Showing papers on "Friedmann–Lemaître–Robertson–Walker metric published in 1991"
TL;DR: In this article, exact cosmological solutions of the Einstein gravitational equations with a non-interacting combination of a classical scalar field and isotropic radiation as source were given.
Abstract: The authors consider exact cosmological solutions of the Einstein gravitational equations with a non-interacting combination of a classical scalar field and isotropic radiation as source. They show how a potential function for the scalar field can be found leading to desired volume behaviour of Robertson-Walker universes, and give a number of exact solutions of the coupled equations. These solutions in general do not obey the 'slow-rolling' approximation usually assumed in inflationary universe models.
279 citations
171 citations
TL;DR: In this paper, the covariant perturbation equations for generalized generalized gravity theories with multicomponent fluids and fields as sources were derived using the raw kinematic variables of the normal frame with an unspecified gauge.
Abstract: Cosmological perturbation equations in the Robertson-Walker background space, considering multicomponent fluid sources with interactions between them, are presented. The perturbation equations, applicable to a class of generalized gravity theories with multicomponent fluids and fields as sources, are generalized. Equations are derived from the covariant equations and presented using the raw kinematic variables of the normal frame with an unspecified gauge. In this way, the equations are easily adaptable to various gauge conditions and also to various gauge-invariant formulations. Relations between different gauges and also to the gauge-invariant formulations are explained
143 citations
TL;DR: In this paper, the authors considered the Einstein field equations with perfect fluid source and variable Λ andG for the Robertson-Walker metric and found perfect gas equation of state models in the Euclidean and non-Euclidean cases.
Abstract: We consider the Einstein field equations with perfect fluid source and variable Λ andG for the Robertson-Walker metric. When conservation of energy momentum is postulated and the deceleration parameter is assumed constant, we find perfect gas equation of state models in the Euclidean and non-Euclidean cases. The resulting models offer an alternative to the inflationary scenario; they also explain the huge value of the cosmological term in the early universe.
101 citations
TL;DR: In this paper, the Robertson-Walker model has been studied in the theory of cosmological theory with cosmologies and in cosmology based on Lyra's geometry, and the necessary relations in each model have been derived.
Abstract: Berman (1983) presented a law of variation of Hubble’s parameter that yields constant deceleration parameter models of the Universe. In this paper, Robertson-Walker models have been studied in Einstein’s theory with cosmological term and in cosmological theory based on Lyra’s geometry. Some simple models have been obtained. The necessary relations in each model have been derived, considering a perfect fluid.
49 citations
TL;DR: This work explicitly compute the back reaction of the inhomogeneous modes on the minisuperspace sector using a coarse-grained effective action and shows that the min is uperspace approximation is valid only when this back reaction is small.
Abstract: We examine the question of the validity of the minisuperspace approximation using the example of an interacting ({lambda}{Phi}{sup 4}) scalar field in a closed Robertson-Walker universe, where the scale factor and the homogeneous mode of the scalar field model the minisuperspace degrees of freedom. We explicitly compute the back reaction of the inhomogeneous modes on the minisuperspace sector using a coarse-grained effective action and show that the minisuperspace approximation is valid only when this back reaction is small.
45 citations
TL;DR: In this article, the authors give the necessary conditions for the matching of a general Robertson-Walker geometry to general spherically symmetric radiating metric and the possible applications of the results to the stellar collapse and to the study of local inhomogeneities in a cosmological context are considered.
Abstract: The authors give the necessary conditions for the matching of a general Robertson-Walker geometry to general spherically symmetric radiating metric. They also found the conditions for the matching of a Vaidya metric (1951) to a general Robertson-Walker metric. The possible applications of the results to the stellar collapse and to the study of local inhomogeneities in a cosmological context are considered. An alternative interpretation of the energy-momentum tensor of the Robertson-Walker part of spacetime is given in such a way that the physical processes can be better understood.
39 citations
TL;DR: In this paper, the scalar field driving inflation in a general Robertson-Walker cosmology is used as a dynamical variable to express the field equations as a first-order differential system.
39 citations
TL;DR: In this article, the authors discuss the relationship of Tod's conjecture to an earlier one of Goode and Wainwright (1985), and reduce the proof of this conjecture to establishing uniqueness of solution to an appropriate initial value problem.
Abstract: According to Penrose's Weyl tensor hypothesis (1979), an appropriate boundary condition to impose at any initial singularity is that the Weyl tensor should vanish there. Cosmological models that admit isotropic singularities provide a mathematical framework for studying this hypothesis. Tod (1957) has conjectured that, within the isotropic singularity framework, the only models that satisfy the Penrose boundary condition are the exact FRW models. The author discusses the relationship of this conjecture to an earlier one of Goode and Wainwright (1985), and reduces the proof of Tod's conjecture to establishing uniqueness of solution to an appropriate initial value problem.
24 citations
TL;DR: This paper extended the FRW scalar field cosmology including matter and discussed exact solutions for potentials like V(ϕ)=0 and (only in the presence of dust) Vϕ =αeηϕ+e-ϕ.
23 citations
TL;DR: A nontrivial redundancy relation, due to the differential structure of the gravitational Bianchi identity as well as the symmetry of the Friedmann-Robertson-Walker metric, in the gravitational field equation is clarified.
Abstract: A nontrivial redundancy relation, due to the differential structure of the gravitational Bianchi identity as well as the symmetry of the Friedmann-Robertson-Walker metric, in the gravitational field equation is clarified. A generalized Friedmann-Robertson-Walker metric is introduced in order to properly define a one-dimensional reduced problem which offers an alternative approach to obtain the gravitational field equations on Friedmann-Robertson-Walker spaces.
TL;DR: In this paper, a simple example of a spacetime in which one region undergoes gravitational collapse while another undergoes inflation is given, where the spacetime is a spherical ball of dust in a region with a cosmological constant.
Abstract: We give a simple example of a spacetime in which one region undergoes gravitational collapse while another undergoes inflation. The spacetime is a spherical ball of dust in a region with a cosmological constant. The implications of this example for the “cosmic no hair” conjecture are discussed.
TL;DR: The exact frequency redshift for fields coupled to gravity in Robertson-Walker backgrounds is calculated and is proportional to the naive Doppler shift times a term representing diffractive effects.
Abstract: We calculate the exact frequency redshift for fields coupled to gravity in Robertson-Walker backgrounds. The exact redshift factorizes and is proportional to the naive Doppler shift times a term representing diffractive effects. These diffractive corrections can be large for field modes with wavelengths on the order of the horizon size. Implications for cosmological density perturbations are discussed.
01 Jan 1991
TL;DR: Einstein this paper revealed maddening thoughts in the physico-mathematical division of the Royal Prussian Academy of the Sciences to his fellow academicians, and a week later the Reichsdruckerei issued the Sitzungsbericht “Kosmologische Betrachtungen zur allgemeinen Relativitatstheorie” (Einstein 1917).
Abstract: On February 4, 1917 Albert Einstein writes to Paul Ehrenfest (Kerszberg 1989, p155): “I have... again perpetrated something about gravitation theory which somewhat exposes me to the danger of being confined to a madhouse.” Four days later he revealed these maddening thoughts in the physico-mathematical division of the Royal Prussian Academy of the Sciences to his fellow academicians. A week later the Reichsdruckerei issued the Sitzungsbericht “Kosmologische Betrachtungen zur allgemeinen Relativitatstheorie” (Einstein 1917). Thus began modem cosmology.
TL;DR: For the open Robertson-Walker cosmology an answer to this question is given in this article, and some observations concerning explicit solution by separation of variables of wave equations for spin 1 in a Riemannian space having an infinitesimal line element are made.
Abstract: Crucial to a knowledge of the perturbations of Robertson–Walker cosmological models are complete sets of functions with which to expand such perturbations. For the open Robertson–Walker cosmology an answer to this question is given. In addition some observations concerning explicit solution by separation of variables of wave equations for spin 1 in a Riemannian space having an infinitesimal line element of which the Robertson–Walker models are a special case are made.
TL;DR: Some new exact solutions to the Einstein equations with an acceleration-free imperfect-fluid source are obtained and cosmological models built out of these solutions are found to have increasing entropy per baryon and not possess any flatness problem.
Abstract: Some new exact solutions to the Einstein equations with an acceleration-free imperfect-fluid source are obtained. Some physical restrictions on the solutions are discussed. Cosmological models built out of these solutions are found to have increasing entropy per baryon and not possess any flatness problem.
TL;DR: In this article, the origin of Friedmann-like behavior of the perturbed model is clarified in a comoving gauge, and thus in a corresponding gauge-invariant formalism, using the covariant equations.
Abstract: A straightforward derivation of the large-scale evolution of a perturbed Robertson-Walker space is presented. The origin of the Friedmann-like behavior of the perturbed model is clarified in a comoving gauge, and thus in a corresponding gauge-invariant formalism, using the covariant equations. Thus, when the imperfect fluid contributions are negligible, the large-scale perturbations in a nearly flat background evolve like separate Friedmann models. However, there exists a preferable gauge-invariant quantity which is conserved in the large scale even considering the background spatial curvature (for a nearly flat background model), the cosmological constant, and the anisotropic pressure
TL;DR: A working classical chaotic vector inflation is demonstrated and then quantum fluctuations of the field are used to constrain the cosmological perturbations.
Abstract: A vector field {ital A}{sub {mu}} is coupled to the Einstein equations with a linearly perturbed Friedmann-Robertson-Walker metric, constructed to generate first-order vector perturbations. A working classical chaotic vector inflation is demonstrated and then quantum fluctuations of the field are used to constrain the cosmological perturbations. In particular, the vector momentum flux {ital T}{sub 0{ital i}} is tracked to the epoch where radiation-dominated matter exists. Matching conditions using observational constraints of the cosmic microwave background radiation give rise to a peculiar cosmological velocity of the order of 10{sup {minus}100}{ital c}. Amplification of this number, e.g., by breaking the conformal invariance of the field, could be used to generate cosmic magnetic fields using a dynamo mechanism.
TL;DR: In this paper, the possibilities to construct a modification of General Relativity (MGR) where the cosmological constant appears as a constant of integration are considered, and a class of new constraints on the metric is found, such that their inclusion in the Hilbert-Einstein action before its variation leads to MGR.
Abstract: The possibilities to construct a modification of General Relativity (MGR), where the cosmological constant appears as a constant of integration are considered. A class of new constraints on the metric is found, such that their inclusion in the Hilbert–Einstein action before its variation leads to MGR.
TL;DR: In this article, the dynamics of the generalized D-dimensional (D = 1+3+d) Friedman-Robertson-Walker (FRW) cosmological models in the framework of an extended gravity theory obtained by adding the Gauss-Bonnet term to the standard Einstein-Hilbert action is studied.
Abstract: We study the dynamics of the generalizedD-dimensional (D = 1+3+d) Friedman-Robertson-Walker (FRW) cosmological models in the framework of an extended gravity theory obtained by adding the Gauss-Bonnet term to the standard Einstein-Hilbert action. In our discussion we extensively use methods of dynamical systems. We consider models filled in with a perfect fluid obeying the equation of statep=(γ−1)ρ and vacuum but non-flat models. We present a detailed analysis of the ten dimensional model and in particular we study the vacuum case. Several phase portraits show how the evolution of this model depends on the parameterγ.
TL;DR: In this paper, the form of the field equations for the generic Robertson-Walker metric is given, and a class of cosmological solutions is found for the generalized field equations.
Abstract: Dynamical dimensional reduction of zero-torsion constrained, first-order effective string field theory is discussed. The form of the field equations for the generic Robertson-Walker metric is given. A class of cosmological solutions is found.
TL;DR: The authors recast the Dirac relativistic equation within the theoretical framework of the Robertson-Walker metric, using spatial hypersurfaces that are essentially curved, and hence more general, as compared to the flat ones employed by Barut and Duru.
Abstract: We recast the Dirac relativistic equation within the theoretical framework of the Robertson-Walker metric, using spatial hypersurfaces that are essentially curved, and hence more general, as compared to the flat ones employed by Barut and Duru.
TL;DR: In this article, the existence of cosmological singularities is shown to be inconsistent with the entropy bound, a new thermodynamic law proposed by Bekenstein, regardless of model peculiarities.
Abstract: Recently, Bekenstein showed that a singularity in the FRW radiation-dominated cosmological model is inconsistent with the “entropy bound,” a new thermodynamic law he put forward a few years ago. In this paper we generalize his results and show that, regardless of model peculiarities, the existence of cosmological singularities is incompatible with thermodynamics.
Journal Article•
TL;DR: In this article, the moduli space of self-dual Yang-Mills equations on a compact Riemannian 4-manifold is shown to be a manifold when the cosmological constant is positive and a Atiyah-Singer index is negative.
Abstract: The self-dual Einstein equations on a compact Riemannian 4-manifold can be expressed as a quadratic condition on the curvature of an $SU(2)$ (spin) connection which is a covariant generalization of the self-dual Yang-Mills equations. Local properties of the moduli space of self-dual Einstein connections are described in the context of an elliptic complex which arises in the linearization of the quadratic equations on the $SU(2)$ curvature. In particular, it is shown that the moduli space is discrete when the cosmological constant is positive; when the cosmological constant is negative the moduli space can be a manifold the dimension of which is controlled by the Atiyah-Singer index theorem.
TL;DR: In this paper, it is shown how the techniques that yield anisotropic and inhomogeneous solutions of the Einstein-Liouville equations for Friedmann-Robertson-Walker (FRW) spacetimes can be used to demonstrate the existence of a possible relativistic kinetic theory basis (and consequently a more selfconsistent basis) for tilting imperfect fluid FRW cosmological models.
Abstract: It is shown how the techniques that yield anisotropic and inhomogeneous solutions of the Einstein-Liouville equations for Friedmann-Robertson-Walker (FRW) spacetimes can be used to demonstrate the existence of anisotropic and inhomogeneous FRW solutions of the Einstein-Boltzmann equations, thereby providing a possible relativistic kinetic theory basis (and consequently a more self-consistent basis) for tilting imperfect fluid FRW cosmological models (based on a set of phenomenological laws of relativistic thermodynamics).
TL;DR: In this paper, the authors applied the discrete lattice formalism to study the time evolution of free scalar field in spatially flat Robertson-Walker space-time, and obtained the exact form of the operator of the system, which enables them to find the exact wave functions readily.
Abstract: The discrete lattice formalism is applied to study the time evolution of free scalar field in spatially flat Robertson-Walker space-time. Using the evolution operator method, we obtain the exact form of the time evolution operator of the system which, in turn, enables us to find the exact wave functions readily. It is found that the time evolution operator is a direct product of single-mode squeeze operators, and thus the initial vacuum state evolves into a direct product of single-mode squeezed vacuum states at a later time. In other words, the time evolution of free scalar field in spatially flat Robertson-Walker space-time is a collective single-mode squeezing process.
Journal Article•
TL;DR: In this article, a scale-invariant effective theory with vanishing cosmological constant was proposed, where the spatial independence of the inflaton is implied by the equation of motion incorporated with the Robertson-Walker metric.
TL;DR: In this article, it was pointed out that the barotropic equation of state splits the family of spherically symmetric shear-free expanding perfect fluid solutions of Einstein's equations into two distinct families: the Wyman solution and the Robertson-Walker (R-W) solutions.
01 Jan 1991
TL;DR: In this paper, a short review of recent works on the application of the third quantization method to the cosmological constant problem is presented, and critical consideration is given to Dirac's scheme of gravity quantization.
Abstract: The paper consists of two main parts. The first part contains a short review of recent works on the application of the third quantization method to the cosmological constant problem. In the second part critical consideration is given to Dirac's scheme of gravity quantization. We suppose that Dirac's scheme may turn out inadequate for gravity quantization because of anomalies arising in the algebra of constraints.
TL;DR: In this paper, the propagator of a massless minimally coupled scalar field in a power-law Robertson-Walker background was studied and no sign of singular infrared behavior was observed for all values of the expansion parameter.