Einstein gravity is recovered, which is related...
Evolution of curvature perturbation in generalized gravity theories
Energy Technology Data Exchange (ETDEWEB)
Matsuda, Tomohiro, E-mail: matsuda@sit.ac.j [Laboratory of Physics, Saitama Institute of Technology, Fusaiji, Okabe-machi, Saitama 369-0293 (Japan)
2009-07-21
Using the cosmological perturbation theory in terms of the deltaN formalism, we find the simple formulation of the evolution of the curvature perturbation in generalized gravity theories. Compared with the standard gravity theory, a crucial difference appears in the end-boundary of the inflationary stage, which is due to the non-ideal form of the energy-momentum tensor that depends explicitly on the curvature scalar. Recent study shows that ultraviolet-complete quantum theory of gravity (Horava-Lifshitz gravity) can be approximated by using a generalized gravity action. Our paper may give an important step in understanding the evolution of the curvature perturbation during inflation, where the energy-momentum tensor may not be given by the ideal form due to the corrections from the fundamental theory.
Wavefunction of the Universe and Chern-Simons perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Soo Chopin [Department of Physics, National Cheng Kung University Tainan 70101, Taiwan (China)
2002-03-21
The Chern-Simons exact solution of four-dimensional quantum gravity with nonvanishing cosmological constant is presented in metric variables as the partition function of Chern-Simons theory with nontrivial source. The perturbative expansion is given, and the wavefunction is computed to the lowest order of approximation for the Cauchy surface which is topologically a 3-sphere. The state is well-defined even at degenerate and vanishing values of the dreibein. Reality conditions for the Ashtekar variables are also taken into account, and remarkable features of the Chern-Simons state and their relevance to cosmology are pointed out.
Gauge theories in local causal perturbation theory
Boas, F M
1999-01-01
In this thesis quantum gauge theories are considered in the framework of local, causal perturbation theory. Gauge invariance is described in terms of the BRS formalism. Local interacting field operators are constructed perturbatively and field equations are established. A nilpotent BRS transformation is defined on the local algebra of fields. It allows the definition of the algebra of local observables as an operator cohomology. This algebra of local observables can be represented in a Hilbert space. The interacting field operators are defined in terms of time ordered products of free field operators. For the results above to hold the time ordered products must satisfy certain normalization conditions. To formulate these conditions also for field operators that contain a spacetime derivative a suitable mathematical description of time ordered products is developed. Among the normalization conditions are Ward identities for the ghost current and the BRS current. The latter are generalizations of a normalizatio...
Eikonal perturbation theory in photoionization
Cajiao Vélez, F.; Krajewska, K.; Kamiński, J. Z.
2016-02-01
The eikonal perturbation theory is formulated and applied to photoionization by strong laser pulses. A special emphasis is put on the first order approximation with respect to the binding potential, which is known as the generalized eikonal approximation [2015 Phys. Rev. A 91 053417]. The ordinary eikonal approximation and its domain of applicability is derived from the generalized eikonal approximation. While the former approach is singular for the electron trajectories which return to the potential center, the generalized eikonal avoids this problem. This property makes it a promising tool for further investigations of rescattering and high-order harmonic generation processes.
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...
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.
The effective field theory of cosmological large scale structures
Energy Technology Data Exchange (ETDEWEB)
Carrasco, John Joseph M. [Stanford Univ., Stanford, CA (United States); Hertzberg, Mark P. [Stanford Univ., Stanford, CA (United States); SLAC National Accelerator Lab., Menlo Park, CA (United States); Senatore, Leonardo [Stanford Univ., Stanford, CA (United States); SLAC National Accelerator Lab., Menlo Park, CA (United States)
2012-09-20
Large scale structure surveys will likely become the next leading cosmological probe. In our universe, matter perturbations are large on short distances and small at long scales, i.e. strongly coupled in the UV and weakly coupled in the IR. To make precise analytical predictions on large scales, we develop an effective field theory formulated in terms of an IR effective fluid characterized by several parameters, such as speed of sound and viscosity. These parameters, determined by the UV physics described by the Boltzmann equation, are measured from N-body simulations. We find that the speed of sound of the effective fluid is c^{2}_{s} ≈ 10^{–6}c^{2} and that the viscosity contributions are of the same order. The fluid describes all the relevant physics at long scales k and permits a manifestly convergent perturbative expansion in the size of the matter perturbations δ(k) for all the observables. As an example, we calculate the correction to the power spectrum at order δ(k)^{4}. As a result, the predictions of the effective field theory are found to be in much better agreement with observation than standard cosmological perturbation theory, already reaching percent precision at this order up to a relatively short scale k ≃ 0.24h Mpc^{–1}.
String Theory and Primordial Cosmology
Gasperini, Maurizio
String cosmology aims at providing a reliable description of the very early Universe in the regime where standard-model physics is no longer appropriate, and where we can safely apply the basic ingredients of superstring models such as dilatonic and axionic forces, duality symmetries, winding modes, limiting sizes and curvatures, higher dimensional interactions among elementary extended object. The sought target is that of resolving (or at least alleviating) the big problems of standard and inflationary cosmology like the spacetime singularity, the physics of the trans-Planckian regime, the initial condition for inflation, and so on.
String theory and primordial cosmology
Gasperini, M
2014-01-01
String cosmology aims at providing a reliable description of the very early Universe in the regime where standard-model physics is no longer appropriate, and where we can safely apply the basic ingredients of superstring models such as dilatonic and axionic forces, duality symmetries, winding modes, limiting sizes and curvatures, higher-dimensional interactions among elementary extended object. The sought target is that of resolving (or at least alleviating) the big problems of standard and inflationary cosmology like the space-time singularity, the physics of the trans-Planckian regime, the initial condition for inflation, and so on.
Cosmological Electromagnetic Fields due to Gravitational Wave Perturbations
Marklund, M; Brodin, G; Marklund, Mattias; Dunsby, Peter K. S.; Brodin, Gert
2000-01-01
We consider the dynamics of electromagnetic fields in an almost-Friedmann-Robertson-Walker universe using the covariant and gauge-invariant approach of Ellis and Bruni. Focusing on the situation where deviations from the background model are generated by tensor perturbations only, we demonstrate that the coupling between gravitational waves and a weak magnetic test field can generate electromagnetic waves. We show that this coupling leads to an initial pulse of electromagnetic waves whose width and amplitude is determined by the wavelengths of the magnetic field and gravitational waves. A number of implications for cosmology are discussed, in particular we calculate an upper bound of the magnitude of this effect using limits on the quadrapole anisotropy of the Cosmic Microwave Background.
Adiabatic density perturbations in a cosmological model with massive neutrinos
Jaroszynski, M.
Lifshitz (1946) has investigated the gravitational instability of a Friedmann Universe model. He treated the matter content of the universe as a single perfect fluid. In other studies, a two fluid approach was used to represent neutrinos and other kinds of matter separately. A distribution function was used by Peebles and Yu (1970), and also by Silk and Wilson (1980) to describe photons of the black-body background during and after the recombination of the primeval plasma. The approach used in the present investigation is similar, except for two differences. No collisional term is used in the kinetic equation, and massive particles are considered. A detailed description is provided of the method used to investigate the gravitational instability of a cosmological model with massive neutrinos. It is pointed out that the obtained results are preliminary. The final spectrum of perturbations is similar to those of Peebles and Yu (1970), and Wilson and Silk (1981).
Geometric Hamiltonian structures and perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Omohundro, S.
1984-08-01
We have been engaged in a program of investigating the Hamiltonian structure of the various perturbation theories used in practice. We describe the geometry of a Hamiltonian structure for non-singular perturbation theory applied to Hamiltonian systems on symplectic manifolds and the connection with singular perturbation techniques based on the method of averaging.
Covariant Hořava-like and mimetic Horndeski gravity: cosmological solutions and perturbations
Cognola, Guido; Myrzakulov, Ratbay; Sebastiani, Lorenzo; Vagnozzi, Sunny; Zerbini, Sergio
2016-11-01
We consider a variant of the Nojiri–Odintsov covariant Hořava-like gravitational model, where diffeomorphism invariance is broken dynamically via a non-standard coupling to a perfect fluid. The theory allows one to address some of the potential instability problems present in Hořava–Lifshitz gravity due to explicit diffeomorphism invariance breaking. The fluid is instead constructed from a scalar field constrained by a Lagrange multiplier. In fact, the Lagrange multiplier construction allows for an extension of the Hořava-like model to include the scalar field of mimetic gravity, an extension which we thoroughly explore. By adding a potential for the scalar field, we show how one can reproduce a number of interesting cosmological scenarios. We then turn to the study of perturbations around a flat FLRW background, showing that the fluid in question behaves as an irrotational fluid, with zero sound speed. To address this problem, we consider a modified version of the theory, adding higher derivative terms in a way which brings us beyond the Horndeski framework. We compute the sound speed in this modified higher order mimetic Hořava-like model and show that it is non-zero, which means that perturbations therein can be sensibly defined. Caveats to our analysis, as well as comparisons to projectable Hořava–Lifshitz gravity, are also discussed. In conclusion, we present a theory of gravity which preserves diffeomorphism invariance at the level of the action but breaks it dynamically in the UV, reduces to General Relativity (GR) in the IR, allows the realization of a number of interesting cosmological scenarios, is well defined when considering perturbations around a flat FLRW background, and features cosmological dark matter emerging as an integration constant.
Perturbation theory and renormalisation group equations
Litim, Daniel F; Litim, Daniel F.; Pawlowski, Jan M.
2002-01-01
We discuss the perturbative expansion of several one-loop improved renormalisation group equations. It is shown that in general the integrated renormalisation group flows fail to reproduce perturbation theory beyond one loop.
Models for the Brane-Bulk Interaction: Toward Understanding Braneworld Cosmological Perturbation
Binétruy, Pierre; Carvalho, Carla
2004-01-01
Using some simple toy models, we explore the nature of the brane-bulk interaction for cosmological models with a large extra dimension. We are in particular interested in understanding the role of the bulk gravitons, which from the point of view of an observer on the brane will appear to generate dissipation and nonlocality, effects which cannot be incorporated into an effective (3+1)-dimensional Lagrangian field theoretic description. We explicitly work out the dynamics of several discrete systems consisting of a finite number of degrees of freedom on the boundary coupled to a (1+1)-dimensional field theory subject to a variety of wave equations. Systems both with and without time translation invariance are considered and moving boundaries are discussed as well. The models considered contain all the qualitative feature of quantized linearized cosmological perturbations for a Randall-Sundrum universe having an arbitrary expansion history, with the sole exception of gravitational gauge invariance, which will b...
Cosmology on all scales: a two-parameter perturbation expansion
Goldberg, Sophia R; Malik, Karim A
2016-01-01
We propose and construct a two-parameter perturbative expansion around a Friedmann-Lema\\^{i}tre-Robertson-Walker geometry that can be used to model high-order gravitational effects in the presence of non-linear structure. This framework reduces to the weak-field and slow-motion post-Newtonian treatment of gravity in the appropriate limits, but also includes the low-amplitude large-scale fluctuations that are important for cosmological modelling. We derive a set of field equations that can be applied to the late Universe, where non-linear structure exists on supercluster scales, and perform a detailed investigation of the associated gauge problem. This allows us to identify a consistent set of perturbed quantities in both the gravitational and matter sectors, and to construct a set of gauge-invariant quantities that correspond to each of them. The field equations, written in terms of these quantities, take on a relatively simple form, and allow the effects of small-scale structure on the large-scale properties...
Gauge-ready formulation of the cosmological kinetic theory in generalized gravity theories
Hwang, J
2002-01-01
We present cosmological perturbations of kinetic components based on relativistic Boltzmann equations in the context of generalized gravity theories. Our general theory considers an arbitrary number of scalar fields generally coupled with the gravity, an arbitrary number of mutually interacting hydrodynamic fluids, and components described by the relativistic Boltzmann equations like massive/massless collisionless particles and the photon. The model includes the general background spatial curvature and the cosmological constant. We consider three different types of perturbations, and all the scalar-type perturbation equations are arranged in a gauge-ready form so that one can implement easily the convenient gauge conditions depending on the situation. In the numerical calculation of the Boltzmann equations we found two new gauge conditions (the uniform-expansion gauge and the uniform-curvature gauge) which show better behavior than the previously employed gauge conditions in the literature. In particular, we ...
TASI lectures on cosmological observables and string theory
Silverstein, Eva
2016-01-01
These lectures provide an updated pedagogical treatment of the theoretical structure and phenomenology of some basic mechanisms for inflation, along with an overview of the structure of cosmological uplifts of holographic duality. A full treatment of the problem requires `ultraviolet completion' because of the sensitivity of inflation to quantum gravity effects, including back reaction and non-adiabatic production of heavy degrees of freedom. Cosmological observations imply accelerated expansion of the late universe, and provide increasingly precise constraints and discovery potential on the amplitude and shape of primordial tensor and scalar perturbations, and some of their correlation functions. Most backgrounds of string theory have positive potential energy, with a rich but still highly constrained landscape of solutions. The theory contains novel mechanisms for inflation, some subject to significant observational tests. Although the detailed ultraviolet completion is not accessible experimentally, some o...
Non-Perturbative Theory of Dispersion Interactions
Boström, M; Persson, C; Parsons, D F; Buhmann, S Y; Brevik, I; Sernelius, Bo E
2015-01-01
Some open questions exist with fluctuation-induced forces between extended dipoles. Conventional intuition derives from large-separation perturbative approximations to dispersion force theory. Here we present a full non-perturbative theory. In addition we discuss how one can take into account finite dipole size corrections. It is of fundamental value to investigate the limits of validity of the perturbative dispersion force theory.
Tensor perturbations in a general class of Palatini theories
Jiménez, Jose Beltrán; Olmo, Gonzalo J
2015-01-01
We study a general class of gravitational theories formulated in the Palatini approach and derive the equations governing the evolution of tensor perturbations. In the absence of torsion, the connection can be solved as the Christoffel symbols of an auxiliary metric which is non-trivially related to the space-time metric. We then consider background solutions corresponding to a perfect fluid and show that the tensor perturbations equations (including anisotropic stresses) for the auxiliary metric around such a background take an Einstein-like form. This facilitates the study in a homogeneous and isotropic cosmological scenario where we explicitly establish the relation between the auxiliary metric and the space-time metric tensor perturbations. As a general result, we show that both tensor perturbations coincide in the absence of anisotropic stresses.
Tensor perturbations in a general class of Palatini theories
Beltrán Jiménez, Jose; Heisenberg, Lavinia; Olmo, Gonzalo J.
2015-06-01
We study a general class of gravitational theories formulated in the Palatini approach and derive the equations governing the evolution of tensor perturbations. In the absence of torsion, the connection can be solved as the Christoffel symbols of an auxiliary metric which is non-trivially related to the space-time metric. We then consider background solutions corresponding to a perfect fluid and show that the tensor perturbations equations (including anisotropic stresses) for the auxiliary metric around such a background take an Einstein-like form. This facilitates the study in a homogeneous and isotropic cosmological scenario where we explicitly establish the relation between the auxiliary metric and the space-time metric tensor perturbations. As a general result, we show that both tensor perturbations coincide in the absence of anisotropic stresses.
Cosmological horizons and reconstruction of quantum field theories
Energy Technology Data Exchange (ETDEWEB)
Dappiaggi, C.; Pinamonti, N. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik]|[Trento Univ., Povo (Italy). Istituto Nazionale di Alta Matematica ' ' F. Severi' ' - GNFM; Moretti, V. [Trento Univ. (Italy). Dipt. di Matematica]|[Istituto Nazionale di Fisica Nucleare - Gruppo Collegato di Trento, Povo (Italy)
2007-12-15
As a starting point for this manuscript, we remark how the cosmological horizon of a certain class of Friedmann-Robertson-Walker backgrounds shares some non trivial geometric properties with null infinity in an asymptotically flat spacetime. Such a feature is generalized to a larger class of expanding spacetimes M admitting a geodesically complete cosmological horizon J{sup -} common to all co-moving observers. This property is later exploited in order to recast, in a cosmological background, some recent results for a linear scalar quantum field theory in spacetimes asymptotically flat at null infinity. Under suitable hypotheses on M - valid for de Sitter spacetime and some other FRW spacetimes obtained by perturbing deSitter space - the algebra of observables for a Klein-Gordon field is mapped into a subalgebra of the algebra of observables W(J{sup -}) constructed on the cosmological horizon. There is exactly one pure quasifree state {lambda} on W(J{sup -}) which fulfills a suitable energy positivity condition with respect to a generator related with the cosmological time displacements. Furthermore {lambda} induces a preferred physically meaningful quantum state {lambda}{sub M} for the quantum theory in the bulk. If M admits a timelike Killing generator preserving J{sup -}, then the associated self-adjoint generator in the GNS representation of {lambda}{sub M} has positive spectrum (i.e. energy). Moreover {lambda}{sub M} turns out to be invariant under every symmetry of the bulk metric which preserves the cosmological horizon. In the case of an expanding de Sitter spacetime, {lambda}{sub M} coincides with the Euclidean (Bunch-Davies) vacuum state, hence being Hadamard in this case. Remarks on the validity of the Hadamard property for {lambda}{sub M} in more general spacetimes are presented. (orig.)
Cosmological perturbations of self-accelerating universe in nonlinear massive gravity
Gumrukcuoglu, A Emir; Mukohyama, Shinji
2011-01-01
We study cosmological perturbations of self-accelerating universe solutions in the recently proposed nonlinear theory of massive gravity, with general matter content. While the broken diffeomorphism invariance implies that there generically are 2 tensor, 2 vector and 2 scalar degrees of freedom in the gravity sector, we find that the scalar and vector degrees have vanishing kinetic terms and nonzero mass terms. Depending on their nonlinear behavior, this indicates either nondynamical nature of these degrees or strong couplings. Assuming the former, we integrate out the 2 vector and 2 scalar degrees of freedom. We then find that in the scalar and vector sectors, gauge-invariant variables constructed from metric and matter perturbations have exactly the same quadratic action as in general relativity. The difference from general relativity arises only in the tensor sector, where the graviton mass modifies the dispersion relation of gravitational waves, with a time-dependent effective mass. This may lead to modif...
Cosmological $N$-body simulations including radiation perturbations
Brandbyge, Jacob; Tram, Thomas; Leclercq, Florent; Fidler, Christian; Hannestad, Steen
2016-01-01
Cosmological $N$-body simulations are the standard tool to study the emergence of the observed large-scale structure of the Universe. Such simulations usually solve for the gravitational dynamics of matter within the Newtonian approximation, thus discarding general relativistic effects such as the coupling between matter and radiation ($\\equiv$ photons and neutrinos). In this paper we investigate novel hybrid simulations which incorporate interactions between radiation and matter to the leading order in General Relativity, whilst evolving the matter dynamics in full non-linearity according to Newtonian theory. Our hybrid simulations come with a relativistic space-time and make it possible to investigate structure formation in a unified framework. In the present work we focus on simulations initialized at $z=99$, and show that the extracted matter power spectrum receives up to $3\\%$ corrections on very large scales through radiation. Our numerical findings compare favourably with linear analytical results from...
A Cosmological Study in Massive Gravity theory
Pan, Supriya
2015-01-01
A detailed study of the various cosmological aspects in massive gravity theory has been presented in the present work. For the homogeneous and isotropic FLRW model, the deceleration parameter has been evaluated, and, it has been examined whether there is any transition from deceleration to acceleration in recent past, or not. With the proper choice of the free parameters, it has been shown that the massive gravity theory is equivalent to Einstein gravity with a modified Newtonian gravitational constant together with a negative cosmological constant. Also, in this context, it has been examined whether the emergent scenario is possible, or not, in massive gravity theory. Finally, we have done a cosmographic analysis in massive gravity theory.
String Theory, Cosmology And Brany Geometry
Pokotilov, A
2005-01-01
Motivated by cosmological applications in this thesis we describe several string theory based models of the early Universe. The major property of these models is that they lead to inflationary-like expansion for early times. The interaction properties of fundamental strings, leading to the velocity dependent potentials are used to describe this accelerating expansion rate. Other types of extended objects such as fivebranes dual to fundamental strings are shown to lead to the similar cosmological implications. Our findings are consistent with recent astronomical observations of an accelerated expansion of the Universe and predict an asymptotically constant late time expansion rate.
The ambiguity in ray perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Snieder, R.; Sambridge, M. [Utrecht Univ., Utrecht (Netherlands)]|[Cambridge Univ., Cambridge (United Kingdom)
1993-12-01
Ray perturbation theory is concerned with the change in ray paths and travel times due to changes in the slowness model or the end-point conditions of rays. Several different formulations of ray perturbation theory have been developed. Even for the same physical problem different perturbation equations have been derived. The reason for this is that ray perturbation theory contains a fundamental ambiguity. One can move a point along a curve without changing the shape of the curve. This means that the mapping from a reference curve to a perturbed curve is not uniquely defined, because on may associated a point on the reference curve with different points on the perturbed curve. The mapping that is used is usually defined implicitly by the choice of the coordinate system or the independent parameter. In this paper, a fomalism is developed where one can specify explicitly the mapping from the reference curve to the perturbed curve by choosing a stretch factor that relates increments in arc length along the reference curve and the perturbed curve. This is incorporated in a theory that is accurate to first order in the ray position and to second order in the travel time. The second order travel time perturbation describes the effect of changes in the position of the ray on the travel time. In the formulation of this paper, paraxial ray perturbations, slowness perturbations, and pure ray bending are treated in a uniform fashion. This may be very useful in nonlinear tomographic inversions which include earthquake relocation.
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.
Perturbation theory in light-cone quantization
Energy Technology Data Exchange (ETDEWEB)
Langnau, A.
1992-01-01
A thorough investigation of light-cone properties which are characteristic for higher dimensions is very important. The easiest way of addressing these issues is by analyzing the perturbative structure of light-cone field theories first. Perturbative studies cannot be substituted for an analysis of problems related to a nonperturbative approach. However, in order to lay down groundwork for upcoming nonperturbative studies, it is indispensable to validate the renormalization methods at the perturbative level, i.e., to gain control over the perturbative treatment first. A clear understanding of divergences in perturbation theory, as well as their numerical treatment, is a necessary first step towards formulating such a program. The first objective of this dissertation is to clarify this issue, at least in second and fourth-order in perturbation theory. The work in this dissertation can provide guidance for the choice of counterterms in Discrete Light-Cone Quantization or the Tamm-Dancoff approach. A second objective of this work is the study of light-cone perturbation theory as a competitive tool for conducting perturbative Feynman diagram calculations. Feynman perturbation theory has become the most practical tool for computing cross sections in high energy physics and other physical properties of field theory. Although this standard covariant method has been applied to a great range of problems, computations beyond one-loop corrections are very difficult. Because of the algebraic complexity of the Feynman calculations in higher-order perturbation theory, it is desirable to automatize Feynman diagram calculations so that algebraic manipulation programs can carry out almost the entire calculation. This thesis presents a step in this direction. The technique we are elaborating on here is known as light-cone perturbation theory.
TASI Lectures on Cosmological Observables and String Theory
Silverstein, Eva
These lectures provide an updated pedagogical treatment of the theoretical structure and phenomenology of some basic mechanisms for inflation, along with an overview of the structure of cosmological uplifts of holographic duality. A full treatment of the problem requires `ultraviolet completion' because of the sensitivity of inflation to quantum gravity effects, including back reaction and non-adiabatic production of heavy degrees of freedom. Cosmological observations imply accelerated expansion of the late universe, and provide increasingly precise constraints and discovery potential on the amplitude and shape of primordial tensor and scalar perturbations, and some of their correlation functions. Most backgrounds of string theory have positive potential energy, with a rich but still highly constrained landscape of solutions. The theory contains novel mechanisms for inflation, some subject to significant observational tests, with highly UV-sensitive tensor mode measurements being a prime example along with certain shapes of primordial correlation functions. Although the detailed ultraviolet completion is not accessible experimentally, some of these mechanisms directly stimulate a more systematic analysis of the space of low energy theories and signatures relevant for analysis of data, which is sensitive to physics orders of magnitude above the energy scale of inflation as a result of long time evolution (dangerous irrelevance) and the substantial amount of data (allowing constraints on quantities with signal/noise. Portions of these lectures appeared previously in Les Houches 2013, "Post-Planck Cosmology".
Perturbative spacetimes from Yang-Mills theory
Luna, Andrés; Nicholson, Isobel; Ochirov, Alexander; O'Connell, Donal; Westerberg, Niclas; White, Chris D.
2017-04-12
The double copy relates scattering amplitudes in gauge and gravity theories. In this paper, we expand the scope of the double copy to construct spacetime metrics through a systematic perturbative expansion. The perturbative procedure is based on direct calculation in Yang-Mills theory, followed by squaring the numerator of certain perturbative diagrams as specified by the double-copy algorithm. The simplest spherically symmetric, stationary spacetime from the point of view of this procedure is a particular member of the Janis-Newman-Winicour family of naked singularities. Our work paves the way for applications of the double copy to physically interesting problems such as perturbative black-hole scattering.
Perturbative spacetimes from Yang-Mills theory
Luna, Andres; Nicholson, Isobel; Ochirov, Alexander; O'Connell, Donal; Westerberg, Niclas; White, Chris D.
2016-01-01
The double copy relates scattering amplitudes in gauge and gravity theories. In this paper, we expand the scope of the double copy to construct spacetime metrics through a systematic perturbative expansion. The perturbative procedure is based on direct calculation in Yang-Mills theory, followed by squaring the numerator of certain perturbative diagrams as specified by the double-copy algorithm. The simplest spherically symmetric, stationary spacetime from the point of view of this procedure is a particular member of the Janis-Newman-Winicour family of naked singularities. Our work paves the way for applications of the double copy to physically interesting problems such as perturbative black-hole scattering.
Cognola, Guido; Sebastiani, Lorenzo; Vagnozzi, Sunny; Zerbini, Sergio
2016-01-01
We consider the Nojiri-Odintsov covariant Horava-like gravitational model, where diffeomorphism invariance is broken dynamically via a non-standard coupling to a perfect fluid. The theory allows to address some of the potential instability problems present in Horava-Lifshitz gravity due to explicit diffeomorphism invariance breaking. The fluid is instead constructed from a scalar field constrained by a Lagrange multiplier. This construction allows to identify the scalar field with the mimetic field of the recently proposed mimetic gravity. Subsequently, we thoroughly explore the consequences of this identification. By adding a potential for the scalar field, we show how one can reproduce a number of interesting cosmological scenarios. We then turn to the study of perturbations around a flat FLRW background, showing that the fluid in question behaves as an irrotational fluid, with zero sound speed. To address this problem, we consider a modified version of the theory, adding higher derivative terms in a way wh...
General degeneracy in density functional perturbation theory
Palenik, Mark C
2016-01-01
Degenerate perturbation theory from quantum mechanics is inadequate in density functional theory (DFT) because of nonlinearity in the Kohn-Sham potential. We develop the fully general degenerate perturbation theory for DFT without assuming that the degeneracy is required by symmetry. The resulting methodology is applied to the iron atom ground state in order to demonstrate the effects of degeneracy that appears both due to symmetry requirements and accidentally, between different representations of the symmetry group.
Quantitative methods in classical perturbation theory.
Giorgilli, A.
Poincaré proved that the series commonly used in Celestial mechanics are typically non convergent, although their usefulness is generally evident. Recent work in perturbation theory has enlightened this conjecture of Poincaré, bringing into evidence that the series of perturbation theory, although non convergent in general, furnish nevertheless valuable approximations to the true orbits for a very large time, which in some practical cases could be comparable with the age of the universe. The aim of the author's paper is to introduce the quantitative methods of perturbation theory which allow to obtain such powerful results.
On the conservation of second-order cosmological perturbations in a scalar field dominated universe
Vernizzi, F
2005-01-01
We discuss second-order cosmological perturbations on super-Hubble scales, in a scalar field dominated universe, such as during single field inflation. In this contest we show that the gauge-invariant curvature perturbations defined on the uniform density and comoving hypersurfaces coincide and that perturbations are adiabatic in the large scale limit. Since it has been recently shown that the uniform curvature perturbation is conserved on large scales if perturbations are adiabatic, we conclude that both the uniform and comoving curvature perturbations at second-order in a scalar field dominated universe are conserved.
String theory and cosmological singularities
Indian Academy of Sciences (India)
Sumit R Das
2007-07-01
In general relativity space-like or null singularities are common: they imply that `time' can have a beginning or end. Well-known examples are singularities inside black holes and initial or final singularities in expanding or contracting universes. In recent times, string theory is providing new perspectives of such singularities which may lead to an understanding of these in the standard framework of time evolution in quantum mechanics. In this article, we describe some of these approaches.
Perturbative Chern-Simons theory revisited
DEFF Research Database (Denmark)
McLellan, Brendan Donald Kenneth
2013-01-01
We reconsider perturbative Chern-Simons theory on a closed and oriented three-manifold with a choice of contact structure following C. Beasley and E. Witten. Closed three manifolds that admit a Sasakian structure are explicitly computed to first order in perturbation in terms of their Seifert dat...
Heckman, Jonathan J.; Tavanfar, Alireza; Vafa, Cumrun
2010-04-01
In this paper we study the interplay between the recently proposed F-theory GUTs and cosmology. Despite the fact that the parameter range for F-theory GUT models is very narrow, we find that F-theory GUTs beautifully satisfy most cosmological constraints without any further restrictions. The viability of the scenario hinges on the interplay between various components of the axion supermultiplet, which in F-theory GUTs is also responsible for breaking supersymmetry. In these models, the gravitino is the LSP and develops a mass by eating the axino mode. The radial component of the axion supermultiplet known as the saxion typically begins to oscillate in the early Universe, eventually coming to dominate the energy density. Its decay reheats the Universe to a temperature of ˜1GeV, igniting BBN and diluting all thermal relics such as the gravitino by a factor of ˜10-4 - 10-5 such that gravitinos contribute a sizable component of the dark matter. In certain cases, non-thermally produced relics such as the axion, or gravitinos generated from the decay of the saxion can also contribute to the abundance of dark matter. Remarkably enough, this cosmological scenario turns out to be independent of the initial reheating temperature of the Universe. This is due to the fact that the initial oscillation temperature of the saxion coincides with the freeze out temperature for gravitinos in F-theory GUTs. We also find that saxion dilution is compatible with generating the desired baryon asymmetry from standard leptogenesis. Finally, the gravitino mass range in F-theory GUTs is 10 - 100MeV, which interestingly coincides with the window of values required for the decay of the NLSP to solve the problem of 7 Li over-production.
Late time behavior of cosmological perturbations in a single brane model
Koyama, K
2004-01-01
We present solutions for the late time evolution of cosmological tensor and scalar perturbations in a single Randall-Sundrum brane world model. Assuming that the bulk is Anti-de Sitter spacetime, the solutions for cosmological perturbations are derived by summing up mode functions in Poincar\\'e coordinate. The junction conditions imposed at the moving brane are solved numerically. The recovery of 4-dimensional Einstein gravity at late times is shown by solving the 5-dimensional perturbations throughout the infinite bulk. We also comment on several possibilities to have deviations from 4-dimensional Einstein gravity.
Interaction Between Massive and Massless Gravitons by Perturbing Topological Field Theory
Institute of Scientific and Technical Information of China (English)
E. Koorambas
2012-01-01
We test the Wu gauge theory of gravity with massive gravitons in the perturbing topological field theory framework. We show that the computation of the correlation function between massive and massless gravitons is reported up to 4-loop and appears to be unaffected by radiative correction. This result ensures the stability of the linking number between massive and massless gravitons with respect to the local perturbation, a result with potential wider applications in cosmology.
Anisotropic cosmological solutions in massive vector theories
Heisenberg, Lavinia; Kase, Ryotaro; Tsujikawa, Shinji
2016-11-01
In beyond-generalized Proca theories including the extension to theories higher than second order, we study the role of a spatial component v of a massive vector field on the anisotropic cosmological background. We show that, as in the case of the isotropic cosmological background, there is no additional ghostly degrees of freedom associated with the Ostrogradski instability. In second-order generalized Proca theories we find the existence of anisotropic solutions on which the ratio between the anisotropic expansion rate Σ and the isotropic expansion rate H remains nearly constant in the radiation-dominated epoch. In the regime where Σ/H is constant, the spatial vector component v works as a dark radiation with the equation of state close to 1/3. During the matter era, the ratio Σ/H decreases with the decrease of v. As long as the conditions |Σ| ll H and v2 ll phi2 are satisfied around the onset of late-time cosmic acceleration, where phi is the temporal vector component, we find that the solutions approach the isotropic de Sitter fixed point (Σ = 0 = v) in accordance with the cosmic no-hair conjecture. In the presence of v and Σ the early evolution of the dark energy equation of state wDE in the radiation era is different from that in the isotropic case, but the approach to the isotropic value wDE(iso) typically occurs at redshifts z much larger than 1. Thus, apart from the existence of dark radiation, the anisotropic cosmological dynamics at low redshifts is similar to that in isotropic generalized Proca theories. In beyond-generalized Proca theories the only consistent solution to avoid the divergence of a determinant of the dynamical system corresponds to v = 0, so Σ always decreases in time.
Holographic Theory of Gravity and Cosmology
Ng, Y Jack
2016-01-01
According to the holographic principle, the maximum amount of information stored in a region of space scales as the area of its two-dimensional surface, like a hologram. We show that the holographic principle can be understood heuristically as originated from quantum fluctuations of spacetime. Applied to cosmology, this consideration leads to a dynamical cosmological constant $\\Lambda$ of the observed magnitude, in agreement with the result obtained for the present and recent cosmic eras, by using unimodular gravity and causal-set theory. By generalizing the concept of entropic gravity, we find a critical acceleration parameter related to $\\Lambda$ in galactic dynamics, and we construct a phenomenological model of dark matter which we call "modified dark matter" (MDM). We provide successful observational tests of MDM at both the galactic and cluster scales. We also discuss the possibility that the quanta of both dark energy and dark matter obey the quantum Boltzmann statistics or infinite statistics as descri...
Manifestly Gauge Invariant Perturbations of Scalar-Tensor Theories of Gravity
Han, Yu; Ma, Yongge
2015-01-01
The general relativistic perturbations of scalar-tensor theories (STT) of gravity are studied in a manifestly gauge invariant Hamiltonian formalism. After the derivation of the Hamiltonian equations of motion in this framework, the gauge invariant formalism is used to compute the evolution equations of linear perturbations around a general relativistic spacetime background in the Jordan frame. These equations are then specialized to the case of a flat FRW cosmological background. Furthermore, the equivalence between the Jordan frame and the Einstein frame of STT in the manifestly gauge invariant Hamiltonian formalism is analyzed, and it is shown that also in this framework they can be related by a conformal transformation. Finally, the obtained evolution equations for the linear perturbations in our formalism are compared with those in the standard cosmological perturbation theory. It turns out that the perturbation equations in the two different formalisms coincide with each other in a suitable limit.
Cosmology in bimetric theory with an effective composite coupling to matter
Gümrükçüoğlu, A. Emir; Heisenberg, Lavinia; Mukohyama, Shinji; Tanahashi, Norihiro
2015-04-01
We study the cosmology of bimetric theory with a composite matter coupling. We find two possible branches of background evolution. We investigate the question of stability of cosmological perturbations. For the tensor and vector perturbations, we derive conditions on the absence of ghost and gradient instabilities. For the scalar modes, we obtain conditions for avoiding ghost degrees. In the first branch, we find that one of the scalar modes becomes a ghost at the late stages of the evolution. Conversely, this problem can be avoided in the second branch. However, we also find that the constraint for the second branch prevents the doubly coupled matter fields from being the standard ingredients of cosmology. We thus conclude that a realistic and stable cosmological model requires additional minimally coupled matter fields.
Cosmology in bimetric theory with an effective composite coupling to matter
Gumrukcuoglu, A Emir; Mukohyama, Shinji; Tanahashi, Norihiro
2015-01-01
We study the cosmology of bimetric theory with a composite matter coupling. We find two possible branches of background evolution. We investigate the question of stability of cosmological perturbations. For the tensor and vector perturbations, we derive conditions on the absence of ghost and gradient instabilities. For the scalar modes, we obtain conditions for avoiding ghost degrees. In the first branch, we find that one of the scalar modes becomes a ghost at the late stages of the evolution. Conversely, this problem can be avoided in the second branch. However, we also find that the constraint for the second branch prevents the doubly coupled matter fields from being the standard ingredients of cosmology. We thus conclude that a realistic and stable cosmological model requires additional minimally coupled matter fields.
Energy Technology Data Exchange (ETDEWEB)
Biswas, Tirthabir [Department of Physics, St. Cloud State University, St. Cloud, MN 56301 U.S.A (United States); Koivisto, Tomi [Institute for Theoretical Physics and Spinoza Institute, Postbus 80.195, 3508 TD Utrecht (Netherlands); Mazumdar, Anupam, E-mail: tbiswas@loyno.edu, E-mail: T.S.Koivisto@uu.nl, E-mail: a.mazumdar@lancaster.ac.uk [Physics Department, Lancaster University, Lancaster, LA1 4YB (United Kingdom)
2010-11-01
One of the greatest problems of standard cosmology is the Big Bang singularity. Previously it has been shown that non-local ghostfree higher-derivative modifications of Einstein gravity in the ultra-violet regime can admit non-singular bouncing solutions. In this paper we study in more details the dynamical properties of the equations of motion for these theories of gravity in presence of positive and negative cosmological constants and radiation. We find stable inflationary attractor solutions in the presence of a positive cosmological constant which renders inflation geodesically complete, while in the presence of a negative cosmological constant a cyclic universe emerges. We also provide an algorithm for tracking the super-Hubble perturbations during the bounce and show that the bouncing solutions are free from any perturbative instability.
Shapiro, P R; Raga, A C; Shapiro, Paul R.; Iliev, Ilian; Raga, Alejandro C.
1998-01-01
The postcollapse structure of objects which form by gravitational condensation out of the expanding cosmological background universe is a key element in the theory of galaxy formation. Towards this end, we have reconsidered the outcome of the nonlinear growth of a uniform, spherical density perturbation in an unperturbed background universe - the cosmological ``top-hat'' problem. We adopt the usual assumption that the collapse to infinite density at a finite time predicted by the top-hat solution is interrupted by a rapid virialization caused by the growth of small-scale inhomogeneities in the initial perturbation. We replace the standard description of the postcollapse object as a uniform sphere in virial equilibrium by a more self-consistent one as a truncated, nonsingular, isothermal sphere in virial and hydrostatic equilibrium, including for the first time a proper treatment of the finite-pressure boundary condition on the sphere. The results differ significantly from both the uniform sphere and the singu...
The Early-Time Evolution of the Cosmological Perturbations in f(R) Gravity
Gu, Je-An; Wu, Yen-Ting; Chen, Pisin; Hwang, W-Y Pauchy
2011-01-01
We investigate the evolution of the linear cosmological perturbations in f(R) gravity, an alternative to dark energy for explaining the late-time cosmic acceleration. We numerically calculate the early-time evolution with an approximation we contrive to solve a problem that commonly appears when one solves the full evolution equations. With the approximate evolution equations we can fairly assess the effect of the gravity modification on the early-time evolution, thereby examining the validity of the general-relativity (GR) approximation that is widely used for the early universe. In particular, we compare the CMB photon density perturbation and the matter density perturbation obtained respectively by our approximation and the conventional GR approximation. We find that the effect of the gravity modification at early times in f(R) gravity may not be negligible. We conclude that to be self-consistent, in the f(R) theory one should employ the approximation presented in this paper instead of that of GR in the tr...
General degeneracy in density functional perturbation theory
Palenik, Mark C.; Dunlap, Brett I.
2017-07-01
Degenerate perturbation theory from quantum mechanics is inadequate in density functional theory (DFT) because of nonlinearity in the Kohn-Sham potential. Herein, we develop the fully general perturbation theory for open-shell, degenerate systems in Kohn-Sham DFT, without assuming the presence of symmetry or equal occupation of degenerate orbitals. To demonstrate the resulting methodology, we apply it to the iron atom in the central field approximation, perturbed by an electric quadrupole. This system was chosen because it displays both symmetry required degeneracy, between the five 3 d orbitals, as well as accidental degeneracy, between the 3 d and 4 s orbitals. The quadrupole potential couples the degenerate 3 d and 4 s states, serving as an example of the most general perturbation.
Heckman, Jonathan J; Vafa, Cumrun
2008-01-01
In this paper we study the interplay between the recently proposed F-theory GUTs and cosmology. Despite the fact that the parameter range for F-theory GUT models is very narrow, we find that F-theory GUTs beautifully satisfy most cosmological constraints without any further restrictions. The viability of the scenario hinges on the interplay between various components of the axion supermultiplet, which in F-theory GUTs is also responsible for breaking supersymmetry. In these models, the gravitino is the LSP and develops a mass by eating the axino mode. The radial component of the axion supermultiplet known as the saxion typically begins to oscillate in the early Universe, eventually coming to dominate the energy density. Its decay reheats the Universe to a temperature of ~ 1 GeV, igniting BBN and diluting all thermal relics such as the gravitino by a factor of ~ 10^(-4) - 10^(-5) such that gravitinos contribute a sizable component of the dark matter. In certain cases, non-thermally produced relics such as the ...
Time-Sliced Perturbation Theory for Large Scale Structure I: General Formalism
Blas, Diego; Ivanov, Mikhail M; Sibiryakov, Sergey
2016-01-01
We present a new analytic approach to describe large scale structure formation in the mildly non-linear regime. The central object of the method is the time-dependent probability distribution function generating correlators of the cosmological observables at a given moment of time. Expanding the distribution function around the Gaussian weight we formulate a perturbative technique to calculate non-linear corrections to cosmological correlators, similar to the diagrammatic expansion in a three-dimensional Euclidean quantum field theory, with time playing the role of an external parameter. For the physically relevant case of cold dark matter in an Einstein--de Sitter universe, the time evolution of the distribution function can be found exactly and is encapsulated by a time-dependent coupling constant controlling the perturbative expansion. We show that all building blocks of the expansion are free from spurious infrared enhanced contributions that plague the standard cosmological perturbation theory. This pave...
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.
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...
Homological Perturbation Theory and Mirror Symmetry
Institute of Scientific and Technical Information of China (English)
Jian ZHOU
2003-01-01
We explain how deformation theories of geometric objects such as complex structures,Poisson structures and holomorphic bundle structures lead to differential Gerstenhaber or Poisson al-gebras. We use homological perturbation theory to construct A∞ algebra structures on the cohomology,and their canonically defined deformations. Such constructions are used to formulate a version of A∞algebraic mirror symmetry.
Quenched chiral perturbation theory to one loop
Colangelo, Gilberto; Pallante, Elisabetta
1998-01-01
We calculate the divergences of the generating functional of quenched chiral perturbation theory at one loop, and renormalize the theory by an appropriate definition of the counterterms. We show that the quenched chiral logarithms can be accounted for by defining a renormalized B0 parameter which, a
Second order perturbation theory for embedded eigenvalues
DEFF Research Database (Denmark)
Faupin, Jeremy; Møller, Jacob Schach; Skibsted, Erik
2011-01-01
We study second order perturbation theory for embedded eigenvalues of an abstract class of self-adjoint operators. Using an extension of the Mourre theory, under assumptions on the regularity of bound states with respect to a conjugate operator, we prove upper semicontinuity of the point spectrum...
Anisotropic cosmological solutions in massive vector theories
Heisenberg, Lavinia; Tsujikawa, Shinji
2016-01-01
In beyond-generalized Proca theories including the extension to theories higher than second order, we study the role of a spatial component $v$ of a massive vector field on the anisotropic cosmological background. We show that, as in the case of the isotropic cosmological background, there is no additional ghostly degrees of freedom associated with the Ostrogradski instability. In second-order generalized Proca theories we find the existence of anisotropic solutions on which the ratio between the anisotropic expansion rate $\\Sigma$ and the isotropic expansion rate $H$ remains nearly constant in the radiation-dominated epoch. In the regime where $\\Sigma/H$ is constant, the spatial vector component $v$ works as a dark radiation with the equation of state close to $1/3$. During the matter era, the ratio $\\Sigma/H$ decreases with the decrease of $v$. As long as the conditions $|\\Sigma| \\ll H$ and $v^2 \\ll \\phi^2$ are satisfied around the onset of late-time cosmic acceleration, where $\\phi$ is the temporal vector ...
World-line perturbation theory
van Holten, Jan-Willem
2016-01-01
The motion of a compact body in space and time is commonly described by the world line of a point representing the instantaneous position of the body. In General Relativity such a world-line formalism is not quite straightforward because of the strict impossibility to accommodate point masses and rigid bodies. In many situations of practical interest it can still be made to work using an effective hamiltonian or energy-momentum tensor for a finite number of collective degrees of freedom of the compact object. Even so exact solutions of the equations of motion are often not available. In such cases families of world lines of compact bodies in curved space-times can be constructed by a perturbative procedure based on generalized geodesic deviation equations. Examples for simple test masses and for spinning test bodies are presented.
Adiabatic density-functional perturbation theory
Gonze, Xavier
1995-08-01
The treatment of adiabatic perturbations within density-functional theory is examined, at arbitrary order of the perturbation expansion. Due to the extremal property of the energy functional, standard variation-perturbation theorems can be used. The different methods (Sternheimer equation, extremal principle, Green's function, and sum over state) for obtaining the perturbation expansion of the wave functions are presented. The invariance of the Hilbert space of occupied wave functions with respect to a unitary transformation leads to the definition of a ``parallel-transport-gauge'' and a ``diagonal-gauge'' perturbation expansion. Then, the general expressions are specialized for the second, third, and fourth derivative of the energy, with an example of application of the method up to third order.
Operator Decomposition Framework for Perturbation Theory
Energy Technology Data Exchange (ETDEWEB)
Abdel-Khalik, Hany S.; Wang, Congjian; Bang, Young Suk [North Carolina State University, Raleigh (United States)
2012-05-15
This summary describes a new framework for perturbation theory intended to improve its performance, in terms of the associated computational cost and the complexity of implementation, for routine reactor calculations in support of design, analysis, and regulation. Since its first introduction in reactor analysis by Winger, perturbation theory has assumed an aura of sophistication with regard to its implementation and its capabilities. Only few reactor physicists, typically mathematically proficient, have contributed to its development, with the general body of the nuclear engineering community remaining unaware of its current status, capabilities, and challenges. Given its perceived sophistication and the small body of community users, the application of perturbation theory has been limited to investigatory analyses only. It is safe to say that the nuclear community is split into two groups, a small one which understands the theory and, and a much bigger group with the perceived notion that perturbation theory is nothing but a fancy mathematical approach that has very little use in practice. Over the past three years, research has demonstrated two goals. First, reduce the computational cost of perturbation theory in order to enable its use for routine reactor calculations. Second, expose some of the myth about perturbation theory and present it in a form that is simple and relatable in order to stimulate the interest of nuclear practitioners, especially those who are currently working on the development of next generation reactor design and analysis tools. The operator decomposition approach has its roots in linear algebra and can be easily understood by code developers, especially those involved in the design of iterative numerical solution strategies
Chiral Perturbation Theory With Lattice Regularization
Ouimet, P P A
2005-01-01
In this work, alternative methods to regularize chiral perturbation theory are discussed. First, Long Distance Regularization will be considered in the presence of the decuplet of the lightest spin 32 baryons for several different observables. This serves motivation and introduction to the use of the lattice regulator for chiral perturbation theory. The mesonic, baryonic and anomalous sectors of chiral perturbation theory will be formulated on a lattice of space time points. The consistency of the lattice as a regulator will be discussed in the context of the meson and baryon masses. Order a effects will also be discussed for the baryon masses, sigma terms and magnetic moments. The work will close with an attempt to derive an effective Wess-Zumino-Witten Lagrangian for Wilson fermions at non-zero a. Following this discussion, there will be a proposal for a phenomenologically useful WZW Lagrangian at non-zero a.
Effects of primordial curvature perturbations on the value of the cosmological constant
Romano, Antonio Enea; Sasaki, Misao
2013-01-01
In this paper we study the effects on the luminosity distance of a local inhomogeneity seeded by primordial curvature perturbations as predicted by the inflationary scenario and constrained by the cosmic microwave background radiation. We find that a local overdensity originated from a one, two or three standard deviations peaks of the primordial curvature perturbations field can induce corrections to the value of the cosmological constant respectively of order of $0.6%,1%,1.5%$. These effects cannot be neglected in the precision cosmology era in which we are entering.
Vector Meson Masses in Chiral Perturbation Theory
Bijnens, J; Talavera, P
1997-01-01
We discuss the vector meson masses within the context of Chiral Perturbation Theory performing an expansion in terms of the momenta, quark masses and 1/Nc. We extend the previous analysis to include isospin breaking effects and also include up to order p^4. We discuss vector meson chiral perturbation theory in some detail and present a derivation from a relativistic lagrangian. The unknown coefficients are estimated in various ways. We also discuss the relevance of electromagnetic corrections and the implications of the present calculation for the determination of quark masses.
The de Sitter limit of inflation and non-linear perturbation theory
DEFF Research Database (Denmark)
Jarnhus, Philip; Sloth, Martin Snoager
2008-01-01
We study the fourth order action of the comoving curvature perturbation in an inflationary universe in order to understand more systematically the de Sitter limit in nonlinear cosmological perturbation theory. We derive the action of the curvature perturbation to fourth order in the comoving gaug......, and show that it vanishes sufficiently fast in the de Sitter limit. By studying the de Sitter limit, we then extrapolate to the n'th order action of the comoving curvature perturbation and discuss the slow-roll order of the n-point correlation function....
The de Sitter limit of inflation and non-linear perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Jarnhus, Philip R; Sloth, Martin S, E-mail: pjarn@phys.au.dk, E-mail: sloth@phys.au.dk [Department of Physics and Astronomy, University of Aarhus, DK-8000 Aarhus C (Denmark)
2008-02-15
We study the fourth-order action of the comoving curvature perturbation in an inflationary universe in order to understand more systematically the de Sitter limit in non-linear cosmological perturbation theory. We derive the action of the curvature perturbation to fourth order in the comoving gauge, and show that it vanishes sufficiently fast in the de Sitter limit. By studying the de Sitter limit, we then extrapolate to the nth-order action of the comoving curvature perturbation and discuss the slow-roll order of the n-point correlation function.
Cosmological phase transitions from lattice field theory
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Jansen, Karl [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC
2011-11-22
In this proceedings contribution we discuss the fate of the electroweak and the quantum chromodynamics phase transitions relevant for the early stage of the universe at non-zero temperature. These phase transitions are related to the Higgs mechanism and the breaking of chiral symmetry, respectively. We will review that non-perturbative lattice field theory simulations show that these phase transitions actually do not occur in nature and that physical observables show a completely smooth behaviour as a function of the temperature.
Cosmological perturbations from a Spectator field during inflation
Wang, Lingfei
2013-01-01
In this paper we will discuss analytically the perturbations created from a slowly rolling subdominant spectator field which decays much before the end of inflation. The quantum fluctuations of such a spectator field can seed perturbations on very large scales and explain the temperature anisotropy in the cosmic microwave background radiation with moderate non-Gaussianity, provided the relevant modes leave the Hubble patch while the spectator is slowly rolling. Furthermore, the perturbations are purely {\\it adiabatic} since the inflaton decay dominates and creates all the Standard Model degrees of freedom. We will provide two examples for the spectator field potential, one with a step function profile, and the other with an inflection point. In both the cases we will compute higher order curvature perturbations, i.e.\\ local bispectrum and trispectrum, which can be constrained by the forthcoming Planck data.
The probability equation for the cosmological comoving curvature perturbation
Energy Technology Data Exchange (ETDEWEB)
Riotto, Antonio; Sloth, Martin S., E-mail: antonio.riotto@pd.infn.it, E-mail: sloth@cern.ch [CERN, PH-TH Division, CH-1211, Genève 23 (Switzerland)
2011-10-01
Fluctuations of the comoving curvature perturbation with wavelengths larger than the horizon length are governed by a Langevin equation whose stochastic noise arise from the quantum fluctuations that are assumed to become classical at horizon crossing. The infrared part of the curvature perturbation performs a random walk under the action of the stochastic noise and, at the same time, it suffers a classical force caused by its self-interaction. By a path-interal approach and, alternatively, by the standard procedure in random walk analysis of adiabatic elimination of fast variables, we derive the corresponding Kramers-Moyal equation which describes how the probability distribution of the comoving curvature perturbation at a given spatial point evolves in time and is a generalization of the Fokker-Planck equation. This approach offers an alternative way to study the late time behaviour of the correlators of the curvature perturbation from infrared effects.
Cosmological perturbations of axion with a dynamical decay constant
Kobayashi, Takeshi; Takahashi, Fuminobu
2016-08-01
A QCD axion with a time-dependent decay constant has been known to be able to accommodate high-scale inflation without producing topological defects or too large isocurvature perturbations on CMB scales. We point out that a dynamical decay constant also has the effect of enhancing the small-scale axion isocurvature perturbations. The enhanced axion perturbations can even exceed the periodicity of the axion potential, and thus lead to the formation of axionic domain walls. Unlike the well-studied axionic walls, the walls produced from the enhanced perturbations are not bounded by cosmic strings, and thus would overclose the universe independently of the number of degenerate vacua along the axion potential.
Adiabatic CMB perturbations in pre-big bang string cosmology
Enqvist, Kari; Enqvist, Kari; Sloth, Martin S.
2002-01-01
We consider the pre-big bang scenario with a massive axion field which starts to dominate energy density when oscillating in an instanton-induced potential and subsequently reheats the universe as it decays into photons, thus creating adiabatic CMB perturbations. We find that the fluctuations in the axion field can give rise to a nearly flat spectrum of adiabatic perturbations with a spectral tilt $\\Delta n$ in the range $-0.1 \\lesssim \\Delta n \\lesssim 0.3$.
Energy Technology Data Exchange (ETDEWEB)
Astashenok, Artyom V., E-mail: artyom.art@gmail.com [Baltic Federal University of I. Kant, Department of Theoretical Physics, 236041, 14, Nevsky st., Kaliningrad (Russian Federation); Odintsov, Sergei D. [Institucio Catalana de Recerca i Estudis Avancats (ICREA), Barcelona (Spain); Institut de Ciencies de l' Espai (CSIC-IEEC), Campus UAB, Torre C5-Par-2a pl, E-08193 Bellaterra (Barcelona) (Spain); Eurasian International Center for Theor. Physics, Eurasian National University, Astana 010008 (Kazakhstan); Tomsk State Pedagogical University, Tomsk (Russian Federation)
2013-01-29
We confront dark energy models which are currently similar to {Lambda}CDM theory with observational data which include the SNe data, matter density perturbations and baryon acoustic oscillations data. DE cosmology under consideration may evolve to Big Rip, type II or type III future singularity, or to Little Rip or Pseudo-Rip universe. It is shown that matter perturbations data define more precisely the possible deviation from {Lambda}CDM model than consideration of SNe data only. The combined data analysis proves that DE models under consideration are as consistent as {Lambda}CDM model. We demonstrate that growth of matter density perturbations may occur at sufficiently small background density but still before the possible disintegration of bound objects (like clusters of galaxies, galaxies, etc.) in Big Rip, type III singularity, Little Rip or Pseudo-Rip universe. This new effect may bring the future universe to chaotic state well before disintegration or Rip.
Four-Dimensional Spin Foam Perturbation Theory
Directory of Open Access Journals (Sweden)
João Faria Martins
2011-10-01
Full Text Available We define a four-dimensional spin-foam perturbation theory for the BF-theory with a B∧B potential term defined for a compact semi-simple Lie group G on a compact orientable 4-manifold M. This is done by using the formal spin foam perturbative series coming from the spin-foam generating functional. We then regularize the terms in the perturbative series by passing to the category of representations of the quantum group U_q(g where g is the Lie algebra of G and q is a root of unity. The Chain-Mail formalism can be used to calculate the perturbative terms when the vector space of intertwiners Λ⊗Λ→A, where A is the adjoint representation of g, is 1-dimensional for each irrep Λ. We calculate the partition function Z in the dilute-gas limit for a special class of triangulations of restricted local complexity, which we conjecture to exist on any 4-manifold M. We prove that the first-order perturbative contribution vanishes for finite triangulations, so that we define a dilute-gas limit by using the second-order contribution. We show that Z is an analytic continuation of the Crane-Yetter partition function. Furthermore, we relate Z to the partition function for the F∧F theory.
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.
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.
Basics of thermal field theory a tutorial on perturbative computations
Laine, Mikko
2016-01-01
This book presents thermal field theory techniques, which can be applied in both cosmology and the theoretical description of the QCD plasma generated in heavy-ion collision experiments. It focuses on gauge interactions (whether weak or strong), which are essential in both contexts. As well as the many differences in the physics questions posed and in the microscopic forces playing a central role, the authors also explain the similarities and the techniques, such as the resummations, that are needed for developing a formally consistent perturbative expansion. The formalism is developed step by step, starting from quantum mechanics; introducing scalar, fermionic and gauge fields; describing the issues of infrared divergences; resummations and effective field theories; and incorporating systems with finite chemical potentials. With this machinery in place, the important class of real-time (dynamic) observables is treated in some detail. This is followed by an overview of a number of applications, ranging from t...
Baryon form factors in chiral perturbation theory
Kubis, B; Kubis, Bastian; Meissner, Ulf-G.
2001-01-01
We analyze the electromagnetic form factors of the ground state baryon octet to fourth order in relativistic baryon chiral perturbation theory. Predictions for the \\Sigma^- charge radius and the \\Lambda-\\Sigma^0 transition moment are found to be in excellent agreement with the available experimental information. Furthermore, the convergence behavior of the hyperon charge radii is shown to be more than satisfactory.
Geometric singular perturbation theory in biological practice
Hek, G.
2010-01-01
Geometric singular perturbation theory is a useful tool in the analysis of problems with a clear separation in time scales. It uses invariant manifolds in phase space in order to understand the global structure of the phase space or to construct orbits with desired properties. This paper explains an
Quenched Chiral Perturbation Theory to one loop
Colangelo, G.; Pallante, E.
1998-01-01
The divergences of the generating functional of quenched Chiral Perturbation theory (qCHPT) to one loop are computed in closed form. We show how the quenched chiral logarithms can be reabsorbed in the renormalization of the B0 parameter of the leading order Lagrangian. Finally, we do the chiral powe
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
Effects of Dark Energy Perturbations on Cosmological Tests of General Relativity
Dossett, Jason
2013-01-01
Cosmological tests to distinguish between dark energy (DE) and modifications to gravity are a promising route to obtain clues on the origin of cosmic acceleration. We study here the robustness of these tests to the presence of DE density, velocity, and anisotropic stress perturbations. We find that the dispersion in the growth index parameter remains small enough to distinguish between extreme cases of DE models and some commonly used modified gravity models. The sign of the slope parameter for a redshift dependent growth index was found to be inconsistent as an additional test in extreme cases of DE models with perturbations. Next, we studied the effect of DE perturbations on the modified growth (MG) parameters that enter the perturbed Einstein equations. We find that while the dark energy perturbations affect the MG parameters, the deviations remain smaller than those due to modified gravity models. Additionally, the deviations due to DE perturbations with a non-zero effective sound speed occur at scale ran...
Evolution of cosmological perturbations in a stage dominated by an oscillatory scalar field
Kodama, H; Kodama, Hideo; Hamazaki, Takashi
1996-01-01
In the investigation of the evolution of cosmological perturbations in inflationary universe models the behavior of perturbations during the reheating stage is the most unclear point. In particular in the early reheating phase in which a rapidly oscillating scalar field dominates the energy density, the behavior of perturbations is not known well because their evolution equation expressed in terms of the curvature perturbation becomes singular. In this paper it is shown that in spite of this singular behavior of the evolution equation the Bardeen parameter stays constant in a good accuracy during this stage for superhorizon-scale perturbations except for a sequence of negligibly short intervals around the zero points of the time derivative of the scalar field. This justifies the conventional formula relating the amplitudes of quantum fluctuations during inflation and those of adiabatic perturbations at horizon crossing in the Friedmann stage, except for possible corrections produced by the energy transfer fro...
Amin, Mustafa A; Blandford, Roger D
2007-01-01
The relationship between the metric and nonrelativistic matter distribution depends on the theory of gravity and additional fields, hence providing a possible way of distinguishing competing theories. With the assumption that the geometry and kinematics of the homogeneous universe have been measured, we present a procedure for understanding and testing the relationship between the cosmological matter distribution and metric perturbations (along with their respective evolution) using the ratio of the physical size of the perturbation to the size of the horizon as our small expansion parameter. We expand around Newtonian gravity on linear, sub-horizon scales with coefficient functions in front of the expansion parameter. Our framework relies on an ansatz which ensures that (i) the Poisson equation is recovered on small scales (ii) the metric variables (and any additional fields) are generated and supported by the nonrelativistic matter overdensity. The scales for which our framework is intended are small enough...
Geometric perturbation theory and plasma physics
Energy Technology Data Exchange (ETDEWEB)
Omohundro, S.M.
1985-04-04
Modern differential geometric techniques are used to unify the physical asymptotics underlying mechanics, wave theory and statistical mechanics. The approach gives new insights into the structure of physical theories and is suited to the needs of modern large-scale computer simulation and symbol manipulation systems. A coordinate-free formulation of non-singular perturbation theory is given, from which a new Hamiltonian perturbation structure is derived and related to the unperturbed structure. The theory of perturbations in the presence of symmetry is developed, and the method of averaging is related to reduction by a circle group action. The pseudo-forces and magnetic Poisson bracket terms due to reduction are given a natural asymptotic interpretation. Similar terms due to changing reference frames are related to the method of variation of parameters, which is also given a Hamiltonian formulation. These methods are used to answer a question about nearly periodic systems. The answer leads to a new secular perturbation theory that contains no ad hoc elements. Eikonal wave theory is given a Hamiltonian formulation that generalizes Whitham's Lagrangian approach. The evolution of wave action density on ray phase space is given a Hamiltonian structure using a Lie-Poisson bracket. The relationship between dissipative and Hamiltonian systems is discussed. A new type of attractor is defined which attracts both forward and backward in time and is shown to occur in infinite-dimensional Hamiltonian systems with dissipative behavior. The theory of Smale horseshoes is applied to gyromotion in the neighborhood of a magnetic field reversal and the phenomenon of reinsertion in area-preserving horseshoes is introduced. The central limit theorem is proved by renormalization group techniques. A natural symplectic structure for thermodynamics is shown to arise asymptotically from the maximum entropy formalism.
Adiabatic CMB perturbations in pre-big bang string cosmology
DEFF Research Database (Denmark)
Enqvist, Kari; Sloth, Martin Snoager
2001-01-01
We consider the pre-big bang scenario with a massive axion field which starts to dominate energy density when oscillating in an instanton-induced potential and subsequently reheats the universe as it decays into photons, thus creating adiabatic CMB perturbations. We find that the fluctuations...
A primer for Chiral Perturbative Theory
Energy Technology Data Exchange (ETDEWEB)
Scherer, Stefan [Mainz Univ. (Germany). Inst. fuer Kernphysik; Schindler, Matthias R. [South Carolina Univ., Columbia, SC (United States). Dept. of Physics; George Washington Univ., Washington, DC (United States). Dept. of Physics
2012-07-01
Chiral Perturbation Theory, as effective field theory, is a commonly accepted and well established working tool, approximating quantum chromodynamics at energies well below typical hadron masses. This volume, based on a number of lectures and supplemented with additional material, provides a pedagogical introduction for graduate students and newcomers entering the field from related areas of nuclear and particle physics. Starting with the the Lagrangian of the strong interactions and general symmetry principles, the basic concepts of Chiral Perturbation Theory in the mesonic and baryonic sectors are developed. The application of these concepts is then illustrated with a number of examples. A large number of exercises (81, with complete solutions) are included to familiarize the reader with helpful calculational techniques. (orig.)
A primer for chiral perturbation theory
Scherer, Stefan
2012-01-01
Chiral Perturbation Theory, as effective field theory, is a commonly accepted and well established working tool, approximating quantum chromodynamics at energies well below typical hadron masses. This volume, based on a number of lectures and supplemented with additional material, provides a pedagogical introduction for graduate students and newcomers entering the field from related areas of nuclear and particle physics. Starting with the the Lagrangian of the strong interactions and general symmetry principles, the basic concepts of Chiral Perturbation Theory in the mesonic and baryonic sectors are developed. The application of these concepts is then illustrated with a number of examples. A large number of exercises (81, with complete solutions) are included to familiarize the reader with helpful calculational techniques.
SPT 2004: Symmetry and Perturbation Theory
Prinari, Barbara; Rauch-Wojciechowski, Stefan; Terracini, Susanna
2005-01-01
This proceedings volume is a collection of papers presented at the International Conference on SPT2004 focusing on symmetry, perturbation theory, and integrability. The book provides an updated overview of the recent developments in the various different fields of nonlinear dynamics, covering both theory and applications. Special emphasis is given to algebraic and geometric integrability, solutions to the N-body problem of the “choreography” type, geometry and symmetry of dynamical systems, integrable evolution equations, various different perturbation theories, and bifurcation analysis. The contributors to this volume include some of the leading scientists in the field, among them: I Anderson, D Bambusi, S Benenti, S Bolotin, M Fels, W Y Hsiang, V Matveev, A V Mikhailov, P J Olver, G Pucacco, G Sartori, M A Teixeira, S Terracini, F Verhulst and I Yehorchenko.
PERTURBATION THEORY FOR THE FOCK-DIRAC DENSITY MATRIX
ATOMIC ENERGY LEVELS, *ATOMIC ORBITALS, *QUANTUM THEORY , ATOMIC SPECTROSCOPY, ELECTRONS, EXCITATION, FUNCTIONS(MATHEMATICS), MATHEMATICAL ANALYSIS, NUCLEAR SPINS, PERTURBATION THEORY , SOLID STATE PHYSICS, THEORY
A new approach to cosmological perturbations in f(R) models
Energy Technology Data Exchange (ETDEWEB)
Bertacca, Daniele; Bartolo, Nicola; Matarrese, Sabino, E-mail: daniele.bertacca@pd.infn.it, E-mail: nicola.bartolo@pd.infn.it, E-mail: sabino.matarrese@pd.infn.it [Dipartimento di Fisica Galileo Galilei, Università di Padova, via F. Marzolo, 8 I-35131 Padova (Italy)
2012-08-01
We propose an analytic procedure that allows to determine quantitatively the deviation in the behavior of cosmological perturbations between a given f(R) modified gravity model and a ΛCDM reference model. Our method allows to study structure formation in these models from the largest scales, of the order of the Hubble horizon, down to scales deeply inside the Hubble radius, without employing the so-called 'quasi-static' approximation. Although we restrict our analysis here to linear perturbations, our technique is completely general and can be extended to any perturbative order.
Dynamics in Nonlocal Cosmological Models Derived from String Field Theory
Joukovskaya, Liudmila
2007-01-01
A general class of nonlocal cosmological models is considered. A new method for solving nonlocal Friedmann equations is proposed, and solutions of the Friedmann equations with nonlocal operator are presented. The cosmological properties of these solutions are discussed. Especially indicated is $p$-adic cosmological model in which we have obtained nonsingular bouncing solution and string field theory tachyon model in which we have obtained full solution of nonlocal Friedmann equations with $w=...
Fully non-linear cosmological perturbations of multicomponent fluid and field systems
Hwang, Jai-chan; Noh, Hyerim; Park, Chan-Gyung
2016-09-01
We present fully non-linear and exact cosmological perturbation equations in the presence of multiple components of fluids and minimally coupled scalar fields. We ignore the tensor-type perturbation. The equations are presented without taking the temporal gauge condition in the Friedmann background with general curvature and the cosmological constant. We include the anisotropic stress. Even in the absence of anisotropic stress of individual component, the multiple component nature introduces the anisotropic stress in the collective fluid quantities. We prove the Newtonian limit of multiple fluids in the zero-shear gauge and the uniform-expansion gauge conditions, present the Newtonian hydrodynamic equations in the presence of general relativistic pressure in the zero-shear gauge, and present the fully non-linear equations and the third-order perturbation equations of the non-relativistic pressure fluids in the CDM-comoving gauge.
Kostouki, Anna
2009-01-01
Applying a novel non-perturbative functional method framework to a two-dimensional bosonic sigma model with tachyon, dilaton and graviton backgrounds we construct exact (non perturbative in the Regge slope) inflationary solutions, consistent with world-sheet Weyl Invariance. The mechanism for inflation entails a (partial) "alignment" between tachyon and dilaton backgrounds in the solution space. Some cosmological solutions which contain inflationary eras for a short period and interpolate between flat universes in the far past and far future are also discussed. These solutions are characterized by the absence of cosmological horizons, and therefore have well-defined scattering amplitudes. This makes them compatible with a perturbative string framework, and therefore it is these solutions that we consider as self-consistent in our approach. Within the context of the interpolating solutions, string production at the end of inflation (preheating) may also be studied. The advantage of our method is that the solut...
Cosmological perturbations of unimodular gravity and general relativity are identical
Basak, Abhishek; Fabre, Ophélia; Shankaranarayanan, S.
2016-10-01
Unimodular gravity (UG) is a restricted version of general relativity (GR) in which the variation of the metric determinant is set to zero and the field equations are given by the trace-free part of the full Einstein equations. The background equations in UG and GR are identical. It was recently claimed that the first order contribution in the temperature fluctuations of the Cosmic Microwave Background (CMB) in UG is different from GR. In this work, we calculate the first order perturbation equations in UG and show that the Sachs-Wolfe effect in UG, in terms of gauge invariant variables, is identical to GR. We also show that the second order perturbation equation of Mukhanov-Sasaki variable in UG, is identical to GR. The only difference comes from the gauge choices due the constraint on the metric determinant. Hence, UG and GR are identical and indistinguishable in CMB data on large scales.
Linear Perturbations in a coupled cosmon-bolon cosmology
Beyer, Joschka
2014-01-01
We investigate linear perturbations in the recently proposed cosmon-bolon model of coupled scalar field dark matter and quintessence. We provide an analytical mechanism to average over the quick oscillations appearing both in the background and at the perturbative level and evolve the effective equations numerically. The resulting matter power spectra are used to predict total halo number counts as well as substructure abundances in a typical galaxy by employing the extended Press-Schechter excursion set approach. We discuss in some detail the ambiguities arising in this formalism, starting from issues with generalizing spherical collapse to our model to filter choices and different barriers. The results are used to put a lower bound on the current bolon mass of roughly $9 \\times 10^{-22}$ eV.
Correlated mixtures of adiabatic and isocurvature cosmological perturbations
Langlois, D; Langlois, David; Riazuelo, Alain
2000-01-01
We examine the consequences of the existence of correlated mixtures of adiabatic and isocurvature perturbations on the CMB and large scale structure. In particular, we consider the four types of ``elementary'' totally correlated hybrid initial conditions, where only one of the four matter species (photons, baryons, neutrinos, CDM) deviates from adiabaticity. We then study the height and position of the acoustic peaks with respect to the large angular scale plateau as a function of the isocurvature to adiabatic ratio.
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...
Acoustic anisotropic wavefields through perturbation theory
Alkhalifah, Tariq Ali
2013-09-01
Solving the anisotropic acoustic wave equation numerically using finite-difference methods introduces many problems and media restriction requirements, and it rarely contributes to the ability to resolve the anisotropy parameters. Among these restrictions are the inability to handle media with η<0 and the presence of shear-wave artifacts in the solution. Both limitations do not exist in the solution of the elliptical anisotropic acoustic wave equation. Using perturbation theory in developing the solution of the anisotropic acoustic wave equation allows direct access to the desired limitation-free solutions, that is, solutions perturbed from the elliptical anisotropic background medium. It also provides a platform for parameter estimation because of the ability to isolate the wavefield dependency on the perturbed anisotropy parameters. As a result, I derive partial differential equations that relate changes in the wavefield to perturbations in the anisotropy parameters. The solutions of the perturbation equations represented the coefficients of a Taylor-series-type expansion of the wavefield as a function of the perturbed parameter, which is in this case η or the tilt of the symmetry axis. The expansion with respect to the symmetry axis allows use of an acoustic transversely isotropic media with a vertical symmetry axis (VTI) kernel to estimate the background wavefield and the corresponding perturbation coefficients. The VTI extrapolation kernel is about one-fourth the cost of the transversely isotropic model with a tilt in the symmetry axis kernel. Thus, for a small symmetry axis tilt, the cost of migration using a first-order expansion can be reduced. The effectiveness of the approach was demonstrated on the Marmousi model.
Stochastic multireference Epstein-Nesbet perturbation theory
Sharma, Sandeep; Jeanmairet, Guillaume; Alavi, Ali; Umrigar, C J
2016-01-01
We extend the recently proposed heat-bath configuration interaction (HCI) method [Holmes, Tubman, Umrigar, J. Chem. Theory Comput. 12, 3674 (2016)], by introducing a stochastic algorithm for performing multireference Epstein-Nesbet perturbation theory, in order to completely eliminate the severe memory bottleneck of the original method. The proposed stochastic algorithm has several attractive features. First, there is no sign problem that plagues several quantum Monte Carlo methods. Second, instead of using Metropolis-Hastings sampling, we use the Alias method to directly sample determinants from the reference wavefunction, thus avoiding correlations between consecutive samples. Third, in addition to removing the memory bottleneck, stochastic-HCI (s-HCI) is faster than the deterministic variant for most systems if a stochastic error of 0.1 mHa is acceptable. Fourth, within the s-HCI algorithm one can trade memory for a modest increase in computer time. Fifth, the perturbative calculation is embarrassingly par...
Gluonic Lorentz violation and chiral perturbation theory
Noordmans, J. P.
2017-04-01
By applying chiral-perturbation-theory methods to the QCD sector of the Lorentz-violating Standard-Model Extension, we investigate Lorentz violation in the strong interactions. In particular, we consider the C P T -even pure-gluon operator of the minimal Standard-Model Extension. We construct the lowest-order chiral effective Lagrangian for three as well as two light quark flavors. We develop the power-counting rules and construct the heavy-baryon chiral-perturbation-theory Lagrangian, which we use to calculate Lorentz-violating contributions to the nucleon self-energy. Using the constructed effective operators, we derive the first stringent limits on many of the components of the relevant Lorentz-violating parameter. We also obtain the Lorentz-violating nucleon-nucleon potential. We suggest that this potential may be used to obtain new limits from atomic-clock or deuteron storage-ring experiments.
Molecular Cluster Perturbation Theory. I. Formalism
Byrd, Jason N; Molt,, Robert W; Bartlett, Rodney J; Sanders, Beverly A; Lotrich, Victor F
2014-01-01
We present second-order molecular cluster perturbation theory (MCPT(2)), a methodology to calculate arbitrarily large systems with explicit calculation of individual wavefunctions in a coupled cluster framework. This new MCPT(2) framework uses coupled cluster perturbation theory and an expansion in terms of molecular dimer interactions to obtain molecular wavefunctions that are infinite order in both the electronic fluctuation operator and all possible dimer (and products of dimers) interactions. The MCPT(2) framework has been implemented in the new SIA/ACES parallel architecture, making use of the advanced dynamic memory control and fine grained parallelism to perform very large explicit molecular cluster calculations. To illustrate the power of this method, we have computed energy shifts and lattice site dipole moments for the polar and non-polar configurations of solid hydrogen fluoride by scaling an explicit lattice to the bulk limit. The explicit lattice size without periodic boundary conditions was scal...
Improving perturbation theory with cactus diagrams
Constantinou, M; Skouroupathis, A; Constantinou, Martha; Panagopoulos, Haralambos; Skouroupathis, Apostolos
2006-01-01
We study a systematic improvement of perturbation theory for gauge fields on the lattice [hep-lat/0606001]; the improvement entails resumming, to all orders in the coupling constant, a dominant subclass of tadpole diagrams. This method, originally proposed for the Wilson gluon action, is extended here to encompass all possible gluon actions made of closed Wilson loops; any fermion action can be employed as well. The effect of resummation is to replace various parameters in the action (coupling constant, Symanzik and clover coefficient) by ``dressed'' values; the latter are solutions to certain coupled integral equations, which are easy to solve numerically. Some positive features of this method are: a) It is gauge invariant, b) it can be systematically applied to improve (to all orders) results obtained at any given order in perturbation theory, c) it does indeed absorb in the dressed parameters the bulk of tadpole contributions. Two different applications are presented: The additive renormalization of fermio...
Kulczycki, Wojciech
2016-01-01
We analyze propagation equations for the polar modes of gravitational waves in cosmological space-times. We prove that polar gravitational waves must perturb --- unlike axial modes --- the material content of the Friedman-Lemaitre-Robertson-Walker spacetimes. The whole gravitational dynamics reduces to the single "master equation" that has the same form as for axial modes. That allows us to conclude that the status of the Huygens principle is the same for axial and gravitational waves. In particular, this principle is valid exactly in radiation spacetimes with the vanishing cosmological constant, and it is broken otherwise.
Perturbation theory for solitons in optical fibers
Kaup, D. J.
1990-11-01
Using a singular perturbation expansion, we study the evolution of a Raman loss compensated soliton in an optical fiber. Our analytical results agree quite well with the numerical results of Mollenauer, Gordon, and Islam [IEEE J. Quantum Electron. QE-22, 157 (1986)]. However, there are some differences in that our theory predicts an additional structure that was only partially seen in the numerical calculations. Our analytical results do give a quite good qualitative and quantitative check of the numerical results.
Wilson, Michael J
2016-01-01
I investigate the consistency of the VIMOS Public Extragalactic Redshift Survey v7 galaxy sample with the expansion history and linear growth rate predicted by General Relativity (GR) and a Planck (2015) cosmology. To do so, I measure the redshift-space power spectrum, which is anisotropic due to both redshift-space distortions (RSD) and the Alcock-Paczynski (AP) effect. In Chapter 6, I place constraints of $f \\sigma_8(0.76) = 0.44 \\pm 0.04$ and $f \\sigma_8(1.05) = 0.28 \\pm 0.08$, which remain consistent with GR at 95% confidence. Marginalising over the anisotropic AP effect degrades the constraints by a factor of three but allows $F_{AP} \\equiv (1+z) D_A H/c$ to be simultaneously constrained. The VIPERS v7 joint-posterior on $(f \\sigma_8, F_{AP})$ shows no compelling deviation from GR. Chapter 7 investigates the inclusion of a simple density transform: `clipping' prior to the RSD analysis. This tackles the root-cause of non-linearity and may extend the validity of perturbation theory. Moreover, this marked s...
Warm-tachyon Gauss-Bonnet inflation and cosmological perturbations
Motaharfar, Maysam
2016-01-01
We study a warm-tachyon inflationary model non-minimally coupled to a Gauss-Bonnet term. The general conditions required for reliability of the model are obtained by considerations of a combined hierarchy of Hubble and Gauss-Bonnet flow functions. The perturbed equations are derived in the longitudinal gauge in the presence of slow-roll and quasi-stable conditions. General expressions for observable quantities of interest such as the tensor-to-scalar ratio, scalar spectral index and its running are found in the high dissipation regime. Finally, the model is solved using exponential and inverse power-law potentials with parameters of the model being constrained within the framework of the Planck 2015 data. We show that the Gauss-Bonnet coupling constant controls termination of inflation in such a way as to be in good agreement with Planck 2015 data.
The cosmology of the nonsymmetric theory of gravitation
Energy Technology Data Exchange (ETDEWEB)
Prokopec, Tomislav [Institute for Theoretical Physics (ITP) and Spinoza Institute, Minnaertgebouw, Leuvenlaan 4, Utrecht University 3584 CE Utrecht (Netherlands)]. E-mail: t.prokopec@phys.uu.nl; Valkenburg, Wessel [Institute for Theoretical Physics (ITP) and Spinoza Institute, Minnaertgebouw, Leuvenlaan 4, Utrecht University 3584 CE Utrecht (Netherlands)]. E-mail: w.valkenburg@phys.uu.nl
2006-04-27
We show that during cosmological inflation the nonsymmetric metric tensor theory of gravitation develops a spectrum which is potentially observable by cosmic microwave background observations, and may be the most sensitive probe of the scale of cosmic inflation.
Perturbative quantum gravity in double field theory
Boels, Rutger H.; Horst, Christoph
2016-04-01
We study perturbative general relativity with a two-form and a dilaton using the double field theory formulation which features explicit index factorisation at the Lagrangian level. Explicit checks to known tree level results are performed. In a natural covariant gauge a ghost-like scalar which contributes even at tree level is shown to decouple consistently as required by perturbative unitarity. In addition, a lightcone gauge is explored which bypasses the problem altogether. Using this gauge to study BCFW on-shell recursion, we can show that most of the D-dimensional tree level S-matrix of the theory, including all pure graviton scattering amplitudes, is reproduced by the double field theory. More generally, we argue that the integrand may be reconstructed from its single cuts and provide limited evidence for off-shell cancellations in the Feynman graphs. As a straightforward application of the developed technology double field theory-like expressions for four field string corrections are derived.
Perturbative quantum gravity in double field theory
Boels, Rutger H
2015-01-01
We study perturbative general relativity with a two-form and a dilaton using the double field theory formulation which features explicit index factorisation at the Lagrangian level. Explicit checks to known tree level results are performed. In a natural covariant gauge a ghost-like scalar which contributes even at tree level is shown to decouple consistently as required by perturbative unitarity. In addition, a lightcone gauge is explored which bypasses the problem altogether. Using this gauge to study BCFW on-shell recursion, we can show that most of the D-dimensional tree level S-matrix of the theory, including all pure graviton scattering amplitudes, is reproduced by the double field theory. More generally, we argue that the integrand may be reconstructed from its single cuts and provide limited evidence for off-shell cancellations in the Feynman graphs. As a straightforward application of the developed technology double field theory-like expressions for four field string corrections are derived.
Anthropic-principle arguments against steady-state cosmological theories
Energy Technology Data Exchange (ETDEWEB)
Tipler, F.J. (Tulane Univ., New Orleans, LA (USA))
1982-04-01
Steady-state theories are very difficult to rule out on observational grounds, particularly if they are adjusted to contain a three-degree isotropic thermal-background radiation. However, anthropic-principle arguments can be used to rule out virtually any cosmological theory which has the universe stationary in the large. For example, anthropic considerations show that the perfect cosmological principle is self-contradictory.
Cosmological Issues in $F(T)$ Gravity Theory
Bamba, Kazuharu
2015-01-01
We review recent developments on cosmology in extended teleparallel gravity, called "$F(T)$ gravity" with $T$ the torsion scalar in teleparallelism. We explore various cosmological aspects of $F(T)$ gravity including the evolution of the equation of state for the universe, finite-time future singularities, thermodynamics, and four-dimensional effective $F(T)$ gravity theories coming from the higher-dimensional Kaluza-Klein (KK) and Randall-Sundrum (RS) theories.
Phenomenology and cosmology of weakly coupled string theory
Energy Technology Data Exchange (ETDEWEB)
Gaillard, Mary K.
1998-05-18
The weakly coupled vacuum of E{sub 8} {circle_times} E{sub 8} heterotic string theory remains an attractive scenario for phenomenology and cosmology. The particle spectrum is reviewed and the issues of gauge coupling unification, dilaton stabilization and modular cosmology are discussed. A specific model for condensation and supersymmetry breaking, that respects known constraints from string theory and is phenomenologically viable, is described.
Grishchuk, L P
1996-01-01
It is likely that the observed large-angular-scale anisotropies in the microwave background radiation are induced by the cosmological perturbations of quantum-mechanical origin. Such perturbations are now placed in squeezed vacuum quantum states and, hence, are characterized by large variances of their amplitude. The statistical properties of the anisotropies should reflect the underlying statistics of the squeezed vacuum quantum states. The theoretical variances for the temperature angular correlation function are derived and described quantitatively. It is shown that they are indeed large. Unfortunately, these large theoretical statistical uncertainties will make the extraction of cosmological information from the measured anisotropies a much more difficult problem than we wanted it to be.
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...
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...
Primordial magnetic fields from second-order cosmological perturbations:Tight coupling approximation
Maeda, Satoshi; Kobayashi, Tsutomu; Shiromizu, Tetsuya
2008-01-01
We explore the possibility of generating large-scale magnetic fields from second-order cosmological perturbations during the pre-recombination era. The key process for this is Thomson scattering between the photons and the charged particles within the cosmic plasma. To tame the multi-component interacting fluid system, we employ the tight coupling approximation. It is shown that the source term for the magnetic field is given by the product of the first order perturbations and so the intrinsically second-order quantities do not contribute to magnetogenesis. The magnetic fields generated by this process are estimated to be \\sim 10^{-26},Gauss on the horizon scale.
Perturbation theory for plasmonic modulation and sensing
Raman, Aaswath
2011-05-25
We develop a general perturbation theory to treat small parameter changes in dispersive plasmonic nanostructures and metamaterials. We specifically apply it to dielectric refractive index and metallic plasma frequency modulation in metal-dielectric nanostructures. As a numerical demonstration, we verify the theory\\'s accuracy against direct calculations for a system of plasmonic rods in air where the metal is defined by a three-pole fit of silver\\'s dielectric function. We also discuss new optical behavior related to plasma frequency modulation in such systems. Our approach provides new physical insight for the design of plasmonic devices for biochemical sensing and optical modulation and future active metamaterial applications. © 2011 American Physical Society.
Chiral perturbation theory for lattice QCD
Energy Technology Data Exchange (ETDEWEB)
Baer, Oliver
2010-07-21
The formulation of chiral perturbation theory (ChPT) for lattice Quantum Chromodynamics (QCD) is reviewed. We start with brief summaries of ChPT for continuum QCD as well as the Symanzik effective theory for lattice QCD. We then review the formulation of ChPT for lattice QCD. After an additional chapter on partial quenching and mixed action theories various concrete applications are discussed: Wilson ChPT, staggered ChPT and Wilson ChPT with a twisted mass term. The remaining chapters deal with the epsilon regime with Wilson fermions and selected results in mixed action ChPT. Finally, the formulation of heavy vector meson ChPT with Wilson fermions is discussed. (orig.)
String theory and pre-big bang cosmology
Gasperini, M.; Veneziano, G.
2016-09-01
In string theory, the traditional picture of a Universe that emerges from the inflation of a very small and highly curved space-time patch is a possibility, not a necessity: quite different initial conditions are possible, and not necessarily unlikely. In particular, the duality symmetries of string theory suggest scenarios in which the Universe starts inflating from an initial state characterized by very small curvature and interactions. Such a state, being gravitationally unstable, will evolve towards higher curvature and coupling, until string-size effects and loop corrections make the Universe "bounce" into a standard, decreasing-curvature regime. In such a context, the hot big bang of conventional cosmology is replaced by a "hot big bounce" in which the bouncing and heating mechanisms originate from the quantum production of particles in the high-curvature, large-coupling pre-bounce phase. Here we briefly summarize the main features of this inflationary scenario, proposed a quarter century ago. In its simplest version (where it represents an alternative and not a complement to standard slow-roll inflation) it can produce a viable spectrum of density perturbations, together with a tensor component characterized by a "blue" spectral index with a peak in the GHz frequency range. That means, phenomenologically, a very small contribution to a primordial B-mode in the CMB polarization, and the possibility of a large enough stochastic background of gravitational waves to be measurable by present or future gravitational wave detectors.
Cosmological Observations in a Modified Theory of Gravity (MOG
Directory of Open Access Journals (Sweden)
John. W. Moffat
2013-06-01
Full Text Available Our Modified Gravity Theory (MOG is a gravitational theory without exotic dark matter, based on an action principle. MOG has been used successfully tomodel astrophysical phenomena, such as galaxy rotation curves, galaxy cluster masses and lensing. MOG may also be able to account for cosmological observations. We assume that the MOG point source solution can be used to describe extended distributions of matter via an appropriately modified Poisson equation. We use this result to model perturbation growth in MOG and find that it agrees well with the observed matter power spectrum at present. As the resolution of the power spectrum improves with increasing survey size, however, significant differences emerge between the predictions of MOG and the standard Λ-cold dark matter (Λ-CDM model, as in the absence of exotic darkmatter, oscillations of the power spectrum in MOG are not suppressed. We can also use MOG to model the acoustic power spectrum of the cosmic microwave background. A suitably adapted semi-analytical model offers a first indication that MOG may pass this test and correctly model the peak of the acoustic spectrum.
Cosmological test of the Yilmaz theory of gravity
Ibison, M
2006-01-01
We test the Yilmaz theory of gravitation by working out the corresponding Friedmann-type equations generated by assuming the Friedmann-Robertson-Walker cosmological metrics. In the case that space is flat the theory is consistent only with either a completely empty universe or a negative energy vacuum that decays to produce a constant density of matter. In both cases the total energy remains zero at all times, and in the latter case the acceleration of the expansion is always negative. To obtain a more flexible and potentially more realistic cosmology, the equation of state relating the pressure and energy density of the matter creation process must be different from the vacuum, as for example is the case in the steady-state models of Gold, Bondi, Hoyle and others. The theory does not support the cosmological principle for curved space K =/= 0 cosmological metrics.
Workshop III – Cosmology: Observations versus theories
Indian Academy of Sciences (India)
T R Seshadri
2000-10-01
The topics on which there were presentations in this workshop can broadly be divided into the following categories: Observational aspects of large-scale structures in the universities; phase transitions in the early universe; cosmic microwave background radiation; observational cosmology.
Wave function of the Universe and Chern-Simons Perturbation Theory
Soo, C P
2002-01-01
The Chern-Simons exact solution of four-dimensional quantum gravity with nonvanishing cosmological constant is presented in metric variable as the partition function of a Chern-Simons theory with nontrivial source. The perturbative expansion is given, and the wave function is computed to the lowest order of approximation for the Cauchy surface which is topologically a 3-sphere. The state is well-defined even at degenerate and vanishing values of the dreibein. Reality conditions for the Ashtekar variables are also taken into account; and remarkable features of the Chern-Simons state and their relevance to cosmology are pointed out.
Tests of Chiral perturbation theory with COMPASS
Directory of Open Access Journals (Sweden)
Friedrich Jan M.
2014-06-01
Full Text Available The COMPASS experiment at CERN accesses pion-photon reactions via the Primakoff effect., where high-energetic pions react with the quasi-real photon field surrounding the target nuclei. When a single real photon is produced, pion Compton scattering is accessed and from the measured cross-section shape, the pion polarisability is determined. The COMPASS measurement is in contradiction to the earlier dedicated measurements, and rather in agreement with the theoretical expectation from ChPT. In the same experimental data taking, reactions with neutral and charged pions in the final state are measured and analyzed in the context of chiral perturbation theory.
Classical Bianchi type I cosmology in K-essence theory
Socorro, J; Espinoza-García, Abraham
2014-01-01
We use one of the simplest forms of the K-essence theory and we apply it to the classical anisotropic Bianchi type I cosmological model, with a barotropic perfect fluid modeling the usual matter content and with cosmological constant. The classical solutions for any but the stiff fluid and without cosmological constant are found in closed form, using a time transformation. We also present the solution whith cosmological constant and some particular values of the barotropic parameter. We present the possible isotropization of the cosmological model, using the ratio between the anisotropic parameters and the volume of the universe and show that this tend to a constant or to zero for different cases. We include also a qualitative analysis of the analog of the Friedmann equation.
Inflationary perturbations in no-scale theories
Energy Technology Data Exchange (ETDEWEB)
Salvio, Alberto [CERN, Theoretical Physics Department, Geneva (Switzerland)
2017-04-15
We study the inflationary perturbations in general (classically) scale-invariant theories. Such scenario is motivated by the hierarchy problem and provides natural inflationary potentials and dark matter candidates. We analyse in detail all sectors (the scalar, vector and tensor perturbations) giving general formulae for the potentially observable power spectra, as well as for the curvature spectral index n{sub s} and the tensor-to-scalar ratio r. We show that the conserved Hamiltonian for all perturbations does not feature negative energies even in the presence of the Weyl-squared term if the appropriate quantisation is performed and argue that this term does not lead to phenomenological problems at least in some relevant setups. The general formulae are then applied to a concrete no-scale model, which includes the Higgs and a scalar, ''the planckion'', whose vacuum expectation value generates the Planck mass. Inflation can be triggered by a combination of the planckion and the Starobinsky scalar and we show that no tension with observations is present even in the case of pure planckion inflation, if the coefficient of the Weyl-squared term is large enough. In general, even quadratic inflation is allowed in this case. Moreover, the Weyl-squared term leads to an isocurvature mode, which currently satisfies the observational bounds, but it may be detectable with future experiments. (orig.)
Chiral Random Matrix Theory and Chiral Perturbation Theory
Damgaard, P H
2011-01-01
Spontaneous breaking of chiral symmetry in QCD has traditionally been inferred indirectly through low-energy theorems and comparison with experiments. Thanks to the understanding of an unexpected connection between chiral Random Matrix Theory and chiral Perturbation Theory, the spontaneous breaking of chiral symmetry in QCD can now be shown unequivocally from first principles and lattice simulations. In these lectures I give an introduction to the subject, starting with an elementary discussion of spontaneous breaking of global symmetries.
Chiral Random Matrix Theory and Chiral Perturbation Theory
Energy Technology Data Exchange (ETDEWEB)
Damgaard, Poul H, E-mail: phdamg@nbi.dk [Niels Bohr International Academy and Discovery Center, The Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen (Denmark)
2011-04-01
Spontaneous breaking of chiral symmetry in QCD has traditionally been inferred indirectly through low-energy theorems and comparison with experiments. Thanks to the understanding of an unexpected connection between chiral Random Matrix Theory and chiral Perturbation Theory, the spontaneous breaking of chiral symmetry in QCD can now be shown unequivocally from first principles and lattice simulations. In these lectures I give an introduction to the subject, starting with an elementary discussion of spontaneous breaking of global symmetries.
Differentiating G-inflation from string gas cosmology using the effective field theory approach
He, Minxi; Liu, Junyu; Lu, Shiyun; Zhou, Siyi; Cai, Yi-Fu; Wang, Yi; Brandenberger, Robert
2016-12-01
A characteristic signature of String Gas Cosmology is primordial power spectra for scalar and tensor modes which are almost scale-invariant but with a red tilt for scalar modes but a blue tilt for tensor modes. This feature, however, can also be realized in the so-called G-inflation model, in which Horndeski operators are introduced which leads to a blue tensor tilt by softly breaking the Null Energy Condition. In this article we search for potential observational differences between these two cosmologies by performing detailed perturbation analyses based on the Effective Field Theory approach. Our results show that, although both two models produce blue tilted tensor perturbations, they behave differently in three aspects. Firstly, String Gas Cosmology predicts a specific consistency relation between the index of the scalar modes ns and that of tensor ones nt, which is hard to be reproduced by G-inflation. Secondly, String Gas Cosmology typically predicts non-Gaussianities which are highly suppressed on observable scales, while G-inflation gives rise to observationally large non-Gaussianities because the kinetic terms in the action become important during inflation. However, after finely tuning the model parameters of G-inflation it is possible to obtain a blue tensor spectrum and negligible non-Gaussianities with a degeneracy between the two models. This degeneracy can be broken by a third observable, namely the scale dependence of the nonlinearity parameter, which vanishes for G-inflation but has a blue tilt in the case of String Gas Cosmology. Therefore, we conclude that String Gas Cosmology is in principle observationally distinguishable from the single field inflationary cosmology, even allowing for modifications such as G-inflation.
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.
SMD-based numerical stochastic perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Dalla Brida, Mattia [Universita di Milano-Bicocca, Dipartimento di Fisica, Milan (Italy); INFN, Sezione di Milano-Bicocca (Italy); Luescher, Martin [CERN, Theoretical Physics Department, Geneva (Switzerland); AEC, Institute for Theoretical Physics, University of Bern (Switzerland)
2017-05-15
The viability of a variant of numerical stochastic perturbation theory, where the Langevin equation is replaced by the SMD algorithm, is examined. In particular, the convergence of the process to a unique stationary state is rigorously established and the use of higher-order symplectic integration schemes is shown to be highly profitable in this context. For illustration, the gradient-flow coupling in finite volume with Schroedinger functional boundary conditions is computed to two-loop (i.e. NNL) order in the SU(3) gauge theory. The scaling behaviour of the algorithm turns out to be rather favourable in this case, which allows the computations to be driven close to the continuum limit. (orig.)
Transport coefficients in Chiral Perturbation Theory
Energy Technology Data Exchange (ETDEWEB)
Fernandez-Fraile, D.; Gomez Nicola, A. [Universidad Complutense, Departamentos de Fisica Teorica I y II, Madrid (Spain)
2007-03-15
We present recent results on the calculation of transport coefficients for a pion gas at zero chemical potential in Chiral Perturbation Theory (ChPT) using the Linear Response Theory (LRT). More precisely, we show the behavior of DC conductivity and shear viscosity at low temperatures. To compute transport coefficients, the standard power counting of ChPT has to be modified. The effects derived from imposing unitarity are also analyzed. As physical applications in relativistic heavy-ion collisions, we show the relation of the DC conductivity to soft-photon production and phenomenological effects related to a non-zero shear viscosity. In addition, our values for the shear viscosity to entropy ratio satisfy the KSS bound. (orig.)
Testing gravity theories using tensor perturbations
Lin, Weikang; Ishak-Boushaki, Mustapha B.
2017-01-01
Primordial gravitational waves constitute a promising probe of the very early universe physics and the laws of gravity. We study the changes to tensor-mode perturbations that can arise in various modified gravity theories. These include a modified friction and a nonstandard dispersion relation. We introduce a physically motivated parametrization of these effects and use current data to obtain excluded parameter spaces. Taking into account the foreground subtraction, we then perform a forecast analysis focusing on the tensor-mode modified-gravity parameters as constrained by future experiments COrE, Stage-IV and PIXIE. For the tensor-to-scalar ratio r=0.01, we find the minimum detectible modified-gravity effects. In particular, the minimum detectable graviton mass is about 7.8˜9.7×10-33 eV, which is of the same order of magnitude as the graviton mass that allows massive gravity to produce late-time cosmic acceleration. Finally, we study the tensor-mode perturbations in modified gravity during inflation. We find that, the tensor spectral index would be additionally related to the friction parameter ν0 by nT=-3ν0-r/8. In some cases, the future experiments will be able to distinguish this relation from the standard one. In sum, primordial gravitational waves provide a complementary avenue to test gravity theories.
Molecular cluster perturbation theory. I. Formalism
Byrd, Jason N.; Jindal, Nakul; Molt, Robert W., Jr.; Bartlett, Rodney J.; Sanders, Beverly A.; Lotrich, Victor F.
2015-11-01
We present second-order molecular cluster perturbation theory (MCPT(2)), a linear scaling methodology to calculate arbitrarily large systems with explicit calculation of individual wave functions in a coupled-cluster framework. This new MCPT(2) framework uses coupled-cluster perturbation theory and an expansion in terms of molecular dimer interactions to obtain molecular wave functions that are infinite order in both the electronic fluctuation operator and all possible dimer (and products of dimers) interactions. The MCPT(2) framework has been implemented in the new SIA/Aces4 parallel architecture, making use of the advanced dynamic memory control and fine-grained parallelism to perform very large explicit molecular cluster calculations. To illustrate the power of this method, we have computed energy shifts, lattice site dipole moments, and harmonic vibrational frequencies via explicit calculation of the bulk system for the polar and non-polar polymorphs of solid hydrogen fluoride. The explicit lattice size (without using any periodic boundary conditions) was expanded up to 1000 HF molecules, with 32,000 basis functions and 10,000 electrons. Our obtained HF lattice site dipole moments and harmonic vibrational frequencies agree well with the existing literature.
New Approaches and Applications for Monte Carlo Perturbation Theory
Energy Technology Data Exchange (ETDEWEB)
Aufiero, Manuele; Bidaud, Adrien; Kotlyar, Dan; Leppänen, Jaakko; Palmiotti, Giuseppe; Salvatores, Massimo; Sen, Sonat; Shwageraus, Eugene; Fratoni, Massimiliano
2017-02-01
This paper presents some of the recent and new advancements in the extension of Monte Carlo Perturbation Theory methodologies and application. In particular, the discussed problems involve Brunup calculation, perturbation calculation based on continuous energy functions, and Monte Carlo Perturbation Theory in loosely coupled systems.
Comment on the "Influence of Cosmological Transitions on the Evolution of Density Perturbations"
Grishchuk, L P
1998-01-01
The "standard inflationary result" has been confirmed once again. This time, by Martin and Schwarz [1]. The fallacy - "the closer the inflationary epoch is to the de Sitter space-time, the less important are large-scale gravitational waves in the CMBR today" - has been repeated and has been claimed to be finally proved. The paper [1] is somewhat better than many other incorrect inflationary papers on the subject of cosmological perurbations. This paper at least operates with correct equations (taken from the criticized work of Grishchuk [2, 3]). Martin and Schwarz say that Grishchuk's conclusion about approximate equality of metric amplitudes for gravitational waves and density perturbations "is wrong because the time evolution of the scalar metric perturbation through the (smooth) reheating transition was not calculated correctly". They reiterate an old inflationary fantasy about "big amplification" of scalar perturbations (in contrast to gravitational waves) during "reheating". They say that after appropria...
Some exact solutions in K-essence theory isotropic cosmology
Pimentel, Luis O
2016-01-01
We use a simple form of the K-essence theory and apply it to the classic isotropic cosmological model and seek exact solutions. The particular form of the kinetic term that we choose is $K \\left(\\phi, X \\right)= K_0(\\phi)X^m +K_1$. The resulting field equations in the homogeneous and isotropic cosmology (FRW)is considered. Several exact solutions are obtained.
Cosmological constant and gravitational theory on D-brane
Shiromizu, T; Torii, T; Shiromizu, Tetsuya; Koyama, Kazuya; Torii, Takashi
2003-01-01
In a toy model we derive the gravitational equation on a self-gravitating curved D-brane. The effective theory on the brane is drastically changed from the ordinal Einstein equation. The net cosmological constant on the brane depends on a tuning between the brane tension and the brane charges. Moreover, non-zero matter stress tensor exists if the net cosmological constant is not zero. This fact indicates a direct connection between matters on the brane and the dark energy.
Iliev, I. T.; Shapiro, P. R.; Raga, A. C.
1998-12-01
The postcollapse structure of objects which form by gravitational condensation out of the expanding cosmological background universe is a key element in the theory of galaxy formation. Towards this end, we have reconsidered the outcome of the nonlinear growth of a uniform, spherical density perturbation in an unperturbed background universe - the cosmological ``top-hat'' problem. We adopt the usual assumption that the collapse to infinite density at a finite time predicted by the top-hat solution is interrupted by a rapid virialization caused by the growth of small-scale inhomogeneities in the initial perturbation. We replace the standard description of the postcollapse object as a uniform sphere in virial equilibrium by a more self-consistent one as a truncated, nonsingular, isothermal sphere in virial and hydrostatic equilibrium, including for the first time a proper treatment of the finite-pressure boundary condition on the sphere. The results differ significantly from both the uniform sphere and the singular isothermal sphere approximations for the postcollapse objects. These results will have a significant effect on a wide range of applications of the Press-Schechter and other semi-analytical models to cosmology. The truncated isothermal sphere solution presented here predicts the virial temperature and integrated mass distribution of the X-ray clusters formed in the CDM model as found by detailed, 3D, numerical gas and N-body dynamical simulations remarkably well. This solution allows us to derive analytically the numerically-calibrated mass-temperature and radius-temperature scaling laws for X-ray clusters which were derived empirically by Evrard, Metzler and Navarro from simulation results for the CDM model.
Time-sliced perturbation theory for large scale structure I: general formalism
Blas, Diego; Garny, Mathias; Ivanov, Mikhail M.; Sibiryakov, Sergey
2016-07-01
We present a new analytic approach to describe large scale structure formation in the mildly non-linear regime. The central object of the method is the time-dependent probability distribution function generating correlators of the cosmological observables at a given moment of time. Expanding the distribution function around the Gaussian weight we formulate a perturbative technique to calculate non-linear corrections to cosmological correlators, similar to the diagrammatic expansion in a three-dimensional Euclidean quantum field theory, with time playing the role of an external parameter. For the physically relevant case of cold dark matter in an Einstein-de Sitter universe, the time evolution of the distribution function can be found exactly and is encapsulated by a time-dependent coupling constant controlling the perturbative expansion. We show that all building blocks of the expansion are free from spurious infrared enhanced contributions that plague the standard cosmological perturbation theory. This paves the way towards the systematic resummation of infrared effects in large scale structure formation. We also argue that the approach proposed here provides a natural framework to account for the influence of short-scale dynamics on larger scales along the lines of effective field theory.
Dynamic field theory and equations of motion in cosmology
Energy Technology Data Exchange (ETDEWEB)
Kopeikin, Sergei M., E-mail: kopeikins@missouri.edu [Department of Physics and Astronomy, University of Missouri, 322 Physics Bldg., Columbia, MO 65211 (United States); Petrov, Alexander N., E-mail: alex.petrov55@gmail.com [Sternberg Astronomical Institute, Lomonosov Moscow State University, Universitetskij Prospect 13, Moscow 119992 (Russian Federation)
2014-11-15
We discuss a field-theoretical approach based on general-relativistic variational principle to derive the covariant field equations and hydrodynamic equations of motion of baryonic matter governed by cosmological perturbations of dark matter and dark energy. The action depends on the gravitational and matter Lagrangian. The gravitational Lagrangian depends on the metric tensor and its first and second derivatives. The matter Lagrangian includes dark matter, dark energy and the ordinary baryonic matter which plays the role of a bare perturbation. The total Lagrangian is expanded in an asymptotic Taylor series around the background cosmological manifold defined as a solution of Einstein’s equations in the form of the Friedmann–Lemaître–Robertson–Walker (FLRW) metric tensor. The small parameter of the decomposition is the magnitude of the metric tensor perturbation. Each term of the series expansion is gauge-invariant and all of them together form a basis for the successive post-Friedmannian approximations around the background metric. The approximation scheme is covariant and the asymptotic nature of the Lagrangian decomposition does not require the post-Friedmannian perturbations to be small though computationally it works the most effectively when the perturbed metric is close enough to the background FLRW metric. The temporal evolution of the background metric is governed by dark matter and dark energy and we associate the large scale inhomogeneities in these two components as those generated by the primordial cosmological perturbations with an effective matter density contrast δρ/ρ≤1. The small scale inhomogeneities are generated by the condensations of baryonic matter considered as the bare perturbations of the background manifold that admits δρ/ρ≫1. Mathematically, the large scale perturbations are given by the homogeneous solution of the linearized field equations while the small scale perturbations are described by a particular solution of
Testing gravity theories using tensor perturbations
Lin, Weikang; Ishak, Mustapha
2016-12-01
Primordial gravitational waves constitute a promising probe of the very early Universe and the laws of gravity. We study in this work changes to tensor-mode perturbations that can arise in various proposed modified gravity theories. These include additional friction effects, nonstandard dispersion relations involving a massive graviton, a modified speed, and a small-scale modification. We introduce a physically motivated parametrization of these effects and use current available data to obtain exclusion regions in the parameter spaces. Taking into account the foreground subtraction, we then perform a forecast analysis focusing on the tensor-mode modified-gravity parameters as constrained by the future experiments COrE, Stage-IV and PIXIE. For a fiducial value of the tensor-to-scalar ratio r =0.01 , we find that an additional friction of 3.5-4.5% compared to GR will be detected at 3 -σ by these experiments, while a decrease in friction will be more difficult to detect. The speed of gravitational waves needs to be by 5-15% different from the speed of light for detection. We find that the minimum detectable graviton mass is about 7.8 - 9.7 ×10-33 eV , which is of the same order of magnitude as the graviton mass that allows massive gravity theories to produce late-time cosmic acceleration. Finally, we study the tensor-mode perturbations in modified gravity during inflation using our parametrization. We find that, in addition to being related to r , the tensor spectral index would be related to the friction parameter ν0 by nT=-3 ν0-r /8 . Assuming that the friction parameter is unchanged throughout the history of the Universe, and that ν0 is much larger than r , the future experiments considered here will be able to distinguish this modified-gravity consistency relation from the standard inflation consistency relation, and thus can be used as a further test of modified gravity. In summary, tensor-mode perturbations and cosmic-microwave-background B
Lie transform Hamiltonian perturbation theory for limit cycle systems
Shah, Tirth; Chakraborty, Sagar
2016-01-01
Usage of a Hamiltonian perturbation theory for nonconservative system is counterintuitive and in general, a technical impossibility by definition. However, the dual (time independent) Hamiltonian formalism for nonconservative systems have opened the door for using various Hamiltonian (and hence, Lagrangian) perturbation theories for investigating the dynamics of such systems. Following the recent extension of the canonical perturbation theory that brings Li\\'enard systems possessing limit cycles under its scope, here we show that the Lie transform Hamiltonian perturbation theory can also be generalized to find perturbative solutions for similar systems. The Lie transform perturbation theories are comparatively easier while seeking higher order corrections in the perturbative series for the solutions and they are also numerically implementable using any symbolic algebra package. For the sake of concreteness, we have illustrated the methodology using the important example of the van der Pol oscillator. While th...
Silent initial conditions for cosmological perturbations with a change of space-time signature
Mielczarek, Jakub; Barrau, Aurelien
2014-01-01
Recent calculations in loop quantum cosmology suggest that a transition from a Lorentzian to an Euclidean space-time might take place in the very early Universe. The transition point leads to a state of silence, characterized by a vanishing speed of light. This behavior can be interpreted as a decoupling of different space points, similar to the one characterizing the BKL phase. In this study, we address the issue of imposing initial conditions for the cosmological perturbations at the transition point between the Lorentzian and Euclidean phases. Motivated by the decoupling of space points, initial conditions characterized by a lack of correlations are investigated. We show that the "white noise" initial conditions are supported by the analysis of the vacuum state in the Euclidean regime adjacent to the state of silence. Furthermore, the possibility of imposing the silent initial conditions at the trans-Planckian surface, characterized by a vanishing speed for the propagation of modes with wavelengths of the ...
Hadronic Lorentz violation in chiral perturbation theory
Kamand, Rasha; Altschul, Brett; Schindler, Matthias R.
2017-03-01
Any possible Lorentz violation in the hadron sector must be tied to Lorentz violation at the underlying quark level. The relationships between the theories at these two levels are studied using chiral perturbation theory. Starting from a two-flavor quark theory that includes dimension-4 Lorentz-violation operators, the effective Lagrangians are derived for both pions and nucleons, with novel terms appearing in both sectors. Since the Lorentz-violation coefficients for nucleons and pions are all related to a single set of underlying quark coefficients, one can compare the sensitivity of different types of experiments. Our analysis shows that atomic physics experiments currently provide constraints on the quark parameters that are stronger by about 10 orders of magnitude than astrophysical experiments with relativistic pions. Alternatively, it is possible to place approximate bounds on pion Lorentz violation using only proton and neutron observations. Under the assumption that the Lorentz-violating operators considered here are the only ones contributing to the relevant observables and taking the currently unknown hadronic low-energy constants to be of natural size, the resulting estimated bounds on four pion parameters are at the 10-23 level, representing improvements of 10 orders of magnitude.
Perturbative analysis in higher-spin theories
Didenko, V. E.; Misuna, N. G.; Vasiliev, M. A.
2016-07-01
A new scheme of the perturbative analysis of the nonlinear HS equations is developed giving directly the final result for the successive application of the homotopy integrations which appear in the standard approach. It drastically simplifies the analysis and results from the application of the standard spectral sequence approach to the higherspin covariant derivatives, allowing us in particular to reduce multiple homotopy integrals resulting from the successive application of the homotopy trick to a single integral. Efficiency of the proposed method is illustrated by various examples. In particular, it is shown how the Central on-shell theorem of the free theory immediately results from the nonlinear HS field equations with no intermediate computations.
Properties of hyperons in chiral perturbation theory
Camalich, J Martin; Alvarez-Ruso, L; Vacas, M J Vicente
2009-01-01
The development of chiral perturbation theory in hyperon phenomenology has been troubled due to power-counting subtleties and to a possible slow convergence. Furthermore, the presence of baryon-resonances, e.g. the lowest-lying decuplet, complicates the approach, and the inclusion of their effects may become necessary. Recently, we have shown that a fairly good convergence is possible using a renormalization prescription of the loop-divergencies which recovers the power counting, is covariant and consistent with analyticity. Moreover, we have systematically incorporated the decuplet resonances taking care of both power-counting and $consistency$ problems. A model-independent understanding of diferent properties including the magnetic moments of the baryon-octet, the electromagnetic structure of the decuplet resonances and the hyperon vector coupling $f_1(0)$, has been successfully achieved within this approach. We will briefly review these developments and stress the important role they play for an accurate d...
Spectral clustering based on matrix perturbation theory
Institute of Scientific and Technical Information of China (English)
TIAN Zheng; LI XiaoBin; JU YanWei
2007-01-01
This paper exposes some intrinsic characteristics of the spectral clustering method by using the tools from the matrix perturbation theory. We construct a weight matrix of a graph and study its eigenvalues and eigenvectors. It shows that the number of clusters is equal to the number of eigenvalues that are larger than 1, and the number of points in each of the clusters can be approximated by the associated eigenvalue. It also shows that the eigenvector of the weight matrix can be used directly to perform clustering; that is, the directional angle between the two-row vectors of the matrix derived from the eigenvectors is a suitable distance measure for clustering. As a result, an unsupervised spectral clustering algorithm based on weight matrix (USCAWM) is developed. The experimental results on a number of artificial and real-world data sets show the correctness of the theoretical analysis.
Modified perturbation theory for the Yukawa model
Poluektov, Yu M
2016-01-01
A new formulation of perturbation theory for a description of the Dirac and scalar fields (the Yukawa model) is suggested. As the main approximation the self-consistent field model is chosen, which allows in a certain degree to account for the effects caused by the interaction of fields. Such choice of the main approximation leads to a normally ordered form of the interaction Hamiltonian. Generation of the fermion mass due to the interaction with exchange of the scalar boson is investigated. It is demonstrated that, for zero bare mass, the fermion can acquire mass only if the coupling constant exceeds the critical value determined by the boson mass. In this connection, the problem of the neutrino mass is discussed.
Hořava Gravity in the Effective Field Theory formalism: From cosmology to observational constraints
Frusciante, Noemi; Raveri, Marco; Vernieri, Daniele; Hu, Bin; Silvestri, Alessandra
2016-09-01
We consider Hořava gravity within the framework of the effective field theory (EFT) of dark energy and modified gravity. We work out a complete mapping of the theory into the EFT language for an action including all the operators which are relevant for linear perturbations with up to sixth order spatial derivatives. We then employ an updated version of the EFTCAMB/EFTCosmoMC package to study the cosmology of the low-energy limit of Hořava gravity and place constraints on its parameters using several cosmological data sets. In particular we use cosmic microwave background (CMB) temperature-temperature and lensing power spectra by Planck 2013, WMAP low- ℓ polarization spectra, WiggleZ galaxy power spectrum, local Hubble measurements, Supernovae data from SNLS, SDSS and HST and the baryon acoustic oscillations measurements from BOSS, SDSS and 6dFGS. We get improved upper bounds, with respect to those from Big Bang Nucleosynthesis, on the deviation of the cosmological gravitational constant from the local Newtonian one. At the level of the background phenomenology, we find a relevant rescaling of the Hubble rate at all epoch, which has a strong impact on the cosmological observables; at the level of perturbations, we discuss in details all the relevant effects on the observables and find that in general the quasi-static approximation is not safe to describe the evolution of perturbations. Overall we find that the effects of the modifications induced by the low-energy Hořava gravity action are quite dramatic and current data place tight bounds on the theory parameters.
Differentiating G-inflation from String Gas Cosmology using the Effective Field Theory Approach
He, Minxi; Lu, Shiyun; Zhou, Siyi; Cai, Yi-Fu; Wang, Yi; Brandenberger, Robert
2016-01-01
A characteristic signature of String Gas Cosmology is primordial power spectra for scalar and tensor modes which are almost scale-invariant but with a red tilt for scalar modes but a blue tilt for tensor modes. This feature, however, can also be realized in the so-called G-inflation model, in which Horndeski operators are introduced which leads to a blue tensor tilt by softly breaking the Null Energy Condition. In this article we search for potential observational differences between these two cosmologies by performing detailed perturbation analyses based on the Effective Field Theory approach. Our results show that, although both two models produce blue tilted tensor perturbations, they behave differently in three aspects. Firstly, String Gas Cosmology predicts a specific consistency relation between the index of the scalar modes $n_s$ and that of tensor ones $n_t$, which is hard to be reproduced by G-inflation. Secondly, String Gas Cosmology typically predicts non-Gaussianities which are highly suppressed o...
Redeveloping gyrokietic theory for multi-scale perturbation
Zhang, Shuangxi; Li, Jiquan
2016-01-01
It's pointed out in this paper that the existing and extensively used pullback transformation of charged particle's Lagrangian 1-form involves an illegal application of the pullback transformation for 1-form not including any perturbed scale to 1-form including perturbed scale. Therefore, modern gyrokinetic theory can not correctly deal with multi-scale perturbation. The coordinate transformation adopted by modern gyrokinetic theory can't avoid the violation of near identity transformation as well, which in fact is the main character that gyrokinetic theory should obey. In this paper, we develop a new Lie perturbed transformation theory for charged particle's Lagrangian 1-form based on the covariant transformation formula for 1-form. Compared with the ordering of modern gyrokinetic theory, this theory widens the amplitude range of perturbation, includes scales of spatial gradient and oscillating frequency of perturbation, and avoids the violation of near identity transformation as well. When combining the new...
Varying-$\\alpha $ Theories and Solutions to the Cosmological Problems
Barrow, John D; Barrow, John D.; Magueijo, Joao
1998-01-01
If the fine structure constant $\\alpha =e^2/(\\hbar c)$ were to change, then a number of interpretations would be possible, attributing this change either to variations in the electron charge, the dielectric constant of the vacuum, the speed of light, or Planck's constant. All these variations should be operationally equivalent and can be related by changes of standard units. We show how the varying speed of light cosmology recently proposed can be rephrased as a dielectric vacuum theory, similar to the one proposed by Bekenstein. The cosmological problems will therefore also be solved in such a theory.
Cosmological perturbation spectra from SL(4,R)-invariant effective actions
Bridgman, H A; Bridgman, Helen A.; Wands, David
2000-01-01
We investigate four-dimensional cosmological vacuum solutions derived from aneffective action invariant under global SL(n,R) transformations. We find thegeneral solutions for linear axion field perturbations about homogeneousdilaton-moduli-vacuum solutions for an SL(4,R)-invariant action and find thespectrum of super-horizon perturbations resulting from vacuum fluctuations in apre big bang scenario. We show that for SL(n,R)-invariant actions with n>3there exists a regime of parameter space of non-zero measure where all theaxion field spectra have positive spectral tilt, as required if light axionfields are to provide a seed for anisotropies in the microwave background andlarge-scale structure in the universe.
Truthing the stretch: Non-perturbative cosmological realizations with multiscale spherical collapse
Neyrinck, Mark C
2015-01-01
Here we present a simple, parameter-free, non-perturbative algorithm that gives low-redshift cosmological particle realizations accurate to few-Megaparsec scales, called muscle (MUltiscale Spherical ColLapse Evolution). It has virtually the same cost as producing N-body-simulation initial conditions, since it works with the 'stretch' parameter {\\psi}, the Lagrangian divergence of the displacement field. It promises to be useful in quickly producing mock catalogs, and to simplify computationally intensive reconstructions of galaxy surveys. muscle applies a spherical-collapse prescription on multiple Gaussian-smoothed scales. It achieves higher accuracy than perturbative schemes (Zel'dovich and 2LPT), and, by including the void-in-cloud process (voids in large-scale collapsing regions), solves problems with a single-scale spherical-collapse scheme. Additionally, we show the behavior of {\\psi} for different morphologies (voids, walls, filaments, and haloes). A Python code to produce these realizations is availab...
Non-perturbative String Theory from Water Waves
Energy Technology Data Exchange (ETDEWEB)
Iyer, Ramakrishnan; Johnson, Clifford V.; /Southern California U.; Pennington, Jeffrey S.; /SLAC
2012-06-14
We use a combination of a 't Hooft limit and numerical methods to find non-perturbative solutions of exactly solvable string theories, showing that perturbative solutions in different asymptotic regimes are connected by smooth interpolating functions. Our earlier perturbative work showed that a large class of minimal string theories arise as special limits of a Painleve IV hierarchy of string equations that can be derived by a similarity reduction of the dispersive water wave hierarchy of differential equations. The hierarchy of string equations contains new perturbative solutions, some of which were conjectured to be the type IIA and IIB string theories coupled to (4, 4k ? 2) superconformal minimal models of type (A, D). Our present paper shows that these new theories have smooth non-perturbative extensions. We also find evidence for putative new string theories that were not apparent in the perturbative analysis.
Cosmological Model Based on Gauge Theory of Gravity
Institute of Scientific and Technical Information of China (English)
WU Ning
2005-01-01
A cosmological model based on gauge theory of gravity is proposed in this paper. Combining cosmological principle and field equation of gravitational gauge field, dynamical equations of the scale factor R(t) of our universe can be obtained. This set of equations has three different solutions. A prediction of the present model is that, if the energy density of the universe is not zero and the universe is expanding, the universe must be space-flat, the total energy density must be the critical density ρc of the universe. For space-flat case, this model gives the same solution as that of the Friedmann model. In other words, though they have different dynamics of gravitational interactions, general relativity and gauge theory of gravity give the same cosmological model.
Cosmological perturbations in an effective and genuinely phantom dark energy Universe
Albarran, Imanol; Morais, João
2016-01-01
We carry out an analysis of the cosmological perturbations in general relativity for three different models which are good candidates to describe the current acceleration of the Universe. These three set-ups are described classically by perfect fluids with a phantom nature and represent deviations from the most widely accepted $\\Lambda$CDM model. In addition, each of the models under study induce different future singularities or abrupt events known as (i) Big Rip, (ii) Little Rip and (iii) Little Sibling of the Big Rip. Only the first one is regarded as a true singularity since it occurs at a finite cosmic time. For this reason, we refer to the others as abrupt events. With the aim to find possible footprints of this scenario in the Universe matter distribution, we not only obtain the evolution of the cosmological scalar perturbations but also calculate the matter power spectrum for each model. Finally, we constrain observationally these models using several measurements of the growth rate function, more pre...
On perturbative field theory and twistor string theory
Bedford, James
2007-01-01
It is well-known that perturbative calculations in field theory can lead to far simpler answers than the Feynman diagram approach might suggest. In some cases scattering amplitudes can be constructed for processes with any desired number of external legs yielding compact expressions which are inaccessible from the point of view of conventional perturbation theory. In this thesis we discuss some attempts to address the nature of this underlying simplicity and then use the results to calculate some previously unknown amplitudes of interest. Witten's twistor string theory is introduced and the CSW rules at tree-level and one-loop are described. We use these techniques to calculate the one-loop gluonic MHV amplitudes in N=1 super-Yang-Mills as a verification of their validity and then proceed to evaluate the general MHV amplitudes in pure Yang-Mills with a scalar running in the loop. This latter amplitude is a new result in QCD. In addition to this, we review some recent on-shell recursion relations for tree-leve...
Gluon Propagator in Fractional Analytic Perturbation Theory
Allendes, Pedro; Cvetič, Gorazd
2014-01-01
We consider the gluon propagator in the Landau gauge at low spacelike momenta and with the dressing function $Z(Q^2)$ at the two-loop order. We incorporate the nonperturbative effects by making the (noninteger) powers of the QCD coupling in the dressing function $Z(Q^2)$ analytic (holomorphic) via the Fractional Analytic Perturbation Theory (FAPT) model, and simultaneously introducing the gluon dynamical mass in the propagator as motivated by the previous analyses of the Dyson-Schwinger equations. The obtained propagator has behavior compatible with the unquenched lattice data ($N_f=2+1$) at low spacelike momenta $0.4 \\ {\\rm GeV} < Q \\lesssim 10$ GeV. We conclude that the removal of the unphysical Landau singularities of the powers of the coupling via the (F)APT prescription, in conjunction with the introduction of the dynamical mass $M \\approx 0.62$ GeV of the gluon, leads to an acceptable behavior of the propagator in the infrared regime.
Properties of hyperons in chiral perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Camalich, J. Martin; Geng, L.S. [Departamento de Fisica Teorica and IFIC, Universidad de Valencia-CSIC (Spain); Alvarez-Ruso, L. [Departamento de Fisica, Universidade de Coimbra (Portugal); Vacas, M.J. Vicente [Departamento de Fisica Teorica and IFIC, Universidad de Valencia-CSIC (Spain)
2010-04-01
The development of chiral perturbation theory in hyperon phenomenology has been troubled due to power-counting subtleties and to a possible slow convergence. Furthermore, the presence of baryon-resonances, e.g. the lowest-lying decuplet, complicates the approach, and the inclusion of their effects may become necessary. Recently, we have shown that a fairly good convergence is possible using a renormalization prescription of the loop-divergencies which recovers the power counting, is covariant and consistent with analyticity. Moreover, we have systematically incorporated the decuplet resonances taking care of both power-counting and consistency problems. A model-independent understanding of different properties including the magnetic moments of the baryon-octet, the electromagnetic structure of the decuplet resonances and the hyperon vector coupling f{sub 1}(0), has been successfully achieved within this approach. We will briefly review these developments and stress the important role they play for an accurate determination of the Cabibbo-Kobayashi-Maskawa matrix element V{sub us} from hyperon semileptonic decay data.
The classification of diagrams in perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Phillips, D.R.; Afnan, I.R. [School of Physical Sciences, The Flinders University of South Australia, GPO Box 2100, Adelaide 5001 (Australia)
1995-06-01
The derivation of scattering equations connecting the amplitudes obtained from diagrammatic expansions is of interest in many branches of physics. One method for deriving such equations is the classification-of-diagrams technique of Taylor. However, as we shall explain in this paper, there are certain points of Taylor`s method which require clarification. First, it is not clear whether Taylor`s original method is equivlant to the simpler classification-of-diagrams scheme used by Thomas, Rinat, Afnan, and Blankleider (TRAB). Second, when the Taylor method is applied to certain problems in a time-dependent perturbation theory it leads to the over-counting of some diagrams. This paper first restates Taylor`s method, in the process uncovering reasons why certain diagrams might be double-counted in the Taylor method. In then explores how far Taylor`s method is equivalent to the simpler TRAB method. Finally, it examines precisely why the double-counting occurs in Taylor`s method and derives corrections which compensate for this double-counting. {copyright} 1995 Academic Press, Inc.
The Classification of Diagrams in Perturbation Theory
Phillips, D. R.; Afnan, I. R.
1995-06-01
The derivation of scattering equations connecting the amplitudes obtained from diagrammatic expansions is of interest in many branches of physics. One method for deriving such equations is the classification-of-diagrams technique of Taylor. However, as we shall explain in this paper, there are certain points of Taylor's method which require clarification. Firstly, it is not clear whether Taylor's original method is equivalent to the simpler classification-of-diagrams scheme used by Thomas, Rinat, Afnan, and Blankleider (TRAB). Secondly, when the Taylor method is applied to certain problems in a time-dependent perturbation theory it leads to the over-counting of some diagrams. This paper first restates Taylor's method, in the process uncovering reasons why certain diagrams might be double-counted in the Taylor method. It then explores how far Taylor's method is equivalent to the simpler TRAB method. Finally, it examines precisely why the double-counting occurs in Taylor's method and derives corrections which compensate for this double-counting.
Testing gravity theories using tensor perturbations
Lin, Weikang
2016-01-01
Primordial gravitational waves constitute a promising probe of the very-early universe and the laws of gravity. We study changes to tensor mode perturbations that can arise in various proposed modified gravity (MG) theories. These include additional friction effects, non-standard dispersion relations involving a massive graviton, a modified speed, and a small-scale modification. We introduce a physically-motivated parameterization of these effects and use current available data to obtain exclusion regions in the parameter spaces. Taking into account the foreground subtraction, we then perform a forecast analysis focusing on the tensor mode MG parameters as constrained by the future experiments COrE, Stage-IV and PIXIE. For a fiducial value of the tensor-to-scalar ratio r=0.01, we find that an additional friction of 3.5-4.5% compared to GR will be detected at $3\\sigma$ by these experiments while a decrease in friction will be more difficult to detect. The speed of gravitational waves needs to be 5-15% differen...
Anisotropic cosmological models and generalized scalar tensor theory
Indian Academy of Sciences (India)
Subenoy Chakraborty; Batul Chandra Santra; Nabajit Chakravarty
2003-10-01
In this paper generalized scalar tensor theory has been considered in the background of anisotropic cosmological models, namely, axially symmetric Bianchi-I, Bianchi-III and Kortowski–Sachs space-time. For bulk viscous ﬂuid, both exponential and power-law solutions have been studied and some assumptions among the physical parameters and solutions have been discussed.
Bimetric gravity doubly coupled to matter: theory and cosmological implications
Energy Technology Data Exchange (ETDEWEB)
Akrami, Yashar; Koivisto, Tomi S.; Mota, David F.; Sandstad, Marit, E-mail: yashar.akrami@astro.uio.no, E-mail: t.s.koivisto@astro.uio.no, E-mail: d.f.mota@astro.uio.no, E-mail: marit.sandstad@astro.uio.no [Institute of Theoretical Astrophysics, University of Oslo P.O. Box 1029 Blindern, N-0315 Oslo (Norway)
2013-10-01
A ghost-free theory of gravity with two dynamical metrics both coupled to matter is shown to be consistent and viable. Its cosmological implications are studied, and the models, in particular in the context of partially massless gravity, are found to explain the cosmic acceleration without resorting to dark energy.
Numerical Stochastic Perturbation Theory and the Gradient Flow
Brida, Mattia Dalla
2013-01-01
We study the Yang-Mills gradient flow using numerical stochastic perturbation theory. As an application of the method we consider the recently proposed gradient flow coupling in the Schr\\"odinger functional for the pure SU(3) gauge theory.
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.
Critique of Coleman's Theory of the Vanishing Cosmological Constant
Susskind, Leonard
In these lectures I would like to review some of the criticisms to the Coleman worm-hole theory of the vanishing cosmological constant. In particular, I would like to focus on the most fundamental assumption that the path integral over topologies defines a probability for the cosmological constant which has the form EXP(A) with A being the Baum-Hawking-Coleman saddle point. Coleman argues that the euclideam path integral over all geometries may be dominated by special configurations which consist of large smooth "spheres" connected by any number of narrow wormholes. Formally summing up such configurations gives a very divergent expression for the path integral…
Perturbative expansion of Chern-Simons theory
SAWON, Justin
2005-01-01
An overview of the perturbative expansion of the Chern--Simons path integral is given. The main goal is to describe how trivalent graphs appear: as they already occur in the perturbative expansion of an analogous finite-dimensional integral, we discuss this case in detail.
Perturbation Theory for Parent Hamiltonians of Matrix Product States
Szehr, Oleg; Wolf, Michael M.
2015-05-01
This article investigates the stability of the ground state subspace of a canonical parent Hamiltonian of a Matrix product state against local perturbations. We prove that the spectral gap of such a Hamiltonian remains stable under weak local perturbations even in the thermodynamic limit, where the entire perturbation might not be bounded. Our discussion is based on preceding work by Yarotsky that develops a perturbation theory for relatively bounded quantum perturbations of classical Hamiltonians. We exploit a renormalization procedure, which on large scale transforms the parent Hamiltonian of a Matrix product state into a classical Hamiltonian plus some perturbation. We can thus extend Yarotsky's results to provide a perturbation theory for parent Hamiltonians of Matrix product states and recover some of the findings of the independent contributions (Cirac et al in Phys Rev B 8(11):115108, 2013) and (Michalakis and Pytel in Comm Math Phys 322(2):277-302, 2013).
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.
The Observational Future of Cosmological Scalar-Tensor Theories
Alonso, David; Ferreira, Pedro G; Zumalacarregui, Miguel
2016-01-01
The next generation of surveys will greatly improve our knowledge of cosmological gravity. In this paper we focus on how Stage IV photometric redshift surveys, including weak lensing and multiple tracers of the matter distribution and radio experiments combined with measurements of the cosmic microwave background will lead to precision constraints on deviations from General Relativity. We use a broad subclass of Horndeski scalar-tensor theories to forecast the accuracy with which we will be able to determine these deviations and their degeneracies with other cosmological parameters. Our analysis includes relativistic effects, does not rely on the quasi-static evolution and makes conservative assumptions about the effect of screening on small scales. We define a figure of merit for cosmological tests of gravity and show how the combination of different types of surveys, probing different length scales and redshifts, can be used to pin down constraints on the gravitational physics to better than a few percent, ...
Particle Creation in Pre-Big-Bang Cosmology theory and observational consequences
Durrer, R; Sakellariadou, M
2000-01-01
We present some phenomenological aspects of the pre-big-bang cosmological model inspired by the duality properties of string theory. In particular, assuming the spatial sections of the homogeneous background geometry to be isotropic, we discuss the quantum production of perturbations of the background fields (gravitons, dilatons, moduli fields), as well as the production of particles which do not contribute to the background, which we call ``seeds''. As such we consider the cases of electromagnetic and axionic seeds. We also discuss their possible observational consequences, for example, we study whether they can provide the origin of primordial galactic magnetic fields, and whether they can generate the initial fluctuations leading to the formation of large-scale structure and the measured cosmic microwave background anisotropies. We finally analyze axion and photon production in four dimensional anisotropic pre-big-bang cosmological models.
Relativistic kinetic theory with applications in astrophysics and cosmology
Vereshchagin, Gregory V
2017-01-01
Relativistic kinetic theory has widespread application in astrophysics and cosmology. The interest has grown in recent years as experimentalists are now able to make reliable measurements on physical systems where relativistic effects are no longer negligible. This ambitious monograph is divided into three parts. It presents the basic ideas and concepts of this theory, equations and methods, including derivation of kinetic equations from the relativistic BBGKY hierarchy and discussion of the relation between kinetic and hydrodynamic levels of description. The second part introduces elements of computational physics with special emphasis on numerical integration of Boltzmann equations and related approaches, as well as multi-component hydrodynamics. The third part presents an overview of applications ranging from covariant theory of plasma response, thermalization of relativistic plasma, comptonization in static and moving media to kinetics of self-gravitating systems, cosmological structure formation and neut...
Perturbative Gravity and Gauge Theory Relations: A Review
Directory of Open Access Journals (Sweden)
Thomas Søndergaard
2012-01-01
Full Text Available This paper is dedicated to the amazing Kawai-Lewellen-Tye relations, connecting perturbative gravity and gauge theories at tree level. The main focus is on n-point derivations and general properties both from a string theory and pure field theory point of view. In particular, the field theory part is based on some very recent developments.
Gauge and motion in perturbation theory
Pound, Adam
2015-01-01
Through second order in perturbative general relativity, a small compact object in an external vacuum spacetime obeys a generalized equivalence principle: although it is accelerated with respect to the external background geometry, it is in free fall with respect to a certain \\emph{effective} vacuum geometry. However, this single principle takes very different mathematical forms, with very different behaviors, depending on how one treats perturbed motion. Furthermore, any description of perturbed motion can be altered by a gauge transformation. In this paper, I clarify the relationship between two treatments of perturbed motion and the gauge freedom in each. I first show explicitly how one common treatment, called the Gralla-Wald approximation, can be derived from a second, called the self-consistent approximation. I next present a general treatment of smooth gauge transformations in both approximations, in which I emphasise that the approximations' governing equations can be formulated in an invariant manner...
Non-Gaussianity of Large-Scale CMB Anisotropies beyond Perturbation Theory
Bartolo, N; Riotto, Antonio
2005-01-01
We compute the fully non-linear Cosmic Microwave Background (CMB) anisotropies on scales larger than the horizon at last-scattering in terms of only the curvature perturbation, providing a generalization of the linear Sachs-Wolfe effect at any order in perturbation theory. We show how to compute the $n$-point connected correlation functions of the large-scale CMB anisotropies for generic primordial seeds provided by standard slow-roll inflation as well as the curvaton and other scenarios for the generation of cosmological perturbations. As an application of our formalism, we compute the three- and four-point connected correlation functions whose detection in future CMB experiments might be used to assess the level of primordial non-Gaussianity, giving the theoretical predictions for the parameters of quadratic and cubic non-linearities f_NL and g_NL.
Massive renormalization scheme and perturbation theory at finite temperature
Energy Technology Data Exchange (ETDEWEB)
Blaizot, Jean-Paul, E-mail: jean-paul.blaizot@cea.fr [Institut de Physique Théorique, CNRS/URA2306, CEA-Saclay, 91191 Gif-sur-Yvette (France); Wschebor, Nicolás [Instituto de Fìsica, Faculdad de Ingeniería, Universidade de la República, 11000 Montevideo (Uruguay)
2015-02-04
We argue that the choice of an appropriate, massive, renormalization scheme can greatly improve the apparent convergence of perturbation theory at finite temperature. This is illustrated by the calculation of the pressure of a scalar field theory with quartic interactions, at 2-loop order. The result, almost identical to that obtained with more sophisticated resummation techniques, shows a remarkable stability as the coupling constant grows, in sharp contrast with standard perturbation theory.
Gauge and motion in perturbation theory
Pound, Adam
2015-08-01
Through second order in perturbative general relativity, a small compact object in an external vacuum spacetime obeys a generalized equivalence principle: although it is accelerated with respect to the external background geometry, it is in free fall with respect to a certain effective vacuum geometry. However, this single principle takes very different mathematical forms, with very different behaviors, depending on how one treats perturbed motion. Furthermore, any description of perturbed motion can be altered by a gauge transformation. In this paper, I clarify the relationship between two treatments of perturbed motion and the gauge freedom in each. I first show explicitly how one common treatment, called the Gralla-Wald approximation, can be derived from a second, called the self-consistent approximation. I next present a general treatment of smooth gauge transformations in both approximations, in which I emphasize that the approximations' governing equations can be formulated in an invariant manner. All of these analyses are carried through second perturbative order, but the methods are general enough to go to any order. Furthermore, the tools I develop, and many of the results, should have broad applicability to any description of perturbed motion, including osculating-geodesic and two-timescale descriptions.
Calculating Luminosity Distance versus Redshift in FRW Cosmology via Homotopy Perturbation Method
Shchigolev, V K
2015-01-01
We propose an efficient analytical method for estimating the luminosity distance in a homogenous Friedmann-Robertson-Walker (FRW) model of the Universe. This method is based on the homotopy perturbation method (HPM), which has high accuracy in many nonlinear problems, and can be easily implemented. For analytical calculation of the luminosity distance, we offer to proceed not from the computation of the integral, which determines it, but from the solution of a certain differential equation with corresponding initial conditions. Solving this equation by means of HPM, we obtain the approximate analytical expressions for the luminosity distance as a function of redshift for two different types of homotopy. Possible extension of this method to other cosmological models is also discussed.
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.
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.
Cosmology of the proxy theory to massive gravity
Heisenberg, Lavinia; Yamamoto, Kazuhiro
2014-01-01
In this paper, we scrutinize very closely the cosmology in the proxy theory to massive gravity obtained in Phys. Rev. D84 (2011) 043503. This proxy theory was constructed by covariantizing the decoupling limit Lagrangian of massive gravity and represents a subclass of Horndeski scalar-tensor theory. Thus, this covariantization unifies two important classes of modified gravity theories, namely massive gravity and Horndeski theories. We go beyond the regime which was studied in Phys. Rev. D84 (2011) 043503 and show that the theory does not admit any homogeneous and isotropic self-accelerated solutions. We illustrate that the only attractor solution is flat Minkowski solution, hence this theory is less appealing as a dark energy model. We also show that the absence of de Sitter solutions is tightly related to the presence of shift symmetry breaking interactions.
Cosmology of the proxy theory to massive gravity
Heisenberg, Lavinia; Kimura, Rampei; Yamamoto, Kazuhiro
2014-05-01
In this paper, we scrutinize very closely the cosmology in the proxy theory to massive gravity obtained in de Rham and Heisenberg [Phys. Rev. D 84, 043503 (2011)]. This proxy theory was constructed by covariantizing the decoupling limit Lagrangian of massive gravity, and it represents a subclass of Horndeski scalar-tensor theory. Thus, this covariantization unifies two important classes of modified gravity theories, namely, massive gravity and Horndeski theories. We go beyond the regime which was studied in de Rham and Heisenberg [Phys. Rev. D 84, 043503 (2011)] and show that the theory does not admit any homogeneous and isotropic self-accelerated solutions. We illustrate that the only attractor solution is the flat Minkowski solution; hence, this theory is less appealing as a dark energy model. We also show that the absence of de Sitter solutions is tightly related to the presence of shift symmetry breaking interactions.
Numerical stochastic perturbation theory in the Schroedinger functional
Energy Technology Data Exchange (ETDEWEB)
Brambilla, Michele; Di Renzo, Francesco; Hesse, Dirk [Parma Univ. (Italy); INFN, Parma (Italy); Dalla Brida, Mattia [Trinity College Dublin (Ireland). School of Mathematics; Sint, Stefan [Trinity College Dublin (Ireland). School of Mathematics; Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC
2013-11-15
The Schroedinger functional (SF) is a powerful and widely used tool for the treatment of a variety of problems in renormalization and related areas. Albeit offering many conceptual advantages, one major downside of the SF scheme is the fact that perturbative calculations quickly become cumbersome with the inclusion of higher orders in the gauge coupling and hence the use of an automated perturbation theory framework is desirable. We present the implementation of the SF in numerical stochastic perturbation theory (NSPT) and compare first results for the running coupling at two loops in pure SU(3) Yang-Mills theory with the literature.
Numerical Stochastic Perturbation Theory in the Schr\\"odinger Functional
Brambilla, Michele; Di Renzo, Francesco; Hesse, Dirk; Sint, Stefan
2013-01-01
The Schr\\"odinger functional (SF) is a powerful and widely used tool for the treatment of a variety of problems in renormalization and related areas. Albeit offering many conceptual advantages, one major downside of the SF scheme is the fact that perturbative calculations quickly become cumbersome with the inclusion of higher orders in the gauge coupling and hence the use of an automated perturbation theory framework is desirable. We present the implementation of the SF in numerical stochastic perturbation theory (NSPT) and compare first results for the running coupling at two loops in pure SU(3) Yang-Mills theory with the literature.
Siegert pseudostate perturbation theory: one- and two-threshold cases
Toyota, K; Watanabe, S; Toyota, Koudai; Morishita, Toru; Watanabe, Shinichi
2005-01-01
Perturbation theory for the Siegert pseudostates (SPS) [Phys.Rev.A 58, 2077 (1998) and Phys.Rev.A 67, 032714 (2003)] is studied for the case of two energetically separated thresholds. The perturbation formulas for the one-threshold case are derived as a limiting case whereby we reconstruct More's theory for the decaying states [Phys.Rev.A 3,1217(1971)] and amend an error. The perturbation formulas for the two-threshold case have additional terms due to the non-standard orthogonality relationship of the Siegert Pseudostates. We apply the theory to a 2-channel model problem, and find the rate of convergence of the perturbation expansion should be examined with the aide of the variance $D= ||E-\\sum_{n}\\lambda^n E^{(n)}||$ instead of the real and imaginary parts of the perturbation energy individually.
Perturbation theory, effective field theory, and oscillations in the power spectrum
Vlah, Zvonimir; Seljak, Uroš; Yat Chu, Man; Feng, Yu
2016-03-01
We explore the relationship between the nonlinear matter power spectrum and the various Lagrangian and Standard Perturbation Theories (LPT and SPT). We first look at it in the context of one dimensional (1-d) dynamics, where 1LPT is exact at the perturbative level and one can exactly resum the SPT series into the 1LPT power spectrum. Shell crossings lead to non-perturbative effects, and the PT ignorance can be quantified in terms of their ratio, which is also the transfer function squared in the absence of stochasticity. At the order of PT we work, this parametrization is equivalent to the results of effective field theory (EFT), and can thus be expanded in terms of the same parameters. We find that its radius of convergence is larger than the SPT loop expansion. The same EFT parametrization applies to all SPT loop terms and if stochasticity can be ignored, to all N-point correlators. In 3-d, the LPT structure is considerably more complicated, and we find that LPT models with parametrization motivated by the EFT exhibit running with k and that SPT is generally a better choice. Since these transfer function expansions contain free parameters that change with cosmological model their usefulness for broadband power is unclear. For this reason we test the predictions of these models on baryonic acoustic oscillations (BAO) and other primordial oscillations, including string monodromy models, for which we ran a series of simulations with and without oscillations. Most models are successful in predicting oscillations beyond their corresponding PT versions, confirming the basic validity of the model. We show that if primordial oscillations are localized to a scale q, the wiggles in power spectrum are approximately suppressed as exp[-k2Σ2(q)/2], where Σ(q) is rms displacement of particles separated by q, which saturates on large scales, and decreases as q is reduced. No oscillatory features survive past k ~ 0.5h/Mpc at z = 0.
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.
Literature in Focus: "Axions: Theory, Cosmology, and Experimental Searches"
2009-01-01
Axions are peculiar hypothetical particles that could both solve the CP problem of quantum chromodynamics and at the same time account for the dark matter of the universe. Based on a series of lectures by world experts in this field held at CERN, this volume provides a pedagogical introduction to the theory, cosmology and astrophysics of these fascinating particles and gives an up-to-date account of the status and prospect of ongoing and planned experimental searches. Learners and practitioners of astroparticle physics will find in this book both a concise introduction and a current reference work to a showcase topic that connects the "inner space" of the elementary particle world with the "outer space" of the universe at large. The book will be presented by Markus Kuster. "Axions: Theory, Cosmology, and Experimental Searches", edited by M. Kuster (Technische Universität Darmstadt), G. Raffelt (Max-Planck-Institu...
Cosmology in new gravitational scalar-tensor theories
Saridakis, Emmanuel N
2016-01-01
We investigate the cosmological applications of new gravitational scalar-tensor theories, which are novel modifications of gravity possessing 2+2 propagating degrees of freedom, arising from a Lagrangian that includes the Ricci scalar and its first and second derivatives. Extracting the field equations we obtain an effective dark energy sector that consists of both extra scalar degrees of freedom, and we determine various observables. We analyze two specific models and we obtain a cosmological behavior in agreement with observations, i.e. transition from matter to dark energy era, with the onset of cosmic acceleration. Additionally, for a particular range of the model parameters, the equation-of-state parameter of the effective dark energy sector can exhibit the phantom-divide crossing. These features reveal the capabilities of these theories, since they arise solely from the novel, higher-derivative terms.
Instantons and cosmologies in string theory
Collinucci, Giulio
2005-01-01
This thesis deals with problems in two subdomains of string theory that are a priori unrelated, and in the last chapter, links are established between those two. The first topic of research is that of D-instantons. These are mathematical objects that allow one to compute physical effects that are mi
Instantons and cosmologies in string theory
Collinucci, Giulio
2005-01-01
This thesis deals with problems in two subdomains of string theory that are a priori unrelated, and in the last chapter, links are established between those two. The first topic of research is that of D-instantons. These are mathematical objects that allow one to compute physical effects that are
Conformal-frame (in)dependence of cosmological observations in scalar-tensor theory
Energy Technology Data Exchange (ETDEWEB)
Chiba, Takeshi [Department of Physics, College of Humanities and Sciences, Nihon University, Tokyo 156-8550 (Japan); Yamaguchi, Masahide, E-mail: chiba@phys.chs.nihon-u.ac.jp, E-mail: gucci@phys.titech.ac.jp [Department of Physics, Tokyo Institute of Technology, Tokyo 152-8551 (Japan)
2013-10-01
We provide the correspondence between the variables in the Jordan frame and those in the Einstein frame in scalar-tensor gravity and consider the frame-(in)dependence of the cosmological observables. In particular, we show that the cosmological observables/relations (redshift, luminosity distance, temperature anisotropies) are frame-independent. We also study the frame-dependence of curvature perturbations and find that the curvature perturbations are conformal invariant if the perturbation is adiabatic and the entropy perturbation between matter and the Brans-Dicke scalar is vanishing. The relation among various definitions of curvature perturbations in the both frames is also discussed, and the condition for the equivalence is clarified.
A study of relative velocity statistics in Lagrangian perturbation theory with PINOCCHIO
Heisenberg, Lavinia; Bartelmann, Matthias
2010-01-01
Subject of this paper is a careful and detailed analysis of the PINOCCHIO algorithm for studying the relative velocity statistics of merging haloes in Lagrangian perturbation theory. Given a cosmological background model, a power spectrum of fluctuations as well as a Gaussian linear density contrast field $\\delta_{\\rm l}$ is generated on a cubic grid, which is then smoothed repeatedly with Gaussian filters. For each Lagrangian particle at position $\\bmath{q}$ and each smoothing radius $R$, the collapse time, the velocities and ellipsoidal truncation are computed using Lagrangian Perturbation Theory. The collapsed medium is then fragmented into isolated objects by an algorithm designed to mimic the accretion and merger events of hierarchical collapse. Directly after the fragmentation process the mass function, merger histories of haloes and the statistics of the relative velocities at merging are evaluated. We reimplemented the algorithm in C++ and optimised the construction of halo merging histories. Comparin...
Cosmological simulations using a static scalar-tensor theory
Energy Technology Data Exchange (ETDEWEB)
RodrIguez-Meza, M A [Depto. de Fisica, Instituto Nacional de Investigaciones Nucleares, Col. Escandon, Apdo. Postal 18-1027, 11801 Mexico D.F (Mexico); Gonzalez-Morales, A X [Departamento Ingenierias, Universidad Iberoamericana, Prol. Paseo de la Reforma 880 Lomas de Santa Fe, Mexico D.F. Mexico (Mexico); Gabbasov, R F [Depto. de Fisica, Instituto Nacional de Investigaciones Nucleares, Col. Escandon, Apdo. Postal 18-1027, 11801 Mexico D.F (Mexico); Cervantes-Cota, Jorge L [Depto. de Fisica, Instituto Nacional de Investigaciones Nucleares, Col. Escandon, Apdo. Postal 18-1027, 11801 Mexico D.F (Mexico)
2007-11-15
We present {lambda}CDM N-body cosmological simulations in the framework of of a static general scalar-tensor theory of gravity. Due to the influence of the non-minimally coupled scalar field, the gravitational potential is modified by a Yukawa type term, yielding a new structure formation dynamics. We present some preliminary results and, in particular, we compute the density and velocity profiles of the most massive group.
Magnetized cosmological models in bimetric theory of gravitation
Indian Academy of Sciences (India)
S D Katore; R S Rane
2006-08-01
Bianchi type-III magnetized cosmological model when the field of gravitation is governed by either a perfect fluid or cosmic string is investigated in Rosen's [1] bimetric theory of gravitation. To complete determinate solution, the condition, viz., = (), where is a constant, between the metric potentials is used. We have assumed different equations of state for cosmic string [2] for the complete solution of the model. Some physical and geometrical properties of the exhibited model are discussed and studied.
Non-perturbative Heavy Quark Effective Theory
DEFF Research Database (Denmark)
Della Morte, Michele; Heitger, Jochen; Simma, Hubert;
2015-01-01
We review a lattice strategy how to non-perturbatively determine the coefficients in the HQET expansion of all components of the heavy-light axial and vector currents, including 1/m_h-corrections. We also discuss recent preliminary results on the form factors parameterizing semi-leptonic B-decays...
Non-perturbative Heavy Quark Effective Theory
DEFF Research Database (Denmark)
Della Morte, Michele; Heitger, Jochen; Simma, Hubert
2015-01-01
We review a lattice strategy how to non-perturbatively determine the coefficients in the HQET expansion of all components of the heavy-light axial and vector currents, including 1/m_h-corrections. We also discuss recent preliminary results on the form factors parameterizing semi-leptonic B-decays...
Perturbation theory for intermolecular forces including exchange
Lekkerkerker, H.N.W.; Laidlaw, W.G.
1970-01-01
Generalized solutions to the Kisenschitz and London perturbation equations are derived. It is pointed out that the results obtained in the formalisms proposed by Hirschfelder (HAV), by Hirschfelder and Silbey, by Murrell and Shaw, and by Musher and Amos are special cases of the generalized treatment
Do we have a theory of early universe cosmology?
Brandenberger, Robert
2014-05-01
The inflationary scenario has become the paradigm of early universe cosmology, and - in conjunction with ideas from superstring theory-has led to speculations about an "inflationary multiverse". From a point of view of phenomenology, the inflationary universe scenario has been very successful. However, the scenario suffers from some conceptual problems, and thus it does not (yet) have the status of a solid theory. There are alternative ideas for the evolution of the very early universe which do not involve inflation but which agree with most current cosmological observations as well as inflation does. In this lecture I will outline the conceptual problems of inflation and introduce two alternative pictures - the "matter bounce" and "string gas cosmology", the latter being a realization of the "emergent universe" scenario based on some key principles of superstring theory. I will demonstrate that these two alternative pictures lead to the same predictions for the power spectrum of the observed large-scale structure and for the angular power spectrum of cosmic microwave background anisotropies as the inflationary scenario, and I will mention predictions for future observations with which the three scenarios can be observationally teased apart.
Observational future of cosmological scalar-tensor theories
Alonso, D.; Bellini, E.; Ferreira, P. G.; Zumalacárregui, M.
2017-03-01
The next generation of surveys will greatly improve our knowledge of cosmological gravity. In this paper we focus on how Stage IV photometric redshift surveys, including weak lensing and multiple tracers of the matter distribution and radio experiments combined with measurements of the cosmic microwave background will lead to precision constraints on deviations from general relativity. We use a broad subclass of Horndeski scalar-tensor theories to forecast the accuracy with which we will be able to determine these deviations and their degeneracies with other cosmological parameters. Our analysis includes relativistic effects, does not rely on the quasistatic evolution and makes conservative assumptions about the effect of screening on small scales. We define a figure of merit for cosmological tests of gravity and show how the combination of different types of surveys, probing different length scales and redshifts, can be used to pin down constraints on the gravitational physics to better than a few percent, roughly an order of magnitude better than present probes. Future cosmological experiments will be able to constrain the Brans-Dicke parameter at a level comparable to Solar System and astrophysical tests.
Cosmological perturbations and observational constraints on non-local massive gravity
Nesseris, Savvas
2014-01-01
Non-local massive gravity can provide an interesting explanation for the late-time cosmic acceleration, with a dark energy equation of state $w_{\\rm DE}$ smaller than $-1$ in the past. We derive the equations of linear cosmological perturbations to confront such models with the observations of large-scale structures. The effective gravitational coupling to non-relativistic matter associated with galaxy clusterings is close to the Newton's gravitational constant $G$ for a mass scale $m$ slightly smaller than the today's Hubble parameter $H_0$. Taking into account the background expansion history as well as the evolution of matter perturbations $\\delta_m$, we test for these models with the Type Ia Supernovae (SnIa) from the Union 2.1, the Cosmic Microwave Background (CMB) measurements from Planck, a collection of baryon acoustic oscillations (BAO), and the growth rate data of $\\delta_m$. Using a higher value of $H_0$ derived from its direct measurement ($H_0 \\gtrsim 70$ km s$^{-1}$ Mpc$^{-1}$) the data strongly...
Survey of mathematical foundations of QFT and perturbative string theory
Sati, H.; Schreiber, U.|info:eu-repo/dai/nl/326056998
2011-01-01
Recent years have seen noteworthy progress in the mathematical formulation of quantum field theory and perturbative string theory. We give a brief survey of these developments. It serves as an introduction to the more detailed collection "Mathematical Foundations of Quantum Field Theory and
Non perturbative methods in two dimensional quantum field theory
Abdalla, Elcio; Rothe, Klaus D
1991-01-01
This book is a survey of methods used in the study of two-dimensional models in quantum field theory as well as applications of these theories in physics. It covers the subject since the first model, studied in the fifties, up to modern developments in string theories, and includes exact solutions, non-perturbative methods of study, and nonlinear sigma models.
Survey of mathematical foundations of QFT and perturbative string theory
Sati, H.; Schreiber, U.
2011-01-01
Recent years have seen noteworthy progress in the mathematical formulation of quantum field theory and perturbative string theory. We give a brief survey of these developments. It serves as an introduction to the more detailed collection "Mathematical Foundations of Quantum Field Theory and Perturba
BRST analysis of QCD$_{2}$ as a perturbed WZW theory
Cabra, D C; Schaposnik, F A
1995-01-01
Integrability of Quantum Chromodynamics in 1+1 dimensions has recently been suggested by formulating it as a perturbed conformal Wess-Zumino-Witten Theory. The present paper further elucidates this formulation, by presenting a detailed BRST analysis.
Integrable Scalar Cosmologies I. Foundations and links with String Theory
Fré, P.; Sagnotti, A.; Sorin, A. S.
2013-12-01
potential, although the corresponding solutions have a long history [19,20]. Possible imprints on the low-ℓ tail of the CMB power spectrum were then discussed in [21], while an analysis of the mechanism near the initial singularity was recently presented in [22]; The eventual collapse in a Big Crunch of systems of this type whenever the scalar tends to settle at a negative extremum of the potential V(ϕ). This was expected: it reflects the fact that AdS has no spatially flat metrics, or that negative extrema are non-admissible fixed points for the corresponding dynamical systems. The fields hi associated with the Cartan generators of the Lie algebra of G, whose number equals the rank r of the coset and whose kinetic terms, determined by the invariant metric of G/H, are canonical up to an overall constant; The axions bI associated with the roots of the Lie algebra of G, whose kinetic terms depend instead on both the Cartan fields hi and the bI. Can the integrable models that we have identified be realized within conventional gauged Supergravity, and for what choices of fluxes? This proviso is important, since some of the simplest potentials in our list do appear, albeit in versions where SUSY is non-linearly realized. Can integrable potentials provide interesting insights on inflationary scenarios behind the slow-roll regime, in addition to those encoded by the single-exponential potential, the simplest member of the set, that already revealed the existence of the climbing phenomenon? How much can one learn from integrable potentials about Cosmology with similar non-integrable potentials? The first question is perhaps the most difficult one, but it is also particularly interesting since a proper understanding of the issue will encode low-energy manifestations of non-perturbative string effects present in these contexts even with supersymmetry broken at high scales. It will be dealt with in detail elsewhere [27].The second question has encouraging answers. There are indeed
Gravitational fixed points from perturbation theory.
Niedermaier, Max R
2009-09-04
The fixed point structure of the renormalization flow in higher derivative gravity is investigated in terms of the background covariant effective action using an operator cutoff that keeps track of powerlike divergences. Spectral positivity of the gauge fixed Hessian can be satisfied upon expansion in the asymptotically free higher derivative coupling. At one-loop order in this coupling strictly positive fixed points are found for the dimensionless Newton constant g(N) and the cosmological constant lambda, which are determined solely by the coefficients of the powerlike divergences. The renormalization flow is asymptotically safe with respect to this fixed point and settles on a lambda(g(N)) trajectory after O(10) units of the renormalization mass scale to accuracy 10(-7).
Adiabaticity and gravity theory independent conservation laws for cosmological perturbations
Directory of Open Access Journals (Sweden)
Antonio Enea Romano
2016-04-01
We then consider an example in which cw=cs, where δPnad=δPc,nad=0 exactly, but the equivalence between Rc and ζ no longer holds. Namely we consider the so-called ultra slow-roll inflation. In this case both Rc and ζ are not conserved. In particular, as for ζ, we find that it is crucial to take into account the next-to-leading order term in ζ's spatial gradient expansion to show its non-conservation, even on superhorizon scales. This is an example of the fact that adiabaticity (in the thermodynamic sense is not always enough to ensure the conservation of Rc or ζ.
Nonlinear Acoustics -- Perturbation Theory and Webster's Equation
Jorge, Rogério
2013-01-01
Webster's horn equation (1919) offers a one-dimensional approximation for low-frequency sound waves along a rigid tube with a variable cross-sectional area. It can be thought as a wave equation with a source term that takes into account the nonlinear geometry of the tube. In this document we derive this equation using a simplified fluid model of an ideal gas. By a simple change of variables, we convert it to a Schr\\"odinger equation and use the well-known variational and perturbative methods to seek perturbative solutions. As an example, we apply these methods to the Gabriel's Horn geometry, deriving the first order corrections to the linear frequency. An algorithm to the harmonic modes in any order for a general horn geometry is derived.
Siegert pseudostate perturbation theory: one- and two-threshold cases
Toyota, Koudai; Morishita, Toru; Watanabe, Shinichi
2005-01-01
Perturbation theory for the Siegert pseudostates (SPS) [Phys.Rev.A 58, 2077 (1998) and Phys.Rev.A 67, 032714 (2003)] is studied for the case of two energetically separated thresholds. The perturbation formulas for the one-threshold case are derived as a limiting case whereby we reconstruct More's theory for the decaying states [Phys.Rev.A 3,1217(1971)] and amend an error. The perturbation formulas for the two-threshold case have additional terms due to the non-standard orthogonality relations...
Energy Continuity in Degenerate Density Functional Perturbation Theory
Palenik, Mark C
2016-01-01
Fractional occupation numbers can produce open-shell degeneracy in density functional theory. We develop the corresponding perturbation theory by requiring that a differentiable map connects the initial and perturbed states. The degenerate state connects to a single perturbed state which extremizes, but does not necessarily minimize or maximize, the energy with respect to occupation numbers. Using a system of three electrons in a harmonic oscillator potential, we relate the counterintuitive sign of first-order occupation numbers to eigenvalues of the electron-electron interaction Hessian.
String theory, cosmology and varying constants
Damour, Thibault
In string theory the coupling `constants' appearing in the low-energy effective Lagrangian are determined by the vacuum expectation values of some (a priori) massless scalar fields (dilaton, moduli). This naturally leads one to expect a correlated variation of all the coupling constants, and an associated violation of the equivalence principle. We review some string-inspired theoretical models which incorporate such a spacetime variation of coupling constants while remaining naturally compatible both with phenomenological constraints coming from geochemical data (Oklo; Rhenium decay) and with present equivalence principle tests. Barring a very unnatural fine-tuning of parameters, a variation of the fine-structure constant as large as that recently `observed' by Webb et al. in quasar absorption spectra appears to be incompatible with these phenomenological constraints. Independently of any model, it is emphasized that the best experimental probe of varying constants are high-precision tests of the universality of free fall, such as MICROSCOPE and STEP.
String theory, cosmology and varying constants
Damour, Thibault Marie Alban Guillaume
2002-01-01
In string theory the coupling ``constants'' appearing in the low-energy effective Lagrangian are determined by the vacuum expectation values of some (a priori) massless scalar fields (dilaton, moduli). This naturally leads one to expect a correlated variation of all the coupling constants, and an associated violation of the equivalence principle. We review some string-inspired theoretical models which incorporate such a spacetime variation of coupling constants while remaining naturally compatible both with phenomenological constraints coming from geochemical data (Oklo; Rhenium decay) and with present equivalence principle tests. Barring a very unnatural fine-tuning of parameters, a variation of the fine-structure constant as large as that recently ``observed'' by Webb et al. in quasar absorption spectra appears to be incompatible with these phenomenological constraints. Independently of any model, it is emphasized that the best experimental probe of varying constants are high-precision tests of the universa...
Non-perturbative Nekrasov partition function from string theory
Energy Technology Data Exchange (ETDEWEB)
Antoniadis, I., E-mail: ignatios.antoniadis@cern.ch [Department of Physics, CERN – Theory Division, CH-1211 Geneva 23 (Switzerland); Florakis, I., E-mail: florakis@mppmu.mpg.de [Max-Planck-Institut für Physik, Werner-Heisenberg-Institut, 80805 München (Germany); Hohenegger, S., E-mail: stefan.hohenegger@cern.ch [Department of Physics, CERN – Theory Division, CH-1211 Geneva 23 (Switzerland); Narain, K.S., E-mail: narain@ictp.trieste.it [High Energy Section, The Abdus Salam International Center for Theoretical Physics, Strada Costiera, 11-34014 Trieste (Italy); Zein Assi, A., E-mail: zeinassi@cern.ch [Department of Physics, CERN – Theory Division, CH-1211 Geneva 23 (Switzerland); Centre de Physique Théorique (UMR CNRS 7644), Ecole Polytechnique, 91128 Palaiseau (France)
2014-03-15
We calculate gauge instanton corrections to a class of higher derivative string effective couplings introduced in [1]. We work in Type I string theory compactified on K3×T{sup 2} and realise gauge instantons in terms of D5-branes wrapping the internal space. In the field theory limit we reproduce the deformed ADHM action on a general Ω-background from which one can compute the non-perturbative gauge theory partition function using localisation. This is a non-perturbative extension of [1] and provides further evidence for our proposal of a string theory realisation of the Ω-background.
Perturbation theories for the thermodynamic properties of fluids and solids
Solana, J R
2013-01-01
This book, Perturbation Theories for the Thermodynamic Properties of Fluids and Solids, provides a comprehensive review of current perturbation theories-as well as integral equation theories and density functional theories-for the equilibrium thermodynamic and structural properties of classical systems. Emphasizing practical applications, the text avoids complex theoretical derivations as much as possible. It begins with discussions of the nature of intermolecular forces and simple potential models. The book also presents a summary of statistical mechanics concepts and formulae. In addition, i
Accelerating cosmologies and a phase transition in M-theory
Energy Technology Data Exchange (ETDEWEB)
Wohlfarth, Mattias N.R
2003-06-19
M-theory compactifies on a seven-dimensional time-dependent hyperbolic or flat space to a four-dimensional FLRW cosmology undergoing a period of accelerated expansion in Einstein conformal frame. The strong energy condition is violated by the scalar fields produced in the compactification, as is necessary to evade the no-go theorem for time-independent compactifications. The four-form field strength of eleven-dimensional supergravity smoothly switches on during the period of accelerated expansion in hyperbolic compactifications, whereas in flat compactifications, the three-form potential smoothly changes its sign. For small acceleration times, this behaviour is like a phase transition of the three-form potential, during which the cosmological scale factor approximately doubles.
Accelerating Cosmologies and a Phase Transition in M-Theory
Wohlfarth, M N R
2003-01-01
M-theory compactifies on a seven-dimensional time-dependent hyperbolic or flat space to a four-dimensional FLRW cosmology undergoing a period of accelerated expansion in Einstein conformal frame. The strong energy condition is violated by the scalar fields produced in the compactification, as is necessary to evade the no-go theorem for time-independent compactifications. The four-form field strength of eleven-dimensional supergravity smoothly switches on during the period of accelerated expansion in hyperbolic compactifications, whereas in flat compactifications, the three-form potential smoothly changes its sign. For small acceleration times, this behaviour is like a phase transition of the three-form potential, during which the cosmological scale factor approximately doubles.
Horava-Lifshitz Theory and Applications to Cosmology and Astrophysics
Energy Technology Data Exchange (ETDEWEB)
Wang, Anzhong [Baylor Univ., Waco, TX (United States). Department of Physics
2014-08-14
This final report describes the activities of the Baylor University Gravity, Cosmology and Astroparticle Physics (GCAP) group on the project: Horava-Lifshitz Theory and Applications to Cosmology and Astrophysics, during the time, August 15, 2010 - August 14, 2014. We are grateful for the financial support provided by the U.S. Department of Energy for this research, which leads to our exceptional success. We are very proud to say that we have achieved all the goals set up in our project and made significant contributions to the understanding of the field. In particular, with this DOE support, we have published 38 articles in the prestigious national/international journals, which have already received about 1000 citations so far.
Quintin, Jerome; Sherkatghanad, Zeinab; Cai, Yi-Fu; Brandenberger, Robert H.
2015-09-01
Assuming that curvature perturbations and gravitational waves originally arise from vacuum fluctuations in a matter-dominated phase of contraction, we study the dynamics of the cosmological perturbations evolving through a nonsingular bouncing phase described by a generic single scalar field Lagrangian minimally coupled to Einstein gravity. In order for such a model to be consistent with the current upper limits on the tensor-to-scalar ratio, there must be an enhancement of the curvature fluctuations during the bounce phase. We show that, while it remains possible to enlarge the amplitude of curvature perturbations due to the nontrivial background evolution, this growth is very limited because of the conservation of curvature perturbations on super-Hubble scales. We further perform a general analysis of the evolution of primordial non-Gaussianities through the bounce phase. By studying the general form of the bispectrum we show that the non-Gaussianity parameter fNL (which is of order unity before the bounce phase) is enhanced during the bounce phase if the curvature fluctuations grow. Hence, in such nonsingular bounce models with matter given by a single scalar field, there appears to be a tension between obtaining a small enough tensor-to-scalar ratio and not obtaining a value of fNL in excess of the current upper bounds. This conclusion may be considered as a "no-go" theorem that rules out any single field matter bounce cosmology starting with vacuum initial conditions for the fluctuations.
Shapiro, Paul R.; Iliev, Ilian T.; Raga, Alejandro C.
1999-07-01
The post-collapse structure of objects that form by gravitational condensation out of the expanding cosmological background universe is a key element in the theory of galaxy formation. Towards this end, we have reconsidered the outcome of the non-linear growth of a uniform, spherical density perturbation in an unperturbed background universe - the cosmological `top-hat' problem. We adopt the usual assumption that the collapse to infinite density at a finite time predicted by the top-hat solution is interrupted by a rapid virialization caused by the growth of small-scale inhomogeneities in the initial perturbation. We replace the standard description of the post-collapse object as a uniform sphere in virial equilibrium by a more self-consistent one as a truncated, non-singular, isothermal sphere in virial and hydrostatic equilibrium, including for the first time a proper treatment of the finite-pressure boundary condition on the sphere. The results differ significantly from both the uniform sphere and the singular isothermal sphere approximations for the post-collapse objects. The virial temperature that results is more than twice the previously used `standard value' of the post-collapse uniform sphere approximation, but 1.4 times smaller than that of the singular, truncated isothermal sphere approximation. The truncation radius is 0.554 times the radius of the top-hat at maximum expansion, and the ratio of the truncation radius to the core radius is 29.4, yielding a central density that is 514 times greater than at the surface and 1.8x10^4 times greater than that of the unperturbed background density at the epoch of infinite collapse predicted by the top-hat solution. For the top-hat fractional overdensity delta_L predicted by extrapolating the linear solution into the non-linear regime, the standard top-hat model assumes that virialization is instantaneous at delta_Ldelta_c=1.686 i.e. the epoch at which the non-linear top-hat reaches infinite density. The surface
The perturbative ghost propagator in Landau gauge from numerical stochastic perturbation theory
Di Renzo, F; Perlt, H; Schiller, A; Torrero, C
2008-01-01
We present one- and two-loop results for the ghost propagator in Landau gauge calculated in Numerical Stochastic Perturbation Theory (NSPT). The one-loop results are compared with available standard Lattice Perturbation Theory in the infinite-volume limit. We discuss in detail how to perform the different necessary limits in the NSPT approach and discuss a recipe to treat logarithmic terms by introducing ``finite-lattice logs''. We find agreement with the one-loop result from standard Lattice Perturbation Theory and estimate, from the non-logarithmic part of the ghost propagator in two-loop order, the unknown constant contribution to the ghost self-energy in the RI'-MOM scheme in Landau gauge. That constant vanishes within our numerical accuracy.
Perturbation Theory of Massive Yang-Mills Fields
Veltman, M.
1968-08-01
Perturbation theory of massive Yang-Mills fields is investigated with the help of the Bell-Treiman transformation. Diagrams containing one closed loop are shown to be convergent if there are more than four external vector boson lines. The investigation presented does not exclude the possibility that the theory is renormalizable.
Perturbative algebraic quantum field theory at finite temperature
Energy Technology Data Exchange (ETDEWEB)
Lindner, Falk
2013-08-15
We present the algebraic approach to perturbative quantum field theory for the real scalar field in Minkowski spacetime. In this work we put a special emphasis on the inherent state-independence of the framework and provide a detailed analysis of the state space. The dynamics of the interacting system is constructed in a novel way by virtue of the time-slice axiom in causal perturbation theory. This method sheds new light in the connection between quantum statistical dynamics and perturbative quantum field theory. In particular it allows the explicit construction of the KMS and vacuum state for the interacting, massive Klein-Gordon field which implies the absence of infrared divergences of the interacting theory at finite temperature, in particular for the interacting Wightman and time-ordered functions.
Renormalization Group Optimized Perturbation Theory at Finite Temperatures
Kneur, J -L
2015-01-01
A recently developed variant of the so-called optimized perturbation theory (OPT), making it perturbatively consistent with renormalization group (RG) properties, RGOPT, was shown to drastically improve its convergence for zero temperature theories. Here the RGOPT adapted to finite temperature is illustrated with a detailed evaluation of the two-loop pressure for the thermal scalar $ \\lambda\\phi^4$ field theory. We show that already at the simple one-loop level this quantity is exactly scale-invariant by construction and turns out to qualitatively reproduce, with a rather simple procedure, results from more sophisticated resummation methods at two-loop order, such as the two-particle irreducible approach typically. This lowest order also reproduces the exact large-$N$ results of the $O(N)$ model. Although very close in spirit, our RGOPT method and corresponding results differ drastically from similar variational approaches, such as the screened perturbation theory or its QCD-version, the (resummed) hard therm...
Convergence of coupled cluster perturbation theory
Eriksen, Janus Juul; Matthews, Devin A; Jørgensen, Poul; Olsen, Jeppe
2016-01-01
The convergence of a recently proposed coupled cluster (CC) family of perturbation series [Eriksen et al., J. Chem. Phys. 140, 064108 (2014)], in which the energetic difference between a parent and a target CC model is expanded in orders of the M{\\o}ller-Plesset (MP) fluctuation potential, is investigated for four prototypical closed-shell systems (Ne, singlet methylene, distorted HF, and the fluoride anion) in standard and augmented basis sets. In these investigations, energy corrections of the various series have been calculated to high orders and their convergence radii determined by probing for possible front- and back-door intruder states. In summary, we conclude how it is primarily the choice of target state, and not the choice of parent state, which ultimately governs the convergence behavior of a given series. For example, restricting the target state to, say, triple or quadruple excitations might remove intruders present in series that target the full configuration interaction (FCI) limit, such as th...
Primordial Perturbations in Einstein-Aether and BPSH Theories
Armendariz-Picon, Cristian; Garriga, Jaume
2010-01-01
We study the primordial perturbations generated during a stage of single-field inflation in Einstein-aether theories. Quantum fluctuations of the inflaton and aether fields seed long wavelength adiabatic and isocurvature scalar perturbations, as well as transverse vector perturbations. Geometrically, the isocurvature mode is the potential for the velocity field of the aether with respect to matter. For a certain range of parameters, this mode may lead to a sizable random velocity of the aether within the observable universe. The adiabatic mode corresponds to curvature perturbations of co-moving slices (where matter is at rest). In contrast with the standard case, it has a non-vanishing anisotropic stress on large scales. Scalar and vector perturbations may leave significant imprints on the cosmic microwave background. We calculate their primordial spectra, analyze their contributions to the temperature anisotropies, and formulate some of the phenomenological constraints that follow from observations. These ma...
Directory of Open Access Journals (Sweden)
Yize Fan
2015-06-01
Full Text Available Cosmological perturbations of the non-minimally coupled scalar field dark energy in both the metric and Palatini formalisms are studied in this paper. We find that on the large scales with the energy density of dark energy becoming more and more important in the low redshift region, the gravitational potential becomes smaller and smaller, and the effect of non-minimal coupling becomes more and more apparent. In the metric formalism the value of the gravitational potential in the non-minimally coupled case with a positive coupling constant is less than that in the minimally coupled case, while it is larger if the coupling constant is negative. This is different from that in the Palatini formalism where the value of gravitational potential is always smaller. Based upon the quasi-static approximation on the sub-horizon scales, the linear growth of matter is also analyzed. We obtain that the effective Newton's constants in the metric and Palatini formalisms have different forms. A negative coupling constant enhances the gravitational interaction, while a positive one weakens it. Although the metric and Palatini formalisms give different linear growth rates, the difference is very small and the current observation cannot distinguish them effectively.
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...
A Theory of the Perturbed Consumer with General Budgets
DEFF Research Database (Denmark)
McFadden, Daniel L; Fosgerau, Mogens
We consider demand systems for utility-maximizing consumers facing general budget constraints whose utilities are perturbed by additive linear shifts in marginal utilities. Budgets are required to be compact but are not required to be convex. We define demand generating functions (DGF) whose......-valued and smooth in their arguments. We also give sufficient conditions for integrability of perturbed demand. Our analysis provides a foundation for applications of consumer theory to problems with nonlinear budget constraints....
Brillouin-Wigner perturbation theory in open electromagnetic systems
Muljarov, E A; Zimmermann, R; 10.1209/0295-5075/92/50010
2012-01-01
A Brillouin-Wigner perturbation theory is developed for open electromagnetic systems which are characterised by discrete resonant states with complex eigenenergies. Since these states are exponentially growing at large distances, a modified normalisation is introduced that allows a simple spectral representation of the Green's function. The perturbed modes are found by solving a linear eigenvalue problem in matrix form. The method is illustrated on exactly solvable one- and three-dimensional examples being, respectively, a dielectric slab and a microsphere.
Cosmological solutions in string theory with dilaton self interaction potential
Mora, C
2003-01-01
In this work we present homogeneous and isotropic cosmological solutions for the low energy limit of string theory with a self interacting potential for the scalar field. For a potential that is a linear combination of two exponential, a family of exact solutions are found for the different spatial curvatures. Among this family a non singular accelerating solution for positive curvature is singled out and the violation of the energy conditions for that solution is studied, and also its astrophysical consequences. The string coupling for this solution is finite. (Author)
Einstein's general theory of relativity with modern applications in cosmology
Grøn, Øyvind
2007-01-01
Many of us have experienced the same; fallen and broken something. Yet supposedly, gravity is the weakest of the fundamental forces; it is claimed to be 10-15 times weaker than electromagnetism. Still, every one of us has more or less had a personal relationship with gravity. Einstein’s General Theory of Relativity: With Modern Applications in Cosmology by Oyvind Gron and Sigbjorn Hervik is about gravity and the concept of gravity as Albert Einstein saw it- curved spaces, four-dimensional manifolds and geodesics. The book starts with the 1st principals of relativity and an introduction to Einstein’s field equations. Next up are the three classical tests of the relativity theory and an introduction to black holes. The book contains several topics not found in other textbooks, such as Kaluza-Klein theory, anisotropic models of the universe, and new developments involving brane cosmology. Gron and Hervik have included a part in the book called "Advanced Topics." These topics range from the very edge of resea...
Extended Theories of Gravity in cosmological and astrophysical applications
Wojnar, Aneta
2016-01-01
The main subjects of the PhD dissertation concern cosmological models considered in Palatini f(R) gravity and scalar-tensor theories. We introduce a simple generalization of the LCDM model based on Palatini modified gravity with quadratic Starobinsky term. A matter source is provided by generalized Chaplygin gas. The statistical analysis of our model is investigated. We use dynamical system approach to study the evolution of the Universe. The model reaches a very good agreement with the newest experimental data and yields an inflationary epoch caused by a singularity of the type III. The present-day accelerated expansion is also provided by the model. We also show that the Lie and Noether symmetry approaches are very useful tools in cosmological considerations. We examine two other models of Extended Theories of Gravity (ETGs): the novel hybrid metric-Palatini gravity and a minimally coupled to gravity scalar field. The first one is applied to homogeneous and isotropic model while in the scalar-tensor theory ...
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...
One-loop Chiral Perturbation Theory with two fermion representations
DeGrand, Thomas; Neil, Ethan T; Shamir, Yigal
2016-01-01
We develop Chiral Perturbation Theory for chirally broken theories with fermions in two different representations of the gauge group. Any such theory has a non-anomalous singlet $U(1)_A$ symmetry, yielding an additional Nambu-Goldstone boson when spontaneously broken. We calculate the next-to-leading order corrections for the pseudoscalar masses and decay constants, which include the singlet Nambu-Goldstone boson, as well as for the two condensates. The results can be generalized to more than two representations.
Perturbation theory for string sigma models
Bianchi, Lorenzo
2016-01-01
In this thesis we investigate quantum aspects of the Green-Schwarz superstring in various AdS backgrounds relevant for the AdS/CFT correspondence, providing several examples of perturbative computations in the corresponding integrable sigma-models. We start by reviewing in details the supercoset construction of the superstring action in $AdS_5 \\times S^5$, pointing out the limits of this procedure for $AdS_4$ and $AdS_3$ backgrounds. For the $AdS_4 \\times CP^3$ case we give a thorough derivation of an alternative action, based on the double-dimensional reduction of eleven-dimensional super-membranes. We then consider the expansion about the BMN vacuum and the S-matrix for the scattering of worldsheet excitations in the decompactification limit. To evaluate its elements efficiently we describe a unitarity-based method resulting in a very compact formula yielding the cut-constructible part of any one-loop two-dimensional S-matrix. In the second part of this review we analyze the superstring action on $AdS_4 \\ti...
Perturbed period-doubling bifurcation. I. Theory
DEFF Research Database (Denmark)
Svensmark, Henrik; Samuelsen, Mogens Rugholm
1990-01-01
-defined way that is a function of the amplitude and the frequency of the signal. New scaling laws between the amplitude of the signal and the detuning δ are found; these scaling laws apply to a variety of quantities, e.g., to the shift of the bifurcation point. It is also found that the stability...... of a microwave-driven Josephson junction confirm the theory. Results should be of interest in parametric-amplification studies....
A brief overview of hard-thermal-loop perturbation theory
Su, Nan
2012-01-01
The poor convergence of quantum field theory at finite temperature has been one of the main obstacles in the practical applications of thermal QCD for decades. Here we briefly review the progress of hard-thermal-loop perturbation theory (HTLpt) in reorganizing the perturbative expansion in order to improve the convergence. The quantum mechanical anharmonic oscillator is used as a simple example to show the breakdown of weak-coupling expansion, and variational perturbation theory is introduced as an effective resummation scheme for divergent weak-coupling expansions. We discuss HTLpt thermodynamic calculations for QED, pure-glue QCD, and QCD with N_f=3 up to three-loop order. The results suggest that HTLpt provides a systematic framework that can be used to calculate both static and dynamic quantities for temperatures relevant at LHC.
A Brief Overview of Hard-Thermal-Loop Perturbation Theory
Institute of Scientific and Technical Information of China (English)
SU Nan
2012-01-01
The poor convergence of quantum field theory at finite temperature has been one of the main obstacles in the practical applications of thermal QCD for decades. Here we briefly review the progress of hard-thermal-loop perturbation theory （HTLpt） in reorganizing the perturbative expansion in order to improve the convergence. The quantum mechanical anharmonic oscillator is used as a simple example to show the breakdown of weak-coupling expansion, and variational perturbation theory is introduced as an effective resummation scheme for divergent weak-coupling expansions. We discuss HTLpt thermodynamic calculations for QED, pure-glue QCD, and QCD with Nf = 3 up to three-loop order. The results suggest that HTLpt provides a systematic framework that can be used to calculate both static and dynamic quantities for temperatures relevant at LHC.
Perturbative study of Yang-Mills theory in the infrared
Siringo, Fabio
2015-01-01
Pure Yang-Mills SU(N) theory is studied in four dimensional space and Landau gauge by a double perturbative expansion based on a massive free-particle propagator. By dimensional regularization, all diverging mass terms cancel exactly in the double expansion, without the need to include mass counterterms that would spoil the symmetry of the original Lagrangian. The emerging perturbation theory is safe in the infrared and shares the same behaviour of the standard perturbation theory in the UV. At one-loop, Gluon and ghost propagators are found in excellent agreement with the data of lattice simulations and an infrared-safe running coupling is derived. A natural scale m=0.5-0.6 GeV is extracted from the data for N=3.
Solomon, Adam R
2015-01-01
The accelerating expansion of the Universe poses a major challenge to our understanding of fundamental physics. One promising avenue is to modify general relativity and obtain a new description of the gravitational force. Because gravitation dominates the other forces mostly on large scales, cosmological probes provide an ideal testing ground for theories of gravity. In this thesis, we describe two complementary approaches to the problem of testing gravity using cosmology. In the first part, we discuss the cosmological solutions of massive gravity and its generalisation to a bimetric theory. These theories describe a graviton with a small mass, and can potentially explain the late-time acceleration in a technically-natural way. We describe these self-accelerating solutions and investigate the cosmological perturbations in depth, beginning with an investigation of their linear stability, followed by the construction of a method for solving these perturbations in the quasistatic limit. This allows the predictio...
The accuracy of QCD perturbation theory at high energies
Dalla Brida, Mattia; Korzec, Tomasz; Ramos, Alberto; Sint, Stefan; Sommer, Rainer
2016-01-01
We discuss the determination of the strong coupling $\\alpha_\\mathrm{\\overline{MS}}^{}(m_\\mathrm{Z})$ or equivalently the QCD $\\Lambda$-parameter. Its determination requires the use of perturbation theory in $\\alpha_s(\\mu)$ in some scheme, $s$, and at some energy scale $\\mu$. The higher the scale $\\mu$ the more accurate perturbation theory becomes, owing to asymptotic freedom. As one step in our computation of the $\\Lambda$-parameter in three-flavor QCD, we perform lattice computations in a scheme which allows us to non-perturbatively reach very high energies, corresponding to $\\alpha_s = 0.1$ and below. We find that perturbation theory is very accurate there, yielding a three percent error in the $\\Lambda$-parameter, while data around $\\alpha_s \\approx 0.2$ is clearly insufficient to quote such a precision. It is important to realize that these findings are expected to be generic, as our scheme has advantageous properties regarding the applicability of perturbation theory.
Translational symmetry breaking in field theories and the cosmological constant
Evans, Nick; Morris, Tim R.; Scott, Marc
2016-01-01
We argue, at a very basic effective field theory level, that higher dimension operators in scalar theories that break symmetries at scales close to their ultraviolet completion cutoff include terms that favor the breaking of translation (Lorentz) invariance, potentially resulting in striped, checkerboard or general crystal-like phases. Such descriptions can be thought of as the effective low energy description of QCD-like gauge theories near their strong coupling scale where terms involving higher dimension operators are generated. Our low energy theory consists of scalar fields describing operators such as q ¯q and q ¯F(2 n )q . Such scalars can have kinetic mixing terms that generate effective momentum dependent contributions to the mass matrix. We show that these can destabilize the translationally invariant vacuum. It is possible that in some real gauge theory such operators could become sufficiently dominant to realize such phases, and it would be interesting to look for them in lattice simulations. We present a holographic model of the same phenomena which includes renormalization group running. A key phenomenological motive to look at such states is recent work that shows that the nonlinear response in R2 gravity to such short-range fluctuations can mimic a cosmological constant. Intriguingly in a cosmology with such a Starobinsky inflation term, to generate the observed value of the present day acceleration would require stripes at the electroweak scale. Unfortunately, low energy phenomenological constraints on Lorentz violation in the electron-photon system appear to strongly rule out any such possibility outside of a disconnected dark sector.
Non-Gaussianities in the Cosmological Perturbation Spectrum due to Primordial Anisotropy II
Dey, Anindya
2012-01-01
We continue to investigate possible signatures of a pre-inflationary anisotropic phase in two-point and three point correlation functions of the curvature perturbation for high-momentum modes which exit the horizon well after isotropization. The late time dynamics of these modes is characterized by a non-Bunch Davies vacuum state which encodes all the information about initial anisotropy in the background space-time. We observe that, unlike the non-planar momenta, there exist regimes of planar momenta for which scale invariance of the power spectrum is strongly broken. This regime of planar momenta gives rise to enhanced non-Gaussianity in certain squeezed triangle configurations, although the enhancement of the $f_{NL}$ parameter is limited by the breakdown of linear perturbation theory at "exact planarity". Finally, we demonstrate that for the range of planar modes for which scale invariance of the power spectrum is preserved, non-Gaussianity in the curvature perturbation spectrum is naturally constrained t...
Perturbative Quantum Field Theory in the String-Inspired Formalism
Schubert, C
2001-01-01
We review the status and present range of applications of the ``string-inspired'' approach to perturbative quantum field theory. This formalism offers the possibility of computing effective actions and S-matrix elements in a way which is similar in spirit to string perturbation theory, and bypasses much of the apparatus of standard second-quantized field theory. Its development was initiated by Bern and Kosower, originally with the aim of simplifying the calculation of scattering amplitudes in quantum chromodynamics and quantum gravity. We give a short account of the original derivation of the Bern-Kosower rules from string theory. Strassler's alternative approach in terms of first-quantized particle path integrals is then used to generalize the formalism to more general field theories, and, in the abelian case, also to higher loop orders. A considerable number of sample calculations are presented in detail, with an emphasis on quantum electrodynamics.
Lie transforms and their use in Hamiltonian perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Cary, J.R.
1978-06-01
A review is presented of the theory of Lie transforms as applied to Hamiltonian systems. We begin by presenting some general background on the Hamiltonian formalism and by introducing the operator notation for canonical transformations. We then derive the general theory of Lie transforms. We derive the formula for the new Hamiltonian when one uses a Lie transform to effect a canonical transformation, and we use Lie transforms to prove a very general version of Noether's theorem, or the symmetry-equals-invariant theorem. Next we use the general Lie transform theory to derive Deprit's perturbation theory. We illustrate this perturbation theory by application to two well-known problems in classical mechanics. Finally we present a chapter on conventions. There are many ways to develop Lie transforms. The last chapter explains the reasons for the choices made here.
The adhesion model as a field theory for cosmological clustering
Energy Technology Data Exchange (ETDEWEB)
Rigopoulos, Gerasimos, E-mail: rigopoulos@thphys.uni-heidelberg.de [Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 12, Heidelberg, 69120 Germany (Germany)
2015-01-01
The adhesion model has been proposed in the past as an improvement of the Zel'dovich approximation, providing a good description of the formation of the cosmic web. We recast the model as a field theory for cosmological large scale structure, adding a stochastic force to account for power generated from very short, highly non-linear scales that is uncorrelated with the initial power spectrum. The dynamics of this Stochastic Adhesion Model (SAM) is reminiscent of the well known Kardar-Parisi-Zhang equation with the difference that the viscosity and the noise spectrum are time dependent. Choosing the viscosity proportional to the growth factor D restricts the form of noise spectrum through a 1-loop renormalization argument. For this choice, the SAM field theory is renormalizable to one loop. We comment on the suitability of this model for describing the non-linear regime of the CDM power spectrum and its utility as a relatively simple approach to cosmological clustering.
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.
Exact Cosmological Solutions in Modified Brans--Dicke Theory
Rasouli, S M M
2016-01-01
In this paper, we obtain exact cosmological vacuum solutions for an extended FLRW homogenous and isotropic Brans-Dicke (BD) universe in five dimensions for all values of the curvature index. Then, by employing the equations associated to a modified Brans-Dicke theory (MBDT) [1], we construct the physics on a four-dimensional hypersurface. We show that the induced matter obeys the equation of state of a fluid of a barotropic type. We discuss the properties of such an induced matter for some values of the equation of state parameter and analyze in detail their corresponding solutions. To illustrate the cosmological behaviors of the solutions, we contrast our solutions with those present the standard Brans-Dicke theory. We retrieve that, in MBDT scenario, it is impossible to find a physically acceptable solution associated to the negative curvature for both the dust-dominated and radiation-dominated universes. However, for a spatially flat and closed universes, we argue that our obtained solutions are more gener...
Algebraic geometry informs perturbative quantum field theory
Broadhurst, David
2014-01-01
Single-scale Feynman diagrams yield integrals that are periods, namely projective integrals of rational functions of Schwinger parameters. Algebraic geometry may therefore inform us of the types of number to which these integrals evaluate. We give examples at 3, 4 and 6 loops of massive Feynman diagrams that evaluate to Dirichlet $L$-series of modular forms and examples at 6, 7 and 8 loops of counterterms that evaluate to multiple zeta values or polylogarithms of the sixth root of unity. At 8 loops and beyond, algebraic geometry informs us that polylogs are insufficient for the evaluation of terms in the beta-function of $\\phi^4$ theory. Here, modular forms appear as obstructions to polylogarithmic evaluation.
Horava Gravity in the Effective Field Theory formalism: from cosmology to observational constraints
Frusciante, Noemi; Vernieri, Daniele; Hu, Bin; Silvestri, Alessandra
2015-01-01
We consider Horava gravity within the framework of the EFT of dark energy and modified gravity. We work out a complete mapping of the theory into the EFT language for an action including all the operators which are relevant for linear perturbations with up to sixth order spatial derivatives. We then employ an updated version of the EFTCAMB/EFTCosmoMC package to study the cosmology of the low-energy limit of Horava gravity and place constraints on its parameters using several cosmological data sets. In particular we consider two cases: the first in which the three parameters of the low-energy theory are all varied and a second case that is tuned to evade PPN constraints, reducing the number of free parameters to two. We employ data sets which include the CMB TT and lensing power spectra by Planck 2013, WMAP low-l polarization spectra, the WiggleZ galaxy power spectrum, the local Hubble measurements, Supernovae data from SNLS, SDSS and HST and the BAO measurements from BOSS, SDSS and 6dFGS. For both cases we es...
Anthropic reasoning and typicality in multiverse cosmology and string theory
Energy Technology Data Exchange (ETDEWEB)
Weinstein, Steven [Perimeter Institute for Theoretical Physics, 31 Caroline St, Waterloo, ON N2L 2Y5 (Canada); Department of Philosophy, University of Waterloo, Waterloo, ON N2L 3G1 (Canada); Department of Physics, University of Waterloo, Waterloo, ON N2L 3G1 (Canada)
2006-06-21
Anthropic arguments in multiverse cosmology and string theory rely on the weak anthropic principle (WAP). We show that the principle is fundamentally ambiguous. It can be formulated in one of two ways, which we refer to as WAP{sub 1} and WAP{sub 2}. We show that WAP{sub 2}, the version most commonly used in anthropic reasoning, makes no physical predictions unless supplemented by a further assumption of 'typicality', and we argue that this assumption is both misguided and unjustified. WAP{sub 1}, however, requires no such supplementation; it directly implies that any theory that assigns a non-zero probability to our universe predicts that we will observe our universe with probability one. We argue, therefore, that WAP{sub 1} is preferable, and note that it has the benefit of avoiding the inductive overreach characteristic of much anthropic reasoning.
Introduction to Palatini theories of gravity and nonsingular cosmologies
Olmo, Gonzalo J
2013-01-01
These notes are a summary of lectures given at the Instituto de Astronomia of the Universidad Nacional Autonoma de Mexico (UNAM), the Dipartimento di Fisica of the Universita degli studi di Salerno (Italy), and the Instituto de Fisica Corpuscular of the Universitat de Valencia (Spain) during the year 2012. Basic mathematical aspects of Palatini theories of gravity, which are constructed assuming that metric and connection are independent geometrical entities, are briefly introduced and discussed, and followed by a detailed derivation of the field equations of some rather general Lagrangian theories. Applications to the early universe are considered paying special attention to the avoidance of the big bang singularity. The analysis of non-singular cosmologies carried out in arXiv:1005.4136 [gr-qc] is extended to include several perfect fluids.
Numerical Stochastic Perturbation Theory and Gradient Flow in {\\phi}^4 Theory
Brida, Mattia Dalla; Kennedy, Anthony D
2015-01-01
In this contribution we present an exploratory study of several novel methods for numerical stochastic perturbation theory. For the investigation we consider observables defined through the gradient flow in the simple {\\phi}^4 theory.
Perturbative Quantum Gravity and its Relation to Gauge Theory
Directory of Open Access Journals (Sweden)
Bern Zvi
2002-01-01
Full Text Available In this review we describe a non-trivial relationship between perturbative gauge theory and gravity scattering amplitudes. At the semi-classical or tree-level, the scattering amplitudes of gravity theories in flat space can be expressed as a sum of products of well defined pieces of gauge theory amplitudes. These relationships were first discovered by Kawai, Lewellen, and Tye in the context of string theory, but hold more generally. In particular, they hold for standard Einstein gravity. A method based on $D$-dimensional unitarity can then be used to systematically construct all quantum loop corrections order-by-order in perturbation theory using as input thegravity tree amplitudes expressed in terms of gauge theory ones. More generally, the unitarity method provides a means for perturbatively quantizing massless gravity theories without the usual formal apparatus associated with the quantization of constrained systems. As one application, this method was used to demonstrate that maximally supersymmetric gravity is less divergent in the ultraviolet than previously thought.
Taming Landau singularities in QCD perturbation theory: The analytic approach
Stefanis, N G
2013-01-01
The aim of this topical article is to outline the fundamental ideas underlying the recently developed Fractional Analytic Perturbation Theory (FAPT) of QCD and present its main calculational tools. For this, it is first necessary to review previous methods to apply QCD perturbation theory at low spacelike momentum scales, where the influence of the Landau singularities becomes inevitable. Several concepts are considered and their limitations are pointed out. The usefulness of FAPT is discussed in terms of two characteristic hadronic quantities: the perturbatively calculable part of the pion's electromagnetic form factor in the spacelike region and the Higgs-boson decay into a b\\bar b pair in the timelike region. In the first case, the focus is on the optimization of the prediction with respect to the choice of the renormalization scheme and the dependence on the renormalization and the factorization scales. The second case serves to show that the application of FAPT to this reaction reaches already at the fou...
Adjoint operators and perturbation theory of black holes
Cartas-Fuentevilla, R
2000-01-01
We present a new approach for finding conservation laws in the perturbation theory of black holes which applies for the more general cases of non-Hermitian equations governing the perturbations. The approach is based on a general result which establishes that a covariantly conserved current can be obtained from a solution of any system of homogeneous linear differential equations and a solution of the adjoint system. It is shown that the results obtained from the present approach become essentially the same (with some diferences) to those obtained by means of the traditional methods in the simplest black hole geometry corresponding to the Schwarzschild space-time. The future applications of our approach for studying the perturbations of black hole space-time in string theory is discussed.
Chishtie, F A
2002-01-01
Pade approximants (PA) have been widely applied in practically all areas of physics. This thesis focuses on developing PA as tools for both perturbative and non- perturbative quantum field theory (QFT). In perturbative QFT, we systematically estimate higher (unknown) loop terms via the asymptotic formula devised by Samuel et al. This algorithm, generally denoted as the asymptotic Pade approximation procedure (APAP), has greatly enhanced scope when it is applied to renormalization-group-(RG-) invariant quantities. A presently-unknown higher-loop quantity can then be matched with the approximant over the entire momentum region of phenomenological interest. Furthermore, the predicted value of the RG coefficients can be compared with the RG-accessible coefficients (at the higher-loop order), allowing a clearer indication of the accuracy of the predicted RG-inaccessible term. This methodology is applied to hadronic Higgs decay rates (H → bb¯ and H → gg, both within the Standard Model and...
The Breakdown of String Perturbation Theory for Many External Particles
Ghosh, Sudip
2016-01-01
We consider massless string scattering amplitudes in a limit where the number of external particles becomes very large, while the energy of each particle remains small. Using the growth of the volume of the relevant moduli space, and by means of independent numerical evidence, we argue that string perturbation theory breaks down in this limit. We discuss some remarkable implications for the information paradox.
A non-perturbative study of massive gauge theories
DEFF Research Database (Denmark)
Della Morte, Michele; Hernandez, Pilar
2013-01-01
We consider a non-perturbative formulation of an SU(2) massive gauge theory on a space-time lattice, which is also a discretised gauged non-linear chiral model. The lattice model is shown to have an exactly conserved global SU(2) symmetry. If a scaling region for the lattice model exists and the ...
Breakdown of String Perturbation Theory for Many External Particles.
Ghosh, Sudip; Raju, Suvrat
2017-03-31
We consider massless string scattering amplitudes in a limit where the number of external particles becomes very large, while the energy of each particle remains small. Using the growth of the volume of the relevant moduli space, and by means of independent numerical evidence, we argue that string perturbation theory breaks down in this limit. We discuss some remarkable implications for the information paradox.
Perturbation theory of massive Yang-Mills fields
Veltman, M.J.G.
1968-01-01
Perturbation theory of massive Yang-Mills fields is investigated with the help of the Bell-Treiman transformation. Primitive diagrams containing one closed loop are shown to be convergent if there are more than four external vector boson lines. The investigation presented does not exclude the possib
Cosmological Implications of the Effective Field Theory of Cosmic Acceleration
Mueller, Eva-Maria; Watson, Scott
2012-01-01
We consider cosmological constraints arising from the background expansion history on the ef- fective field theory of cosmic acceleration, a theoretical framework that allows for a unified way to classify both models of dark energy and modified gravity within the linear regime. In the Einstein frame, the most general action for the background can be written in terms of a canonical scalar field which is non-minimally coupled to matter. The leading corrections to the action are expressible through a quartic kinetic term, and scalar couplings to a Gauss-Bonnet curvature term and the Einstein tensor. We determine the implications of the terms in this general action for the predicted expansion history in the context of dynamical attractors. We find that each modifies the matter dominated and/or accelerative eras in ways that allow us to place cosmological constraints on them. We present current constraints on the effective action using the latest Type Ia supernovae, Cosmic Microwave Background, and Baryonic Acoust...
Non-Perturbative Asymptotic Improvement of Perturbation Theory and Mellin-Barnes Representation
Directory of Open Access Journals (Sweden)
Samuel Friot
2010-10-01
Full Text Available Using a method mixing Mellin-Barnes representation and Borel resummation we show how to obtain hyperasymptotic expansions from the (divergent formal power series which follow from the perturbative evaluation of arbitrary ''N-point'' functions for the simple case of zero-dimensional φ4 field theory. This hyperasymptotic improvement appears from an iterative procedure, based on inverse factorial expansions, and gives birth to interwoven non-perturbative partial sums whose coefficients are related to the perturbative ones by an interesting resurgence phenomenon. It is a non-perturbative improvement in the sense that, for some optimal truncations of the partial sums, the remainder at a given hyperasymptotic level is exponentially suppressed compared to the remainder at the preceding hyperasymptotic level. The Mellin-Barnes representation allows our results to be automatically valid for a wide range of the phase of the complex coupling constant, including Stokes lines. A numerical analysis is performed to emphasize the improved accuracy that this method allows to reach compared to the usual perturbative approach, and the importance of hyperasymptotic optimal truncation schemes.
Nonperturbative Quantum Physics from Low-Order Perturbation Theory.
Mera, Héctor; Pedersen, Thomas G; Nikolić, Branislav K
2015-10-02
The Stark effect in hydrogen and the cubic anharmonic oscillator furnish examples of quantum systems where the perturbation results in a certain ionization probability by tunneling processes. Accordingly, the perturbed ground-state energy is shifted and broadened, thus acquiring an imaginary part which is considered to be a paradigm of nonperturbative behavior. Here we demonstrate how the low order coefficients of a divergent perturbation series can be used to obtain excellent approximations to both real and imaginary parts of the perturbed ground state eigenenergy. The key is to use analytic continuation functions with a built-in singularity structure within the complex plane of the coupling constant, which is tailored by means of Bender-Wu dispersion relations. In the examples discussed the analytic continuation functions are Gauss hypergeometric functions, which take as input fourth order perturbation theory and return excellent approximations to the complex perturbed eigenvalue. These functions are Borel consistent and dramatically outperform widely used Padé and Borel-Padé approaches, even for rather large values of the coupling constant.
Invariant exchange perturbation theory for multicenter systems: Time-dependent perturbations
Energy Technology Data Exchange (ETDEWEB)
Orlenko, E. V., E-mail: eorlenko@mail.ru; Evstafev, A. V.; Orlenko, F. E. [St. Petersburg State Technical University (Russian Federation)
2015-02-15
A formalism of exchange perturbation theory (EPT) is developed for the case of interactions that explicitly depend on time. Corrections to the wave function obtained in any order of perturbation theory and represented in an invariant form include exchange contributions due to intercenter electron permutations in complex multicenter systems. For collisions of atomic systems with an arbitrary type of interaction, general expressions are obtained for the transfer (T) and scattering (S) matrices in which intercenter electron permutations between overlapping nonorthogonal states belonging to different centers (atoms) are consistently taken into account. The problem of collision of alpha particles with lithium atoms accompanied by the redistribution of electrons between centers is considered. The differential and total charge-exchange cross sections of lithium are calculated.
Alien calculus and non perturbative effects in Quantum Field Theory
Bellon, Marc P.
2016-12-01
In many domains of physics, methods for dealing with non-perturbative aspects are required. Here, I want to argue that a good approach for this is to work on the Borel transforms of the quantities of interest, the singularities of which give non-perturbative contributions. These singularities in many cases can be largely determined by using the alien calculus developed by Jean Écalle. My main example will be the two point function of a massless theory given as a solution of a renormalization group equation.
Advanced Methods in Black-Hole Perturbation Theory
Pani, Paolo
2013-01-01
Black-hole perturbation theory is a useful tool to investigate issues in astrophysics, high-energy physics, and fundamental problems in gravity. It is often complementary to fully-fledged nonlinear evolutions and instrumental to interpret some results of numerical simulations. Several modern applications require advanced tools to investigate the linear dynamics of generic small perturbations around stationary black holes. Here, we present an overview of these applications and introduce extensions of the standard semianalytical methods to construct and solve the linearized field equations in curved spacetime. Current state-of-the-art techniques are pedagogically explained and exciting open problems are presented.
Equivalence of Two Contour Prescriptions in Superstring Perturbation Theory
Sen, Ashoke
2016-01-01
Conventional superstring perturbation theory based on the world-sheet approach gives divergent results for the S-matrix whenever the total center of mass energy of the incoming particles exceeds the threshold of production of any final state consistent with conservation laws. Two systematic approaches have been suggested for dealing with this difficulty. The first one involves deforming the integration cycles over the moduli space of punctured Riemann surfaces into complexified moduli space. The second one treats the amplitude as a sum of superstring field theory Feynman diagrams and deforms the integration contours over loop energies of the Feynman diagram into the complex plane. In this paper we establish the equivalence of the two prescriptions to all orders in perturbation theory. Since the second approach is known to lead to unitary amplitudes, this establishes the consistency of the first prescription with unitarity.
Unified cosmology with scalar-tensor theory of gravity
Energy Technology Data Exchange (ETDEWEB)
Tajahmad, Behzad [Faculty of Physics, University of Tabriz, Tabriz (Iran, Islamic Republic of); Sanyal, Abhik Kumar [Jangipur College, Department of Physics, Murshidabad (India)
2017-04-15
Unlike the Noether symmetry, a metric independent general conserved current exists for non-minimally coupled scalar-tensor theory of gravity if the trace of the energy-momentum tensor vanishes. Thus, in the context of cosmology, a symmetry exists both in the early vacuum and radiation dominated era. For slow roll, symmetry is sacrificed, but at the end of early inflation, such a symmetry leads to a Friedmann-like radiation era. Late-time cosmic acceleration in the matter dominated era is realized in the absence of symmetry, in view of the same decayed and redshifted scalar field. Thus, unification of early inflation with late-time cosmic acceleration with a single scalar field may be realized. (orig.)
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.
Optimized Perturbation Theory at Finite Temperature Two-Loop Analysis
Chiku, S
2000-01-01
We study the optimized perturbation theory (OPT) at finite temperature, which is a self-consistent resummation method. Firstly, we generalize the idea of the OPT to optimize the coupling constant in lambda phi^4 theory, and give a proof of the renormalizability of this generalized OPT. Secondly, the principle of minimal sensitivity and the criterion of the fastest apparent convergence, which are conditions to determine the optimal parameter values, are examined in lambda phi^4 theory. Both conditions exhibit a second-order transition at finite temperature with critical exponent beta = 0.5 in the two-loop approximation.
Vector and Axial Currents in Wilson Chiral Perturbation Theory
Aoki, Sinya; Sharpe, Stephen R
2009-01-01
We reconsider the construction of the vector and axial-vector currents in Wilson Chiral Perturbation Theory (WChPT), the low-energy effective theory for lattice QCD with Wilson fermions. We discuss in detail the finite renormalization of the currents that has to be taken into account in order to properly match the currents. We explicitly show that imposing the chiral Ward identities on the currents does, in general, affect the axial-vector current at O(a). As an application of our results we compute the pion decay constant to one loop in the two flavor theory. Our result differs from previously published ones.
Chiral Perturbation Theory with Virtual Photons and Leptons
Knecht, M; Rupertsberger, H W; Talavera, P
2000-01-01
We construct a low-energy effective field theory which allows the full treatment of isospin-breaking effects in semileptonic weak interactions. To this end, we enlarge the particle spectrum of chiral perturbation theory with virtual photons by including also the light leptons as dynamical degrees of freedom. Using super-heat-kernel techniques, we determine the additional one-loop divergences generated by the presence of virtual leptons and give the full list of associated local counterterms. We illustrate the use of our effective theory by applying it to the decays pi -> l nu_{l} and K -> l nu_{l}.
Generalized Møller-Plesset Partitioning in Multiconfiguration Perturbation Theory.
Kobayashi, Masato; Szabados, Ágnes; Nakai, Hiromi; Surján, Péter R
2010-07-13
Two perturbation (PT) theories are developed starting from a multiconfiguration (MC) zero-order function. To span the configuration space, the theories employ biorthogonal vector sets introduced in the MCPT framework. At odds with previous formulations, the present construction operates with the full Fockian corresponding to a principal determinant, giving rise to a nondiagonal matrix of the zero-order resolvent. The theories provide a simple, generalized Møller-Plesset (MP) second-order correction to improve any reference function, corresponding either to a complete or incomplete model space. Computational demand of the procedure is determined by the iterative inversion of the Fockian, similarly to the single reference MP theory calculated in a localized basis. Relation of the theory to existing multireference (MR) PT formalisms is discussed. The performance of the present theories is assessed by adopting the antisymmetric product of strongly orthogonal geminal (APSG) wave functions as the reference function.
Introduction to non-perturbative heavy quark effective theory
Energy Technology Data Exchange (ETDEWEB)
Sommer, R. [DESY, Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC
2010-08-15
My lectures on the effective field theory for heavy quarks, an expansion around the static limit, concentrate on the motivation and formulation of HQET, its renormalization and discretization. This provides the basis for understanding that and how this effective theory can be formulated fully non-perturbatively in the QCD coupling, while by the very nature of an effective field theory, it is perturbative in the expansion parameter 1/m. After the couplings in the effective theory have been determined, the result at a certain order in 1/m is unique up to higher order terms in 1/m. In particular the continuum limit of the lattice regularized theory exists and leaves no trace of how it was regularized. In other words, the theory yields an asymptotic expansion of the QCD observables in 1/m - as usual in a quantum field theory modified by powers of logarithms. None of these properties has been shown rigorously (e.g. to all orders in perturbation theory) but perturbative computations and recently also non-perturbative lattice results give strong support to this ''standard wisdom''. A subtle issue is that a theoretically consistent formulation of the theory is only possible through a non-perturbative matching of its parameters with QCD at finite values of 1/m. As a consequence one finds immediately that the splitting of a result for a certain observable into, for example, lowest order and first order is ambiguous. Depending on how the matching between effective theory and QCD is done, a first order contribution may vanish and appear instead in the lowest order. For example, the often cited phenomenological HQET parameters anti {lambda} and {lambda}{sub 1} lack a unique non-perturbative definition. But this does not affect the precision of the asymptotic expansion in 1/m. The final result for an observable is correct up to order (1/m){sup n+1} if the theory was treated including (1/m){sup n} terms. Clearly, the weakest point of HQET is that it
String and M-theory cosmological solutions with Ramond forms
Lukas, André; Ovruta, Burt A.; Waldram, Daniel
1997-02-01
A general framework for studying a large class of cosmological solutions of the low-energy limit of type II string theory and of M-theory, with non-trivial Ramond form fields excited, is presented. The framework is applicable to space-times decomposable into a set of flat or, more generally, maximally symmetric spatial subspaces, with multiple non-trivial form fields spanning one or more of the subspaces. It is shown that the corresponding low-energy equations of motion are equivalent to those describing a particle moving in a moduli space consisting of the scale factors of the subspaces together with the dilaton. The choice of which form fields are excited controls the potential term in the particle equations. Two classes of exact solutions are given, those corresponding to exciting only a single form and those with multiple forms excited which correspond to Toda theories. Although typically these solutions begin or end in a curvature singularity, there is a subclass with positive spatial curvature which appears to be singularity free. Elements of this class are directly related to certain black p-brane solutions.
Anisotropic Cosmological Model in Modified Brans--Dicke Theory
Rasouli, S M M; Sepangi, Hamid R
2011-01-01
It has been shown that four dimensional Brans-Dicke theory with effective matter field and self interacting potential can be achieved from vacuum 5D BD field equations, where we refer to as modified Brans-Dicke theory (MBDT). We investigate a generalized Bianchi type I anisotropic cosmology in 5D BD theory, and by employing obtained formalism, we derive induced-matter on any 4D hypersurface in context of the MBDT. We illustrate that if the usual spatial scale factors are functions of time while scale factor of extra dimension is constant, and scalar field depends on time and fifth coordinate, then in general, one will encounter inconsistencies in field equations. Then, we assume the scale factors and scalar field depend on time and extra coordinate as separated variables in power law forms. Hence, we find a few classes of solutions in 5D spacetime through which, we probe the one which leads to a generalized Kasner relations among Kasner parameters. The induced scalar potential is found to be in power law or i...
Driven similarity renormalization group: Third-order multireference perturbation theory.
Li, Chenyang; Evangelista, Francesco A
2017-03-28
A third-order multireference perturbation theory based on the driven similarity renormalization group (DSRG-MRPT3) approach is presented. The DSRG-MRPT3 method has several appealing features: (a) it is intruder free, (b) it is size consistent, (c) it leads to a non-iterative algorithm with O(N(6)) scaling, and (d) it includes reference relaxation effects. The DSRG-MRPT3 scheme is benchmarked on the potential energy curves of F2, H2O2, C2H6, and N2 along the F-F, O-O, C-C, and N-N bond dissociation coordinates, respectively. The nonparallelism errors of DSRG-MRPT3 are consistent with those of complete active space third-order perturbation theory and multireference configuration interaction with singles and doubles and show significant improvements over those obtained from DSRG second-order multireference perturbation theory. Our efficient implementation of the DSRG-MRPT3 based on factorized electron repulsion integrals enables studies of medium-sized open-shell organic compounds. This point is demonstrated with computations of the singlet-triplet splitting (ΔST=ET-ES) of 9,10-anthracyne. At the DSRG-MRPT3 level of theory, our best estimate of the adiabatic ΔST is 3.9 kcal mol(-1), a value that is within 0.1 kcal mol(-1) from multireference coupled cluster results.
Perturbations of single-field inflation in modified gravity theory
Directory of Open Access Journals (Sweden)
Taotao Qiu
2015-05-01
Full Text Available In this paper, we study the case of single field inflation within the framework of modified gravity theory where the gravity part has an arbitrary form f(R. Via a conformal transformation, this case can be transformed into its Einstein frame where it looks like a two-field inflation model. However, due to the existence of the isocurvature modes in such a multi-degree-of-freedom (m.d.o.f. system, the (curvature perturbations are not equivalent in two frames, so despite of its convenience, it is illegal to treat the perturbations in its Einstein frame as the “real” ones as we always do for pure f(R theory or single field with nonminimal coupling. Here by pulling the results of curvature perturbations back into its original Jordan frame, we show explicitly the power spectrum and spectral index of the perturbations in the Jordan frame, as well as how it differs from the Einstein frame. We also fit our results with the newest Planck data. Since there is large parameter space in these models, we show that it is easy to fit the data very well.
Ultraviolet finiteness of Chiral Perturbation Theory for two-dimensional Quantum Electrodynamics
Paston, S A; Franke, V A
2003-01-01
We consider the perturbation theory in the fermion mass (chiral perturbation theory) for the two-dimensional quantum electrodynamics. With this aim, we rewrite the theory in the equivalent bosonic form in which the interaction is exponential and the fermion mass becomes the coupling constant. We reformulate the bosonic perturbation theory in the superpropagator language and analyze its ultraviolet behavior. We show that the boson Green's functions without vacuum loops remain finite in all orders of the perturbation theory in the fermion mass.
Impacts of biasing schemes in the one-loop integrated perturbation theory
Matsubara, Takahiko; Desjacques, Vincent
2016-06-01
The impact of biasing schemes on the clustering of tracers of the large-scale structure is analytically studied in the weakly nonlinear regime. For this purpose, we use the one-loop approximation of the integrated perturbation theory together with the renormalized bias functions of various, physically motivated Lagrangian bias schemes. These include the halo, peaks, and excursion set peaks model, for which we derive useful formulas for the evaluation of their renormalized bias functions. The shapes of the power spectra and correlation functions are affected by the different bias models at the level of a few percent on weakly nonlinear scales. These effects are studied quantitatively both in real and redshift space. The amplitude of the scale-dependent bias in the presence of primordial non-Gaussianity also depends on the details of the bias models. If left unaccounted for, these theoretical uncertainties could affect the robustness of the cosmological constraints extracted from galaxy clustering data.
Perturbative algebraic quantum field theory an introduction for mathematicians
Rejzner, Kasia
2016-01-01
Perturbative Algebraic Quantum Field Theory (pAQFT), the subject of this book, is a complete and mathematically rigorous treatment of perturbative quantum field theory (pQFT) that doesn’t require the use of divergent quantities. We discuss in detail the examples of scalar fields and gauge theories and generalize them to QFT on curved spacetimes. pQFT models describe a wide range of physical phenomena and have remarkable agreement with experimental results. Despite this success, the theory suffers from many conceptual problems. pAQFT is a good candidate to solve many, if not all of these conceptual problems. Chapters 1-3 provide some background in mathematics and physics. Chapter 4 concerns classical theory of the scalar field, which is subsequently quantized in chapters 5 and 6. Chapter 7 covers gauge theory and chapter 8 discusses QFT on curved spacetimes and effective quantum gravity. The book aims to be accessible researchers and graduate students interested in the mathematical foundations of pQFT are th...
Chiral perturbation theory of muonic hydrogen Lamb shift: polarizability contribution
Alarcón, Jose Manuel; Pascalutsa, Vladimir
2013-01-01
The proton polarizability effect in the muonic-hydrogen Lamb shift comes out as a prediction of baryon chiral perturbation theory at leading order and our calculation yields for it: $\\Delta E^{(\\mathrm{pol})} (2P-2S) = 8^{+3}_{-1}\\, \\mu$eV. This result is consistent with most of evaluations based on dispersive sum rules, but is about a factor of two smaller than the recent result obtained in {\\em heavy-baryon} chiral perturbation theory. We also find that the effect of $\\Delta(1232)$-resonance excitation on the Lamb-shift is suppressed, as is the entire contribution of the magnetic polarizability; the electric polarizability dominates. Our results reaffirm the point of view that the proton structure effects, beyond the charge radius, are too small to resolve the `proton radius puzzle'.
A gravitational memory effect in "boosted" black hole perturbation theory
Gleiser, R J; Dominguez, Alfredo E.; Gleiser, Reinaldo J.
2003-01-01
Black hole perturbation theory, or more generally, perturbation theory on a Schwarzschild bockground, has been applied in several contexts, but usually under the simplifying assumption that the ADM momentum vanishes, namely, that the evolution is carried out and observed in the ``center of momentum frame''. In this paper we consider some consequences of the inclusion of a non vanishing ADM momentum in the initial data. We first provide a justification for the validity of the transformation of the initial data to the ``center of momentum frame'', and then analyze the effect of this transformation on the gravitational wave amplitude. The most significant result is the possibility of a type of gravitational memory effect that appears to have no simple relation with the well known Christodoulou effect.
Perturbation Theory in Supersymmetric QED: Infrared Divergences and Gauge Invariance
Dine, Michael; Haber, Howard E; Haskins, Laurel Stephenson
2016-01-01
We study some aspects of perturbation theory in $N=1$ supersymmetric abelian gauge theories with massive charged matter. In general gauges, infrared (IR) divergences and nonlocal behavior arise in 1PI diagrams, associated with a $1/k^4$ term in the propagator for the vector superfield. We examine this structure in supersymmetric QED. The IR divergences are gauge-dependent and must cancel in physical quantities like the electron pole mass. We demonstrate that cancellation takes place in a nontrivial way, amounting to a reorganization of the perturbative series from powers of $e^2$ to powers of $e$. We also show how these complications are avoided in cases where a Wilsonian effective action can be defined.
Perturbation theory and nonperturbative effects: A happy marriage ?
Chýla, J.
1992-03-01
Perturbation expansions in renormalized quantum field theories are reformulated in a way that permits a straightforward handling of situations when in the conventional approach, i.e. in fixed renormalization scheme, these expansions are factorially divergent and even of asymptotically constant sign. The result takes the form of convergent (under certain circumstances) expansions in a set of functions Z k(a, χ) of the couplant and the free parameter χ which specifies the procedure involved. The value of χ is shown to be correlated to the basic properties of nonperturbative effects as embodied in power corrections. Close connection of this procedure to Borel summation technique is demonstrated and its relation to conventional perturbation theory in fixed renormalization schemes elucidated.
Inflationary perturbation theory is geometrical optics in phase space
Seery, David; Frazer, Jonathan; Ribeiro, Raquel H
2012-01-01
A pressing problem in comparing inflationary models with observation is the accurate calculation of correlation functions. One approach is to evolve them using ordinary differential equations ("transport equations"), analogous to the Schwinger-Dyson hierarchy of in-out quantum field theory. We extend this approach to the complete set of momentum space correlation functions. A formal solution can be obtained using raytracing techniques adapted from geometrical optics. We reformulate inflationary perturbation theory in this language, and show that raytracing reproduces the familiar "delta N" Taylor expansion. Our method produces ordinary differential equations which allow the Taylor coefficients to be computed efficiently. We use raytracing methods to express the gauge transformation between field fluctuations and the curvature perturbation, zeta, in geometrical terms. Using these results we give a compact expression for the nonlinear gauge-transform part of fNL in terms of the principal curvatures of uniform e...
Perturbation theory calculations of model pair potential systems
Energy Technology Data Exchange (ETDEWEB)
Gong, Jianwu [Iowa State Univ., Ames, IA (United States)
2016-01-01
Helmholtz free energy is one of the most important thermodynamic properties for condensed matter systems. It is closely related to other thermodynamic properties such as chemical potential and compressibility. It is also the starting point for studies of interfacial properties and phase coexistence if free energies of different phases can be obtained. In this thesis, we will use an approach based on the Weeks-Chandler-Anderson (WCA) perturbation theory to calculate the free energy of both solid and liquid phases of Lennard-Jones pair potential systems and the free energy of liquid states of Yukawa pair potentials. Our results indicate that the perturbation theory provides an accurate approach to the free energy calculations of liquid and solid phases based upon comparisons with results from molecular dynamics (MD) and Monte Carlo (MC) simulations.
SUSY sine-Gordon theory as a perturbed conformal field theory and finite size effects
Bajnok, Z; Palla, L; Takács, G; Wagner, F
2004-01-01
We consider SUSY sine-Gordon theory in the framework of perturbed conformal field theory. Using an argument from Zamolodchikov, we obtain the vacuum structure and the kink adjacency diagram of the theory, which is cross-checked against the exact S matrix prediction, first-order perturbed conformal field theory (PCFT), the NLIE method and truncated conformal space approach. We provide evidence for consistency between the usual Lagrangian description and PCFT on the one hand, and between PCFT, NLIE and a massgap formula conjectured by Baseilhac and Fateev, on the other. In addition, we extend the NLIE description to all the vacua of the theory.
A modified multi-reference second order perturbation theory
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
A new scheme with extended model space is proposed to improve the calculation of multi-reference second order perturbation theory (MRPT2). The new scheme preserves the concise code structure of the original program, and avoids intruder states in constructions of the potential energy surface, which is confirmed by a series of comparable calculations. The new MRPT2 program is an available tool for the research of molecular excited states and electronic spectrum.
Automated Methods in Chiral Perturbation Theory on the Lattice
Borasoy, B; Krebs, H; Lewis, R; Borasoy, Bugra; Hippel, Georg M. von; Krebs, Hermann; Lewis, Randy
2005-01-01
We present a method to automatically derive the Feynman rules for mesonic chiral perturbation theory with a lattice regulator. The Feynman rules can be output both in a human-readable format and in a form suitable for an automated numerical evaluation of lattice Feynman diagrams. The automated method significantly simplifies working with improved or extended actions. Some applications to the study of finite-volume effects will be presented.
Hyperon decay form factors in chiral perturbation theory
Lacour, Andre; Meißner, Ulf-G
2007-01-01
We present a complete calculation of the SU(3)-breaking corrections to the hyperon vector form factors up to O(p^4) in covariant baryon chiral perturbation theory. Partial higher-order contributions are obtained, and we discuss chiral extrapolations of the vector form factor at zero momentum transfer. In addition we derive low-energy theorems for the subleading moments in hyperon decays, the weak Dirac radii and the weak anomalous magnetic moments, up to O(p^4).
Radiative four-meson amplitudes in chiral perturbation theory
D'Ambrosio, G; Isidori, Gino; Neufeld, H
1996-01-01
We present a general discussion of radiative four--meson processes to O(p^4) in chiral perturbation theory. We propose a definition of ``generalized bremsstrahlung'' that takes full advantage of experimental information on the corresponding non--radiative process. We also derive general formulae for one--loop amplitudes which can be applied, for instance, to \\eta \\ra 3\\pi\\gamma, \\pi \\pi \\ra \\pi \\pi \\gamma and K \\ra 3\\pi\\gamma.
Radiative four-meson amplitudes in chiral perturbation theory
Energy Technology Data Exchange (ETDEWEB)
D`Ambrosio, G. [Naples Univ. (Italy). Dip. di Scienze Fisiche]|[INFN, Naples (Italy); Ecker, G.; Neufeld, H. [Wien Univ. (Austria). Inst. fuer Theoretische Physik; Isidori, G. [INFN, Laboratori Nazionali di Frascati, Rome (Italy)
1996-03-01
This paper presents a general discussion of radiative four-meson processes to O(p{sup 4}) in chiral perturbation theory. A definition of `generalized Bremsstrahlung` that takes full advantage of experimental information on the corresponding non-radiative process is proposed. General formulae for one-loop amplitudes which can be applied, for instance, to {eta}{yields}3{pi}{gamma}, {pi}{pi}{yields}{pi}{pi}{gamma} and K{yields}3{pi}{gamma}.
Feynman integral and perturbation theory in quantum tomography
Fedorov, Aleksey
2013-11-01
We present a definition for tomographic Feynman path integral as representation for quantum tomograms via Feynman path integral in the phase space. The proposed representation is the potential basis for investigation of Path Integral Monte Carlo numerical methods with quantum tomograms. Tomographic Feynman path integral is a representation of solution of initial problem for evolution equation for tomograms. The perturbation theory for quantum tomograms is constructed.
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.
From the elasticity theory to cosmology and vice versa
Levrino, Luca
2012-01-01
The paper shows how a generalization of the elasticity theory to four dimensions and to space-time allows for a consistent description of the homogeneous and isotropic universe, including the accelerated expansion. The analogy is manifested by the inclusion in the traditional Lagrangian of general relativity of an additional term accounting for the strain induced in the manifold (i.e. in space-time) by the curvature, be it induced by the presence of a texture defect or by a matter/energy distribution. The additional term is sufficient to account for various observed features of the universe and to give a simple interpretation for the so called dark energy. Then, we show how the same approach can be adopted back in three dimensions to obtain the equilibrium configuration of a given solid subject to strain induced by defects or applied forces. Finally, it is shown how concepts coming from the familiar elasticity theory can inspire new approaches to cosmology and in return how methods appropriated to General Rel...
M-theory resolution of four-dimensional cosmological singularities via U-duality
Feinstein, A.; Vazquez-Mozo, M.A.
2000-01-01
We consider cosmological solutions of string and M-theory compactified to four dimensions by giving a general prescription to construct four-dimensional modular cosmologies with two commuting Killing vectors from vacuum solutions. By lifting these solutions to higher dimensions we analyze the existe
Institute of Scientific and Technical Information of China (English)
吴亚波; 李磊
2002-01-01
We establish the double complex Ashtekar gravitational theory with the cosmological term. In particular, by performing the 3+1 decomposition of the double Ashtekar action containing the cosmological term to pass on the Hamiltonian framework, the double Ashtekar constraint equations are derived, which respectively correspond to Lorentzian and Euclidean gravity.
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 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.
Density-functional perturbation theory goes time-dependent
Gebauer, Ralph; Rocca, Dario; Baroni, Stefano
2009-01-01
The scope of time-dependent density-functional theory (TDDFT) is limited to the lowest portion of the spectrum of rather small systems (a few tens of atoms at most). In the static regime, density-functional perturbation theory (DFPT) allows one to calculate response functions of systems as large as currently dealt with in ground-state simulations. In this paper we present an effective way of combining DFPT with TDDFT. The dynamical polarizability is first expressed as an off-diagonal matrix e...
Efficient perturbation theory to improve the density matrix renormalization group
Tirrito, Emanuele; Ran, Shi-Ju; Ferris, Andrew J.; McCulloch, Ian P.; Lewenstein, Maciej
2017-02-01
The density matrix renormalization group (DMRG) is one of the most powerful numerical methods available for many-body systems. It has been applied to solve many physical problems, including the calculation of ground states and dynamical properties. In this work, we develop a perturbation theory of the DMRG (PT-DMRG) to greatly increase its accuracy in an extremely simple and efficient way. Using the canonical matrix product state (MPS) representation for the ground state of the considered system, a set of orthogonal basis functions {| ψi> } is introduced to describe the perturbations to the ground state obtained by the conventional DMRG. The Schmidt numbers of the MPS that are beyond the bond dimension cutoff are used to define these perturbation terms. The perturbed Hamiltonian is then defined as H˜i j= ; its ground state permits us to calculate physical observables with a considerably improved accuracy compared to the original DMRG results. We benchmark the second-order perturbation theory with the help of a one-dimensional Ising chain in a transverse field and the Heisenberg chain, where the precision of the DMRG is shown to be improved O (10 ) times. Furthermore, for moderate L the errors of the DMRG and PT-DMRG both scale linearly with L-1 (with L being the length of the chain). The linear relation between the dimension cutoff of the DMRG and that of the PT-DMRG at the same precision shows a considerable improvement in efficiency, especially for large dimension cutoffs. In the thermodynamic limit we show that the errors of the PT-DMRG scale with √{L-1}. Our work suggests an effective way to define the tangent space of the ground-state MPS, which may shed light on the properties beyond the ground state. This second-order PT-DMRG can be readily generalized to higher orders, as well as applied to models in higher dimensions.
A study of relative velocity statistics in Lagrangian perturbation theory with PINOCCHIO
Heisenberg, Lavinia; Schäfer, Björn Malte; Bartelmann, Matthias
2011-10-01
Subject of this paper is a detailed analysis of the PINpointing Orbit-Crossing Collapsed HIerarchical Object (PINOCCHIO) algorithm for studying the relative velocity statistics of merging haloes in Lagrangian perturbation theory. Given a cosmological background model, a power spectrum of fluctuations as well as a Gaussian linear density contrast field δl is generated on a cubic grid, which is then smoothed repeatedly with Gaussian filters. For each Lagrangian particle at position q and each smoothing radius R, the collapse time, the velocities and ellipsoidal truncation are computed using Lagrangian perturbation theory. The collapsed medium is then fragmented into isolated objects by an algorithm designed to mimic the accretion and merger events of hierarchical collapse. Directly after the fragmentation process the mass function, merger histories of haloes and the statistics of the relative velocities at merging are evaluated. We reimplemented the algorithm in C++, recovered the mass function and optimized the construction of halo merging histories. When compared with the output of the Millennium Simulation our results suggest that the PINOCCHIO is well suited for studying relative velocities of merging haloes and is able to reproduce the pairwise velocity distribution.
Post-inflation increase of the cosmological tensor-to-scalar perturbation ratio
Energy Technology Data Exchange (ETDEWEB)
Bartolo, N.; /ICTP, Trieste; Kolb, Edward W.; /Fermilab /Chicago U., Astron. Astrophys. Ctr. /Chicago U., EFI; Riotto, A.; /Padua U. /INFN, Padua
2005-07-01
We investigate the possibility that the amplitude of scalar density perturbations may be damped after inflation. This would imply that CMB anisotropies do not uniquely fix the amplitude of the perturbations generated during inflation and that the present tensor-to-scalar ratio might be larger than produced in inflation, increasing the prospects of detection of primordial gravitational radiation. It turns out, however, that the damping of density perturbations is hard to achieve.
Roth, Nina
2011-01-01
We test third-order standard perturbation theory (SPT) as an approximation to non-linear cosmological structure formation. A novel approach is used to numerically calculate the three-dimensional dark matter density field using SPT from the initial conditions of two high-resolution cosmological simulations. The calculated density field is compared to the non-linear dark matter field of the simulations both point-by-point and statistically. For smoothing scales above 8 Mpc/h it shows a good agreement up to redshift 0. We present a simple fitting formula to relate the linear and non-linear density contrast that accurately recovers the non-linear time evolution for 0 <= z <= 10 at the per cent level. To address the problem of biasing between the matter field and the haloes identified in the simulation, we employ the Eulerian local bias model (ELB), including non-linear bias up to the third order. The bias parameters are obtained by fitting a scatter plot of halo and matter density (both from the simulation ...
System-reservoir theory with anharmonic baths: a perturbative approach
Bhadra, Chitrak; Banerjee, Dhruba
2016-04-01
In this paper we develop the formalism of a general system coupled to a reservoir (the words ‘bath’ and ‘reservoir’ will be used interchangeably) consisting of nonlinear oscillators, based on perturbation theory at the classical level, by extending the standard Zwanzig approach of elimination of bath degrees of freedom order by order in perturbation. We observe that the fluctuation dissipation relation (FDR) of the second kind in its standard form for harmonic baths gets modified due to the nonlinearity and this is manifested through higher powers of {{k}\\text{B}}T in the expression for two-time noise correlation. On the flip side, this very modification allows us to define a dressed (renormalized) system-bath coupling that depends on the temperature and the nonlinear parameters of the bath in such a way that the structure of the FDR (of the second kind) is maintained. As an aside, we also observe that the first moment of the noise arising from a nonlinear bath can be non-zero, even in the absence of any external drive, if the reservoir potential is asymmetric with respect to one of its minima, about which one builds up the perturbation theory.
A Review of Heavy-Quark and Chiral Perturbation Theory
Naboulsi, R
2003-01-01
In this paper we discuss the relations between various decays that can be obtained by combining heavy-quark perturbation theory and chiral perturbation theory for the emission of soft pseudoscalar particles. In the heavy-quark limit of QCD the interactions of the heavy quark Q are simplified because of a new set of symmetries not manifestly present in the full QCD. This fact is usually used in the construction of the new effective theory where the heavy-quark mass goes to infinity $(m_Q\\gg \\Lambda_{QCD})$ with its four-velocity fixed. The spin-flavor symmetry group of this new theory with N heavy quarks is SU(2N) because the interactions of the heavy quarks are independent of their spins and flavors. This fact is widely used in the description of the semileptonic decays of $B$ mesons to $D$ and $D^\\ast$ mesons where heavy-quark symmetry allows a parameterization of the decay amplitudes in terms of the single Isgur-Wise function [1].
Renewal theory for perturbed random walks and similar processes
Iksanov, Alexander
2016-01-01
This book offers a detailed review of perturbed random walks, perpetuities, and random processes with immigration. Being of major importance in modern probability theory, both theoretical and applied, these objects have been used to model various phenomena in the natural sciences as well as in insurance and finance. The book also presents the many significant results and efficient techniques and methods that have been worked out in the last decade. The first chapter is devoted to perturbed random walks and discusses their asymptotic behavior and various functionals pertaining to them, including supremum and first-passage time. The second chapter examines perpetuities, presenting results on continuity of their distributions and the existence of moments, as well as weak convergence of divergent perpetuities. Focusing on random processes with immigration, the third chapter investigates the existence of moments, describes long-time behavior and discusses limit theorems, both with and without scaling. Chapters fou...
Superstring Perturbation Theory and Ramond-Ramond Backgrounds
Berenstein, D E; Berenstein, David; Leigh, Robert G.
1999-01-01
We consider perturbative Type II superstring theory in the covariant NSR formalism in the presence of NSNS and RR backgrounds. A concrete example that we have in mind is the geometry of D3-branes which in the near-horizon region is AdS_5 x S_5, although our methods may be applied to other backgrounds as well. We show how conformal invariance of the string path integral is maintained order by order in the number of holes. This procedure makes uses of the Fischler-Susskind mechanism to build up the background geometry. A simple formal expression is given for a \\sigma-model Lagrangian. This suggests a perturbative expansion in 1/g^2N and 1/N. As applications, we consider at leading order the mixing of RR and NSNS states, and the realization of the spacetime supersymmetry algebra.
Path integral for inflationary perturbations
Prokopec, T.; Rigopoulos, G.
2010-01-01
The quantum theory of cosmological perturbations in single-field inflation is formulated in terms of a path integral. Starting from a canonical formulation, we show how the free propagators can be obtained from the well-known gauge-invariant quadratic action for scalar and tensor perturbations, and
Applications Of Chiral Perturbation Theory To Lattice Qcd
Van de Water, R S
2005-01-01
Quantum chromodynamics (QCD) is the fundamental theory that describes the interaction of quarks and gluons. Thus, in principle, one should be able to calculate all properties of hadrons from the QCD Lagrangian. It turns out, however, that such calculations can only be performed numerically on a computer using the nonperturbative method of lattice QCD, in which QCD is simulated on a discrete spacetime grid. Because lattice simulations use unphysically heavy quark masses (for computational reasons), lattice results must be connected to the real world using expressions calculated in chiral perturbation theory (χPT), the low-energy effective theory of QCD. Moreover, because real spacetime is continuous, they must be extrapolated to the continuum using an extension of χPT that includes lattice discretization effects, such as staggered χPT. This thesis is organized as follows. We motivate the need for lattice QCD and present the basic methodology in Chapter 1. We describe a common approximat...
Cosmological singularities and bounce in Cartan-Einstein theory
Lucat, Stefano
2015-01-01
We consider a generalized Einstein-Cartan theory, in which we add the unique covariant dimension four operators to general relativity that couples fermionic spin current to the torsion tensor (with an arbitrary strength). Since torsion is local and non-dynamical, when integrated out it yields an effective four-fermion interaction of the gravitational strength. We show how to renormalize the theory, in the one-loop perturbative expansion in generally curved space-times, obtaining the first order correction to the 2PI effective action in Schwinger-Keldysh (${\\it in-in}$) formalism. We then apply the renormalized theory to study the dynamics of a collapsing universe that begins in a thermal state and find that -- instead of a big crunch singularity -- the Universe with torsion undergoes a ${\\it bounce}$. We solve the dynamical equations (a) classically (without particle production); (b) including the production of fermions in a fixed background in the Hartree-Fock approximation and (c) including the quantum back...
Bounce and cyclic cosmology in weakly broken galileon theories
Banerjee, Shreya
2016-01-01
We investigate the bounce and cyclicity realization in the framework of weakly broken galileon theories. We study bouncing and cyclic solutions at the background level, reconstructing the potential that can give rise to a given scale factor, and presenting analytical expressions for the bounce requirements. We proceed to a detailed investigation of the perturbations, which after crossing the bouncing point give rise to various observables, such as the scalar and tensor spectral indices and the tensor-to-scalar ratio. Although the scenario at hand shares the disadvantage of all bouncing models, namely that it provides a large tensor-to-scalar ratio, introducing an additional light scalar significantly reduces it through the kinetic amplification of the isocurvature fluctuations.
String Scale Cosmological Constant
Chalmers, Gordon
2006-01-01
The cosmological constant is an unexplained until now phenomena of nature that requires an explanation through string effects. The apparent discrepancy between theory and experiment is enourmous and has already been explained several times by the author including mechanisms. In this work the string theory theory of abolished string modes is documented and given perturbatively to all loop orders. The holographic underpinning is also exposed. The matching with the data of the LIGO and D0 experi...
$K_{\\ell3}$ decays in Chiral Perturbation Theory
Bijnens, J; Bijnens, Johan; Talavera, Pere
2003-01-01
The process $K_{\\ell3}$ is calculated to two-loop order ($p^6$) in Chiral Perturbation Theory (ChPT) in the isospin conserved case. We use expressions suitable for use with previous work in two-loop CHPT where the order $p^4$ parameters ($L_i^r$) were determined from experiment. We point out that all the order $p^6$ parameters ($C_i^r$) that appear in the value of $f_+(0)$ relevant for the determination of $|V_{us}|$ can be determined from $K_{\\ell3}$ measurements via the slope and the curvature of the scalar form-factor.
Masses and Sigma Terms of Pentaquarks in Chiral Perturbation Theory
Institute of Scientific and Technical Information of China (English)
LI Xiao-Ya; L(U) Xiao-Fu
2006-01-01
Assuming that the recently θ+ and other exotic resonances belong to the pentaquark (-1-0) of SU(3)f with JP= 1/2, we constructed a relativistic effective lagrangian in the frame work of baryon chiral perturbation theory.The masses of pentaquarks under isospin symmetry is determined by calculating the propagator to one loop, where the extended on-mass-shell renormalization scheme is applied. Using the experimental data for masses of θ+, (I) and N, we estimated the mass of Σ. And the σ terms.
Perturbative Vacuum Wavefunctional for Gauge Theories in the Milne Space
Jeon, Sangyong
2015-01-01
The spectrum of vacuum fluctuations in the Milne space (i.e. the tau-eta coordinate system) is an important ingredient in the thermalization studies in relativistic heavy ion collisions. In this paper, the Schrodinger functional for the gauge theory perturbative vacuum is derived for the Milne space. The Wigner-transform of the corresponding vacuum density functional is also found together with the propagators. We finally identify the fluctuation spectrum in vacuum, and show the equivalence between the present approach and the symplectic product based method.
Gauge origin independence in finite basis sets and perturbation theory
Sørensen, Lasse Kragh; Lindh, Roland; Lundberg, Marcus
2017-09-01
We show that origin independence in finite basis sets for the oscillator strengths is possibly in any gauge contrary to what is stated in literature. This is proved from a discussion of the consequences in perturbation theory when the exact eigenfunctions and eigenvalues to the zeroth order Hamiltonian H0 cannot be found. We demonstrate that the erroneous conclusion for the lack of gauge origin independence in the length gauge stems from not transforming the magnetic terms in the multipole expansion leading to the use of a mixed gauge. Numerical examples of exact origin dependence are shown.
Perfect Lattice Perturbation Theory A Study of the Anharmonic Oscillator
Bietenholz, W
1999-01-01
As an application of perfect lattice perturbation theory, we construct an O(\\lambda) perfect lattice action for the anharmonic oscillator analytically in momentum space. In coordinate space we obtain a set of 2-spin and 4-spin couplings \\propto \\lambda, which we evaluate for various masses. These couplings never involve variables separated by more than two lattice spacings. The O(\\lambda) perfect action is simulated and compared to the standard action. We discuss the improvement for the first two energy gaps \\Delta E_1, \\Delta E_2 and for the scaling quantity \\Delta E_2 / \\Delta E1 in different regimes of the interaction parameter, and of the correlation length.
SIMP model at NNLO in chiral perturbation theory
DEFF Research Database (Denmark)
Hansen, Martin Rasmus Lundquist; Langaeble, K.; Sannino, F.
2015-01-01
We investigate the phenomenological viability of a recently proposed class of composite dark matter models where the relic density is determined by 3 to 2 number-changing processes in the dark sector. Here the pions of the strongly interacting field theory constitute the dark matter particles....... By performing a consistent next-to-leading and next-to-next-to-leading order chiral perturbative investigation we demonstrate that the leading order analysis cannot be used to draw conclusions about the viability of the model. We further show that higher order corrections substantially increase the tension...
Nonequilibrium chiral perturbation theory and disoriented chiral condensates
Nicola, A G
1999-01-01
We analyse the extension of Chiral Perturbation Theory to describe a meson gas out of thermal equilibrium. For that purpose, we let the pion decay constant be a time-dependent function and work within the Schwinger-Keldysh contour technique. A useful connection with curved space-time QFT allows to consistently renormalise the model, introducing two new low-energy constants in the chiral limit. We discuss the applicability of our approach within a Relativistic Heavy-Ion Collision environment. In particular, we investigate the formation of Disoriented Chiral Condensate domains in this model, via the parametric resonance mechanism.
Fluctuations in a Cosmology with a Space-Like Singularity and their Gauge Theory Dual Description
Brandenberger, Robert H; Das, Sumit R; Ferreira, Elisa G M; Morrison, Ian A; Wang, Yi
2016-01-01
We consider a time-dependent deformation of anti-de-Sitter (AdS) space-time which contains a cosmological "singularity" - a space-like region of high curvature. Making use of the AdS/CFT correspondence we can map the bulk dynamics onto the boundary. The boundary theory has a time dependent coupling constant which becomes small at times when the bulk space-time is highly curved. We investigate the propagation of small fluctuations of a test scalar field from early times before the bulk singularity to late times after the singularity. Under the assumption that the AdS/CFT correspondence extends to deformed AdS space-times, we can map the bulk evolution of the scalar field onto the evolution of the boundary gauge field. The time evolution of linearized fluctuations is well defined in the boundary theory as long as the coupling remains finite, so that we can extend the boundary perturbations to late times after the singularity. Assuming that the spacetime in the future of the singularity has a weakly coupled regi...
Higgs boson mass limits in perturbative unification theories
Tobe, K; Tobe, Kazuhiro; Wells, James D.
2002-01-01
Motivated in part by recent demonstrations that electroweak unification into a simple group may occur at a low scale, we detail the requirements on the Higgs mass if the unification is to be perturbative. We do this for the Standard Model effective theory, minimal supersymmetry, and next-to-minimal supersymmetry with an additional singlet field. Within the Standard Model framework, we find that perturbative unification with sin2(thetaW)=1/4 occurs at Lambda=3.8 TeV and requires m_h<460 GeV, whereas perturbative unification with sin2(thetaW)=3/8 requires mh<200 GeV. In supersymmetry, the presentation of the Higgs mass predictions can be significantly simplified, yet remain meaningful, by using a single supersymmetry breaking parameter Delta_S. We present Higgs mass limits in terms of Delta_S for the minimal supersymmetric model and the next-to-minimal supersymmetric model. We show that in next-to-minimal supersymmetry, the Higgs mass upper limit can be as large as 500 GeV even for moderate supersymmetry ...