Showing papers on "Friedmann–Lemaître–Robertson–Walker metric published in 1995"
TL;DR: The equations by which matter imposes anisotropies on freely propagating background radiation are considered, leading to a new way of using anisotropy measurements to limit the deviations of the Universe from a Friedmann-Robertson-Walker geometry.
Abstract: We consider directly the equations by which matter imposes anisotropies on freely propagating background radiation, leading to a new way of using anisotropy measurements to limit the deviations of the Universe from a Friedmann-Robertson-Walker (FRW) geometry. This approach is complementary to the usual Sachs-Wolfe approach: the limits obtained are not as detailed, but they are more model independent. We also give new results about combined matter-radiation perturbations in an almost-FRW universe, and a new exact solution of the linearized equations.
88 citations
TL;DR: In this paper, a local void in the globally Friedmann-Robertson-Walker (FRW) cosmological model is studied and the inhomogeneity is described using the Lema\^{\i}tre-Tolman-Bondi (LTB) solution with spherically symmetric matter distribution based on the faint galaxies number counts.
Abstract: A local void in the globally Friedmann-Robertson-Walker (FRW) cosmological model is studied. The inhomogeneity is described using the Lema\^{\i}tre-Tolman-Bondi (LTB) solution with the spherically symmetric matter distribution based on the faint galaxies number counts. We investigate the effects this has on the measurement of the Hubble constant and the redshift--luminosity distance relation for moderately and very distant objects ($z \approx 0.1$ and more). The results, while fully compatible with cosmological observations, indicate that if we happened to live in such a void, but insisted on interpreting cosmological observations through the FRW model, we could get a few unexpected results. For example the Hubble constant measurement could give results depending on the separation of the source and the observer.
73 citations
TL;DR: Several isotropic, homogeneous cosmological models containing a self-interacting minimally coupled scalar field, a perfect fluid source and a constant constant are solved in this paper.
Abstract: Several isotropic, homogeneous cosmological models containing a self-interacting minimally coupled scalar field, a perfect fluid source and cosmological constant are solved. New exact, asymptotically stable solutions with an inflationary regime or a final Friedmann stage are found for some simple, interesting potentials. It is shown that the fluid and the curvature may determine how these models evolve for large times.
57 citations
TL;DR: It is shown that the electric part of the Weyl conformal tensor E and the shearigma constitute the two basic perturbed variables in terms of which all remaining observable quantities can be described.
Abstract: The theory of perturbation of Friedmann-Robertson-Walker (FRW) cosmology is analyzed exclusively in terms of observable quantities. Although this can be a very complete and general procedure we limit our presentation here to the case of scalar perturbations for simplicity. That is, we do not consider rotational or gravitational wave contributions to the perturbations. We show that the electric part of the Weyl conformal tensor E and the shear \ensuremath{\Sigma} constitute the two basic perturbed variables in terms of which all remaining observable quantities can be described. Einstein's equations of general relativity reduce to a closed set of dynamical systems for E and \ensuremath{\Sigma}. The basis for a gauge-invariant Hamiltonian treatment of the perturbation theory in the FRW background is then set up.
36 citations
TL;DR: In this paper, the authors consider the claim of Hawking and Page that the canonical measure applied to Friedmann-Robertson-Walker models with a massive scalar field can solve the flatness problem, regardless of inflation occurring or not.
Abstract: We consider the claim of Hawking and Page that the canonical measure applied to Friedmann--Robertson--Walker models with a massive scalar field can solve the flatness problem, i.e. , regardless of inflation occurring or not. We point out a number of ways in which this prediction, which relies predominantly on post-Planckian regions of the classical phase space, could break down. By considering a general potential we are able to understand how the ambiguity for found by Page in the -theory is present, in general, for scalar field models when the potential is bounded from above. We suggest reasons why such potentials are more realistic, which then results in the value of being arbitrary. Although the canonical measure gives an ambiguity (due to the infinite measure over arbitrary scale factors) for the possibility of inflation, the inclusion of an input from quantum cosmology could resolve this ambiguity. This could simply be that due to a `quantum event' the Universe started small, and provided a suitable scalar potential is present an inflationary period could then be `near certain' to proceed in order to set infinitesimally close to unity. We contrast the measure obtained in this way with the more usual ones obtained in quantum cosmology: the Hartle--Hawking and tunnelling ones.
35 citations
TL;DR: A new asymptotic expansion method is developed to separate the Wheeler-DeWitt equation into the time-dependent Schrodinger equation for a matter field and the Einstein-Hamilton-Jacobi equation for the gravitational field including the quantum back reaction of the matter field.
Abstract: A new asymptotic expansion method is developed to separate the Wheeler-DeWitt equation into the time-dependent Schr\"odinger equation for a matter field and the Einstein-Hamilton-Jacobi equation for the gravitational field including the quantum back reaction of the matter field. In particular, the nonadiabatic basis of the generalized invariant for the matter field Hamiltonian separates the Wheeler-DeWitt equation completely in the asymptotic limit of ${\mathit{m}}_{\mathit{P}}^{2}$ approaching infinity. The higher order quantum corrections of the gravity to the matter field are found. The new asymptotic expansion method is valid throughout all regions of superspace compared with other expansion methods with a certain limited region of validity. We apply the new asymptotic expansion method to the minimal FRW universe.
32 citations
TL;DR: A class of theories of two-dimensional gravity which admits homogeneous and isotropic solutions that are nonsingular and asymptotically approach a FRW matter-dominated universe at late times is presented.
Abstract: We present a class of theories of two-dimensional gravity which admits homogeneous and isotropic solutions that are nonsingular and asymptotically approach a FRW matter-dominated universe at late times. These models are generalizations of two-dimensional dilaton gravity and both vacuum solutions and those including conformally coupled matter are investigated. In each case our construction leads to an inflationary stage driven by the gravitational sector. Our work comprises a simple example of the nonsingular universe'' constructions of Brandenberger and co-workers.
24 citations
CERN1
TL;DR: In this article, a generalization of the FRW backgrounds with three transitive spacelike Killing symmetries, but without any a priori assumption of isotropy in the 3D sections of homogeneity, is presented.
23 citations
TL;DR: In this paper, a covariant Hamiltonian method was used to quantize constrained systems using Rieffel induction, and a wave function of the universe was found to coincide with the latter in the open case.
Abstract: The ADM approach to canonical general relativity combined with Dirac's method of quantizing constrained systems leads to the Wheeler - DeWitt equation. A number of mathematical as well as physical difficulties that arise in connection with this equation may be circumvented if one employs a covariant Hamiltonian method in conjunction with a recently developed, mathematically rigorous technique to quantize constrained systems using Rieffel induction. The classical constraints are cleanly separated into four components of a covariant momentum map coming from the diffeomorphism group of spacetime, each of which is linear in the canonical momenta, plus a single finite-dimensional quadratic constraint that arises in any theory, parametrized or not. The new quantization method is carried through in a minisuperspace example, and is found to produce a `wavefunction of the universe'. This differs from the proposals of both Vilenkin and Hartle - Hawking for a closed FRW universe, but happens to coincide with the latter in the open case.
22 citations
TL;DR: In this paper, the cosmological constant and a homogeneous minimally coupled scalar field are considered as matter sources and the general condition of existence of the solutions with static internal spaces is obtained and applied to physically important cases.
Abstract: Multidimensional cosmological models with Einstein spaces are investigated. The cosmological constant and a homogeneous minimally coupled scalar field are considered as matter sources. The scalar field has a potential of general form depending on the scalar field as well as on the scale factors of the . The general condition of existence of the solutions with static internal spaces is obtained and applied to physically important cases.
22 citations
CERN1
TL;DR: In this article, a new class of spatially homogeneous 4D string backgrounds, the χ (d →) according to a recent classification, is presented, and a leading-order solution exists only for Bianchi types χ = I, II, III, VI−1, VII0.
TL;DR: In this paper, a class of exact cosmological solutions of Brans-Dicke (B-D) equations was presented, based on the relation oRn = constant between the B-D field and the scale factor.
Abstract: We present a class of exact cosmological solutions of Brans-Dicke (B-D) equations with cosmological constant in flat Robertson-Walker metric. These solutions are based on the relation oRn= constant between the B-D field and the scale factor of the universe. This relation turns out to be consistent with the equation of statep =mρ for the cosmic matter, provided thatn andm are suitably related to each other. Several special cases and asymptotic solutions are derived and discussed.
TL;DR: Cosmological perturbations on a manifold admitting signature change are studied and it is shown that no regular solution exist satisfying the junction conditions at the surface of change.
Abstract: Cosmological perturbations on a manifold admitting signature change are studied. The background solution consists in a Friedmann-Lemaitre-Robertson- Walker (FLRW) Universe filled by a constant scalar field playing the role of a cosmological constant. It is shown that no regular solution exist satisfying the junction conditions at the surface of change. The comparison with similar studies in quantum cosmology is made.
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TL;DR: In this paper, a review of string theory in FRW and inflatio-nary spacetimes is presented, with a focus on string dynamics in cosmological and black hole Spacetimes.
Abstract: Recent progress on string theory in curved spacetimes is reviewed. The string dynamics in cosmological and black hole spacetimes is investigated.The methods to solve the string equations of motion in curved spacetimes are described.That is, the perturbation approach, the null approach, the $\tau$-expansion, and the construction of global solutions.The behaviour of strings in FRW and inflatio- nary spacetimes is obtained from the various types of string solutions. Three different types of behaviour appear:{\bf unstable, dual} to unstable and {\bf stable}.For the unstable strings, the energy and size grow proportional to $R$ for large scale factors $R \to \infty$. For the dual to unstable strings, the energy and size blow up for R\to 0 as 1/R. For stable strings, the energy and size are bounded. (In Minkowski, all solutions are of the stable type). The self-consistent solution to the Einstein equations for string dominated universes is reviewed. The energy-momentum tensor for a gas of strings is taken as source and from the above behaviours the string equation of state is {\bf derived}. The self-consistent string solution exhibits realistic matter dominated behaviour for large times and radiation dominated behaviour for early times. We report on the {\bf exact integrability} of the string dynamics in de Sitter spacetime that allows to systematically find {\bf exact} string solutions by soliton methods. {\bf Multistring solutions} are a new feature in curved spacetimes. That is, a single world-sheet simultaneously describes many different and independent strings. This phenomenon has no analogue in flat spacetime and follows from the coupling of the strings with the geometry. Finally, the string dynamics next and inside a Schwarzschild black hole is analyzed and their physical properties discussed.
TL;DR: The multipole moments of the correlation function for these temperature fluctuations in a spatially-closed Friedman-Robertson-Walker (FRW) cosmological model are calculated and the results are compared to the corresponding multipoles in the spatial-flat case.
Abstract: Primordial gravitational waves are created during the de Sitter phase of an exponentially-expanding (inflationary) universe, due to quantum zero-point vacuum fluctuations. These waves produce fluctuations in the temperature of the Cosmic Background Radiation (CBR). We calculate the multipole moments of the correlation function for these temperature fluctuations in a spatially-closed Friedman-Robertson-Walker (FRW) cosmological model. The results are compared to the corresponding multipoles in the spatially-flat case. The differences are small unless the density parameter today, $\Omega_0$, is greater than 2. (Submitted to Physical Review D).
TL;DR: In this article, the theory of perturbation of Friedmann-Robertson-Walker (FRW) cosmology was analyzed in terms of observable quantities in the framework of quasi-Maxwellian equations of gravitation.
Abstract: In a previous paper we analyzed the theory of perturbation of Friedmann-Robertson-Walker (FRW) cosmology exclusively in terms of observable quantities in the framework of quasi-Maxwellian equations of gravitation In that paper we limited ourselves to the case of irrotational perturbations for simplicity We complete here the previous task by presenting the remaining cases of vector and tensor perturbations Following the same reasoning as for the scalar case, we show here that the vorticity \ensuremath{\Omega} and the shear \ensuremath{\Sigma} constitute the two basic perturbed variables in terms of which all remaining observable quantities can be described for the vectorial case The tensorial case can be described by the variables E and H, the electric and magnetic parts of the Weyl conformal tensor Einstein's equations of general relativity reduce to a closed set of dynamical systems for those pairs of variables We then obtain a Hamiltonian treatment of the perturbation theory in FRW cosmology
TL;DR: In this article, the authors use Boulware's Hamiltonian formalism of quadratic gravity theories in order to analyse the classical behaviour of Bianchi cosmological models for a Lagrangian density in four spacetime dimensions.
Abstract: We use Boulware's Hamiltonian formalism of quadratic gravity theories in order to analyse the classical behaviour of Bianchi cosmological models for a Lagrangian density in four spacetime dimensions. For this purpose we define a canonical transformation which leads to a clear distinction between two main variants of the general quadratic theory, i.e. for or conformal Lagrangian densities. In this paper we restrict the study to the first variant. For the Bianchi-type I and IX models, we give the explicit forms of the super-Hamiltonian constraint, of the ADM Hamiltonian density and of the corresponding canonical equations. In the case of a pure quadratic theory , we solve them analytically for the Bianchi I model. For the Bianchi-type IX model, we reduce the first-order equations of the Hamiltonian system to three coupled second-order equations for the true physical degrees of freedom. This discussion is extended to isotropic FLRW models.
TL;DR: In this article, the authors consider a homogeneous, isotropic universe with a flat FriedmannRobertson-Walker (FRW) metric described by a scale factor a(t).
Abstract: Inflation involves a period of rapid growth of the Universe. This is most easily illustrated by considering a homogeneous, isotropic Universe with a flat FriedmannRobertson―Walker (FRW) metric described by a scale factor a(t). Here, “rapid growth” means a positive value of a/a = ―(4πGN/3)(ρ+3p) where ρ is the energy density and p the pressure. It is useful to identify the energy density driving inflation with some sort of scalar “potential” energy density V > 0 that is positive, and results in an effective equation of state \(\rho \simeq - p \simeq V\), which satisfies a > 0. If one identifies the potential energy as arising from the potential of some scalar field o, then o is known as the inflaton field.
TL;DR: The consistency of the thermodynamics of the most general class of a conformally flat solution with an irrotational perfect fluid source (the Stephani Universes) is examined in this article.
Abstract: The consistency of the thermodynamics of the most general class of a conformally flat solution with an irrotational perfect fluid source (the Stephani Universes) is examined herein. For the case when the isometry group has dimension r≥2, the Gibbs–Duhem relation is always integrable, but if r<2 it is only integrable for the particular subclass [containing Friedman–Robertson–Walker (FRW) cosmologies] characterized by r=1 and by admitting a conformal motion parallel to the four‐velocity. Explicit forms of the state variables and equations of state linking them are provided. These formal thermodynamic relations are determined up to an arbitrary function of time which reduces to the FRW scale factor in the FRW limit of the solutions. It is shown that a formal identification of this free parameter with a FRW scale factor determined by FRW dynamics leads to an unphysical temperature evolution law. If this parameter is not identified with a FRW scale factor, it is possible to find examples of solutions and formal equations of state complying with suitable energy conditions and reasonable asymptotic behavior and temperature laws.
TL;DR: In this article, self-similar solutions to O(4) textures in Minkowski space and if flat Friedmann-Robertson-Walker back-grounds were discussed. But they were not shown to be valid on intermediate scales, and the applicability of the nonlinear sigma model approximation was discussed.
Journal Article•
TL;DR: In this paper, the general theory of N = 1 supergravity with supermatter using a canonical approach is described, and the supersymmetry and gauge constraint generators are presented for the Friedmann minisuperspace model.
Abstract: The general theory of N = 1 supergravity with supermatter using a canonical approach is described. The supersymmetry and gauge constraint generators are presented. The framework is applied to the study of a Friedmann minisuperspace model. We consider a Friedmann k = +1 geometry anda family of spin-0 as well as spin-1 gauge fields together with their odd (anti-commuting) spin-1/2 partners. When both the spin-1 field and its fermionic partner are set equal to zero, the physical states of our simplifiedmod el correspondeffectively to those of a minisuperspace quantum cosmological model possessing N=4 local supersymmetry coupled to complex scalars with
TL;DR: In this article, the field equations of the New General Relativity NGR, constructed by Hayashi and Shirafuji (1979), have been applied to two geometric structures, given by Robertson (1932), in the domain of cosmology.
Abstract: The field equations of the New General Relativity NGR, constructed by Hayashi and Shirafuji (1979), have been applied to two geometric structures, given by Robertson (1932), in the domain of cosmology. In the first application a family of models, involving two of the parameters characterizing the field equations of the NGR, is obtained. In the second application the models obtained are found to involve one parameter only. The cosmological parameters in both applications are calculated and some cosmological problems are discussed in comparison with the corresponding results of other field theories .
TL;DR: A general formalism treating fluctuations around circular strings embedded in arbitrary spatially flat FRW spacetimes finds that in certain cases the fluctuations grow much slower than the radius of the underlying unperturbed circular string.
Abstract: It was shown by Garriga and Vilenkin that the circular shape of nucleated cosmic strings, of zero loop energy in de Sitter space, is stable in the sense that the ratio of the mean fluctuation amplitude to the loop radius is constant. This result can be generalized to all expanding strings (of nonzero loop energy) in de Sitter space. In other curved spacetimes the situation, however, may be different. In this paper we develop a general formalism treating fluctuations around circular strings embedded in arbitrary spatially flat FRW spacetimes. As examples we consider Minkowski space, de Sitter space, and power law expanding universes. In the special case of power law inflation we find that in certain cases the fluctuations grow much slower than the radius of the underlying unperturbed circular string. The inflation of the Universe thus tends to wash out the fluctuations and to stabilize these strings.
TL;DR: In this article, the authors give conditions to obtain cosmological asymptotic freedom in scalar-tensor theories of gravity and show that this feature can be achieved in FRW flat spacetimes.
TL;DR: In this article, a covariant Hamiltonian method was used to quantize constrained systems using Rieffel induction, and the new quantization method was carried through in a minisuperspace example, and was found to produce a ''wavefunction of the universe''.
Abstract: The ADM approach to canonical general relativity combined with Dirac's method of quantizing constrained systems leads to the Wheeler-DeWitt equation. A number of mathematical as well as physical difficulties that arise in connection with this equation may be circumvented if one employs a covariant Hamiltonian method in conjunction with a recently developed, mathematically rigorous technique to quantize constrained systems using Rieffel induction. The classical constraints are cleanly separated into four components of a covariant momentum map coming from the diffeomorphism group of spacetime, each of which is linear in the canonical momenta, plus a single finite-dimensional quadratic constraint that arises in any theory, parametrized or not. The new quantization method is carried through in a minisuperspace example, and is found to produce a ``wavefunction of the universe". This differs from the proposals of both Vilenkin and Hartle-Hawking for a closed FRW universe, but happens to coincide with the latter in the open case.
Journal Article•
TL;DR: In the R+αR2 gravity theory, if freely propagating massless particles have an almost isotropic distribution, then the spacetime is almost Friedmann-Robertson-Walker (frw) as mentioned in this paper.
Abstract: In the R+αR2 gravity theory, we show that if freely propagating massless particles have an almost isotropic distribution, then the spacetime is almost Friedmann-Robertson-Walker (frw). This extends the result proved recently in general relativity (α = 0), which is applicable to the microwave background after photon decoupling. The higher-order result is in principle applicable to a massless species that decouples in the early universe, such as a relic graviton background. Any future observations that show small anisotropies in such a background would imply that the geometry of the early universe were almostfrw.
Journal Article•
TL;DR: In this article, it was shown that the Einstein equations on M without cosmologicaI constant and with perfect fluid as source, can be obtained from the field equations for vacuum with cosmologicI constant on the principal libre bundle P (tM, U(I)), M being the space-time and 1 the radius of the internal space u(I).
Abstract: In the present work we show that the Einstein equations on M without cosmologicaI constant and with perfect fluid as source, can be obtained from the field equations for vacuum with cosmologicaI constant on the principal libre bundle P (tM, U(I)), M being the space-time and 1 the radius of the internal space U(I).