Showing papers on "Friedmann–Lemaître–Robertson–Walker metric published in 1993"
TL;DR: In the context of nonminimally coupled theories of gravity, the existence of Noether symmetries in pointlike Friedman- Robertson-Walker (FRW) Lagrangians allows one to exactly integrate the dynamics.
112 citations
TL;DR: The distinction between Hubble's linear redshift distance z(L) law and the linear velocity distance V(L), which emerged later is discussed, using first the expanding space paradigm and then the Robertson-Walker metric as discussed by the authors.
Abstract: The distinction between Hubble's linear redshift-distance z(L) law and the linear velocity-distance V(L) law that emerged later is discussed, using first the expanding space paradigm and then the Robertson-Walker metric. The z(L) and V(L) laws are theoretically equivalent only in the limit of small redshifts, and failure to distinguish between the two laws obscures the basic elementary principles of modern cosmology. The linear V(L) law [V=HL, where H(t) is the Hubble term] applies quite generally in expanding homogeneous and isotropic cosmological models, and recession velocities can exceed the velocity of light
103 citations
TL;DR: In this article, the authors study the dynamics of flat Friedmann-Robertson-Walker cosmologies in the presence of a triplet of massive vector fields with SO(3) global symmetry.
Abstract: The authors study the dynamics of flat Friedmann-Robertson-Walker cosmologies (FRW) in the presence of a triplet of massive vector fields with SO(3) global symmetry. They find an E3-symmetric ansatz for the vector fields that is compatible with the E3-invariant FRW metric and propose a method to make an invariant ansatz for more general cosmological models. They use the techniques of dynamical systems to study qualitatively the behaviour of the model and find, in particular, that the effective equation of state of the system changes gradually from a radiation-dominated to a matter-dominated form and that the scale of the transition depends on the mass of the gauge fields.
98 citations
TL;DR: In this paper, it was shown that the dynamics of a spatially dosed Friedmann-Robertson-Walker universe conformally coupled to a real, free, massive scalar field, is chaotic, for large enough field amplitudes.
Abstract: We show that the dynamics of a spatially dosed Friedmann-Robertson-Walker universe conformally coupled to a real, free, massive scalar field, is chaotic, for large enough field amplitudes. We do so by proving that this system is integrable under the adiabatic approximation, but that the corresponding KAM tori break up when non-adiabatic terms are considered. This finding is confirmed by numerical evaluation of the Lyapunov exponents associated with the system, among other criteria. Chaos sets strong limitations on our ability to predict the value of the field at the big crunch, from its given value at the big bang.
70 citations
TL;DR: In this article, the authors study the dynamics of flat Friedmann-Robertson-Walker cosmologies in the presence of a triplet of massive vector fields with SO(3) global symmetry.
Abstract: The authors study the dynamics of flat Friedmann-Robertson-Walker cosmologies (FRW) in the presence of a triplet of massive vector fields with SO(3) global symmetry. They find an E3-symmetric ansatz for the vector fields that is compatible with the E3-invariant FRW metric and propose a method to make an invariant ansatz for more general cosmological models. They use the techniques of dynamical systems to study qualitatively the behaviour of the model and find, in particular, that the effective equation of state of the system changes gradually from a radiation-dominated to a matter-dominated form and that the scale of the transition depends on the mass of the gauge fields.
65 citations
TL;DR: It is shown, in agreement with previous studies, that for a wide range of initial conditions the late-time behavior of the models is that of a power-law inflating Friedmann-Robertson-Walker (FRW) universe.
Abstract: We obtain a general exact solution of the Einstein field equations for the anisotropic Bianchi type I universes filled with an exponential-potential scalar field and study their dynamics. It is shown, in agreement with previous studies, that for a wide range of initial conditions the late-time behavior of the models is that of a power-law inflating Friedmann-Robertson-Walker (FRW) universe. This property does not hold, in contrast, when some degree of inhomogeneity is introduced, as discussed in our following paper.
63 citations
TL;DR: In this paper, the authors investigated the behavior of the solutions to the Einstein equations with a causal viscous fluid source in the case of the spatially flat Robertson-Walker metric, and they found that the qualitative asymptotic behavior in the far future is not altered by relaxation processes, but they change the behaviour in the past.
Abstract: We investigate the behaviour of the solutions to the Einstein equations with a causal viscous fluid source in the case of the spatially flat Robertson-Walker metric. In our model, the bulk viscosity coefficient is related to the energy density as zeta = alpha rho m, and the relaxation time is given by zeta / rho . We find the exact solutions when m = 1/2 , and we study analytically the asymptotic stability of the distinct families of solutions for arbitrary m. We find that the qualitative asymptotic behaviour in the far future is not altered by relaxation processes, but they change the behaviour in the past, either excluding deflationary evolutions or making the Universe bounce due to the violation of the energy conditions.
57 citations
TL;DR: The 3 + 1 formalism of Thorne and Macdonald is used to formulate the electrodynamic equations for a plasma in a spatially flat Robertson-Walker metric, and the results are compared with those of classical kinetic theory and quantum field theory in special relativity.
Abstract: The 3+1 formalism of Thorne and Macdonald is used to formulate the electrodynamic equations for a plasma in a spatially flat Robertson-Walker metric. The conformal flatness of this space-time ensures that these equations closely mirror those of flat space-time. The linearized Vlasov-Maxwell equations are solved for the case of an unmagnetized plasma of ultrarelativistic particles and antiparticles, and the results are compared with those of classical kinetic theory and quantum field theory in special relativity. The Vlasov-Maxwell equations for a plasma of nonrelativistic particles are not conformally invariant, so a fluid approximation is used to obtain the linear modes of oscillation, again for an unmagnetized plasma. The plasma modes redshift at rates which depend on the rate of expansion of the Universe, and whether the electromagnetic fields or the particles dominate the dynamics.
54 citations
TL;DR: In this article, the authors consider the evolution of the dilaton in a Friedmann-Robertson-Walker background by numerically integrating the equations of motion as determined by the low-energy expansion of the string theory action.
53 citations
TL;DR: In this article, the cosmological state of the universe can be described in terms of a statistical state, and a dynamical model with infinite degrees of freedom that describes a Robertson-Walker universe with nonhomogeneous electromagnetic radiation is defined.
Abstract: The idea that the cosmological state of the universe can be described in terms of a statistical state is discussed. A dynamical model with infinite degrees of freedom that describes a Robertson-Walker universe with nonhomogeneous electromagnetic radiation is defined. Its statistical mechanics is studied by using the covariant statistical theory. A simple statistical state that represents the cosmic background radiation is constructed. The properties of this state support the general theory; in particular, the idea that a preferred time variable, denoted thermodynamical time, is singled out by the statistical state can be tested within this model. The thermodynamical time is computed and shown to agree with the standard Robertson-Walker time. In addition, an application of the general theory to a simple special relativistic system, and a proposal for an application to full general relativity are also presented. The relevance of this application for the physics of the very early universe is discussed.
52 citations
TL;DR: In this article, the general expression for the entropy production in cosmologies with variable effective cosmological "constant" (Lambda ) is presented, by assuming that Lambda decays as Lambda = alpha R-m+ beta (R/R)2, where R(t) is the scale factor of the FRW models, the second law of thermodynamics and the Landau-Lifshitz theory for non-equilibrium fluctuations are used to establish constraints on the parameters alpha, beta and m.
Abstract: The general expression for the entropy production in cosmologies with variable effective cosmological 'constant' ( Lambda ) is presented. By assuming that Lambda decays as Lambda = alpha R-m+ beta (R/R)2, where R(t) is the scale factor of the FRW models, the second law of thermodynamics and the Landau-Lifshitz theory for non-equilibrium fluctuations are used to establish constraints on the parameters alpha , beta and m.
TL;DR: In this paper, the authors investigate Brans-Dicke vacuum solutions in the presence of a cosmological constant A from the point of view of dynamical system theory, assuming a Friedmann-Robertson-Walker metric.
Abstract: We investigate Brans-Dicke vacuum solutions in the presence of a cosmological constant A from the point of view of dynamical system theory. Assuming a Friedmann-Robertson-Walker metric we plot the phase diagrams corresponding to all values ofω. The analysis of the diagrams allows us to determine several physical properties of the solutions as well as their global dynamical behaviour.
TL;DR: In this article, the authors studied the dynamics of a flat Friedmann-Robertson-Walker (FRW) inflationary model in the presence of gauge fields and showed that inflation is a general property and that the gauge field enhances inflation.
Abstract: The authors study the dynamics of a flat Friedmann-Robertson-Walker (FRW) inflationary model in the presence of gauge fields. A qualitative analysis of the dynamical system associated with their model is presented. It is shown that inflation is a general property and that the gauge field enhances inflation.
TL;DR: In this article, a nonminimally coupled cosmological model and the existence of a Noether symmetry in the point-like Friedman-Robertson-Walker (FRW) Lagrangian describing the model are discussed.
TL;DR: In this paper, the authors consider anisotropic model universes with a homogeneous self-interacting scalar field with exponential potential and find exact solutions of the Einstein equations for homogeneous Bianchi III and VI cosmologies.
Abstract: The authors consider some anisotropic model universes filled with a homogeneous self-interacting scalar field with exponential potential (V approximately ealpha phi ). Specifically, by assuming power law behaviour for the scale factors they are able to find exact solutions of Einstein equations for homogeneous Bianchi III and VI cosmologies. They compare the behaviour of these models with that of flat and open FRW solutions with similar scalar fields and show that neither of the obtained anisotropic solutions inflate.
TL;DR: A general method to obtain the power spectrum and energy density of the relic gravitational waves is described and the results are applied for a simple three-stage model involving both an inflationary and noninflationary initial phase.
Abstract: Graviton production in flat three-space Robertson-Walker universes is studied. An arbitrary sequence or stages governed by scale factors exhibiting exponential or power-law behavior is considered. By the derivation or exact expressions for the Bogolubov coefficients associated with the several transitions between different cosmic eras, a general method to obtain the power spectrum and energy density of the relic gravitational waves is described. The results are applied for a simple three-stage model involving both an inflationary and noninflationary initial phase. Exact and explicit formulas for the spectrum and time evolution or the energy density parameter Ω g are found
TL;DR: In this article, a phenomenological decay law for the cosmological Λ-term is proposed and its influence on the universe evolution is investigated and explicit analytic solutions are given for the flat case both for parametric and cosmologically times.
Abstract: A new phenomenological decay law for the cosmological Λ-term is proposed and its influence on the universe evolution is investigated. Unlike the standard FRW model are the possibility of nonsingular solutions, recollapsing open universes and an everexpanding closed model. Explicit analytic solutions are given for the flat case both for parametric and cosmological times. In this case, models with the present density parameter Ω0 smaller than 2/3 and age bigger than can always be obtained. It is also shown that kinematic expressions as the luminosity distance and angular diameter versus redshift relation are significantly modified.
TL;DR: In this article, a family of exact solutions to the Einstein field equations which describe inhomogeneous generalizations of spatially flat FRW cosmologies is presented, and it is shown that these inhomogenous models never inflate and briefly discuss the implications of their results on the genericity of inflation and isotropization.
Abstract: We present a family of exact solutions to the Einstein field equations which describe inhomogeneous generalizations of spatially flat FRW cosmologies. The self-interacting scalar field with an exponential potential of the form V approximately ek phi serves as a source for the expansion. We show that these inhomogeneous models never inflate and briefly discuss the implications of our results on the genericity of inflation and isotropization at late times.
Journal Article•
TL;DR: In this article, a singularity-free general solution of the big-bang singularity was obtained for perfect fluid in the Friedman-Robertson-Walker (FRW) model with negative curvature.
Abstract: In 1990 Senovilla$^1$ obtained an interestisng cosmological solution of Einstein's equations that was free of the big-bang singularity. It represented an inhomogeneous and anisotropic cylindrical model filled with disordered radiation, ${\bf \rho = 3p}$. The model was valid for ${\bf t \rightarrow - \infty }$ to ${\bf t \rightarrow \infty}$ having all physical and geometrical invariants finite and regular for the whole of spacetime. This was the first instance of a singularity free cosmological model satisfying all the energy and causality conditions and remaining true to general relativity (GR). Subsequently a family of singularity free models has been identified${\bf ^2}$. In this letter we wish to point out that a simple and natural inhomogenisation and anisotropisation, appropriate for cylindrical symmetry, of the Friedman-Robertson-Walker (FRW) model with negative curvature leads to the same singularity free family. It consists of the complete set of singularity free general solutions of Einstein's equations for perfect fluid when cylindrically symmetric metric potentials are assumed to be separable functions of radial and time coordinates.
TL;DR: In this article, the authors present solutions of cosmological perturbations for an ideal-fluid medium with a constant pressure (p) to density (μ) relation in a flat Friedmann-Lemaitre-Robertson-Walker (FLRW) background model.
Abstract: We present solutions of cosmological perturbations for an ideal-fluid medium with a constant pressure (p) to density (μ) relation in a flat Friedmann-Lemaitre-Robertson-Walker (FLRW) background model. Solutions are presented for six different gauge choices which include most of those conventionally used. Both exact and asymptotic solutions are shown in tabular forms. Solutions span a range in w(≡p/μ) from -1 to 1. On subhorizon scales except for the uniform-density gauge, for general w, the density perturbations in all gauge choices behave in the same way; also for a pressureless medium the behavior is in accord with the Newtonian results
TL;DR: In this paper, the minimal low-energy action for gravity up to six derivatives is considered and the classical solutions corresponding to the Schwarzschild and the Robertson-Walker metrics are studied at two-loop level modulo higher derivative corrections.
TL;DR: Every radiation solution in general relativity is an exact solution in higher order gravity provided there are no nonzero constants and the Einstein term is present in the gravitational Lagrangian of the f (R) theory.
Abstract: We analyze the behavior of radiation-filled, homogeneous, and isotropic cosmological solutions to a generalized higher order gravity theory which is derived from a gravitational Lagrangian that is an arbitrary function of the scalar spacetime curvature f (R). We give necessary and sufficient conditions for the existence and stability of general relativistic σ = ± 1,0 FRW solutions within this general theory. We show that under some general conditions any homogeneous and isotropic solution of general relativity is also an exact solution of the f (R) theory, and every radiation solution (not necessarily isotropic) in general relativity is an exact solution in higher order gravity provided there are no nonzero constants and the Einstein term is present in the gravitational Lagrangian of our theory
TL;DR: The retarded Green's function for gravitational waves propagating through a cosmological fluid composed of both radiation and dust is calculated analytically for the first time and it is shown that for all FRW spacetimes in which the Ricci scalar curvature does not vanish, the Green'sfunction violates Huygens' principle.
Abstract: A method for calculating the retarded Green's function for the gravitational wave equation in Friedmann-Robertson-Walker spacetimes within the formalism of linearized Einstein gravity is developed. Hadamard's general solution to Cauchy's problem for second-order, linear partial differential equations is applied to the FRW gravitational wave equation. The retarded Green's function may be calculated for any FRW spacetime, with curved or flat spatial sections, for which the functional form of the Ricci scalar curvature $R$ is known. The retarded Green's function for gravitational waves propagating through a cosmological fluid composed of both radiation and dust is calculated analytically for the first time. It is also shown that for all FRW spacetimes in which the Ricci scalar curvatures does not vanish, $R\ensuremath{
e}0$, the Green's function violates Huygens' principle; the Green's function has support inside the light cone due to the scattering of gravitational waves off the background curvature.
TL;DR: In this paper, the influence of adiabatic particle production processes on the dynamics of a homogeneous and isotropic universe was studied on a phenomenological level using a previously developed thermodynamically oriented gauge-invariant formalism.
Abstract: In a recent paper the influence of adiabatic particle production processes on the dynamics of a homogeneous and isotropic universe was studied on a phenomenological level. For a sufficiently high particle production rate these investigations resulted in a nonsingular cosmological model starting with a de Sitter phase and finite maximum values of all matter quantities. As the particle production rate decays there is a smooth transition to the familiar Friedmann-Lemaitre-Robertson-Walker (FLRW) behaviour. In the present paper, scalar perturbations about this homogeneous and isotropic background are studied using a previously developed thermodynamically oriented gauge-invariant formalism. It turns out that the gauge-invariantly defined fractional adiabatic energy density perturbations are unstable on large scales during the initial de Sitter phase. These perturbations may grow quadratically with the cosmic time. Approaching the radiation-dominated period there is a change to the well known linear growth.
TL;DR: In this paper, the case of a similar, but spatially flat, universe (k = 0) is investigated, where there is an initial geometric singularity (the scale factorR = 0), but not a physical one, since the initial density is finite.
Abstract: Recently a homogeneous cosmological model free from singularities was proposed, based on the general relativity theory. It described a closed universe (k = +1), initially filled with prematter, characterized by a density ρ equal to the Planck density and a pressureP = −ρ, and undergoing oscillations. In the present work the case of a similar, but spatially flat, universe (k = 0) is investigated. In this case there is an initial geometric singularity (the scale factorR = 0), but not a physical one, since the initial density is finite. This universe begins its existence at a timet = −∞ and, after going through the prematter and radiation-dominated eras, reaches the matter-dominated state and continues to expand indefinitely.
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TL;DR: Certain wormhole solutions that have so far been found are closely related to their corresponding bounces in Lorentzian space: their Friedmann equations are invariant under t to i tau, k to -k.
Abstract: Certain wormhole solutions that have so far been found are closely related to their corresponding bounces in Lorentzian space: their Friedmann equations are invariant under (t to i tau , k to -k). Matter sources being used to give Euclidean wormholes could be used instead to get 'real' Lorentzian wormholes.
TL;DR: In this article, the authors derived the Wheeler-DeWitt equation from the bosonic sector of the heterotic string effective action assuming a toroidal compactification, and investigated the spatially closed, higher dimensional Friedmann-Robertson-Walker cosmology.
Abstract: The Wheeler-DeWitt equation is derived from the bosonic sector of the heterotic string effective action assuming a toroidal compactification. The spatially closed, higher dimensional Friedmann-Robertson-Walker (FRW) cosmology is investigated and a suitable change of variables rewrites the equation in a canonical form. Real- and imaginary-phase exact solutions are found and a method of successive approximations is employed to find more general power series solutions. The quantum cosmology of the Bianchi IX universe is also investigated and a class of exact solutions is found.
TL;DR: In this article, a probabilistic model for the instability of world lines in Robertson-Walker universes of negative spatial curvature is proposed, and a covariant evolution equation for the probability density on which this flow acts is constructed.
Abstract: The instability of world lines in Robertson–Walker universes of negative spatial curvature is investigated. A probabilistic description of this instability, similar to the Liouville equation, is developed, but in a manifestly covariant, non‐Hamiltonian form. To achieve this the concept of a horospherical geodesic flow of expanding bundles of parallel world lines is introduced. An invariant measure and a covariant evolution equation for the probability density on which this flow acts is constructed. The orthogonal surfaces to these bundles of trajectories are horospheres, closed surfaces in three‐space, touching the boundary at infinity of hyperbolic space, where the flow lines emerge. These horospheres are just the wave fronts of spherical waves, which constitute a complete set of eigenfunctions of the Klein–Gordon equation. This fact suggests that the evolution of the quantum mechanical density with the classical one be compared, and asymptotic identity in the asymptotically flat region is found. This leads, furthermore, to the study of the time behavior of the dispersion of the energy and the coordinates and the energy‐time uncertainty relation, and identity in the late stage of the cosmic evolution is again found. In an example it is finally demonstrated that this identity can persist in the early phase of the expansion with a rapidly varying scale factor, provided the fields are conformally coupled to the curvature.
TL;DR: In this article, the evolution of a massless, conformally coupled scalar field interacting with an environment in a spatially flat FRW metric is investigated, and it is shown that classical behaviour emerges for wavelengths greater than the Hubble radius.
Abstract: The author investigates the evolution of a massless, conformally coupled scalar field interacting with an environment in a spatially flat FRW metric. The environment is taken to be a second massless, conformally coupled scalar field. By finding the ground state wavefunctional of the coupled system and integrating out the unobservable scalar field the author obtains a reduced density matrix for the system, and then uses the reduced density matrix to show that classical behaviour emerges for wavelengths greater than the Hubble radius. This occurs despite the absence of particle creation.