Showing papers on "Friedmann–Lemaître–Robertson–Walker metric published in 2001"
TL;DR: In this paper, the authors consider a FRW cosmological model with an exotic fluid known as Chaplygin gas and show that the resulting evolution of the universe is not in disagreement with the current observation of cosmic acceleration.
Abstract: We consider a FRW cosmological model with an exotic fluid known as Chaplygin gas. We show that the resulting evolution of the universe is not in disagreement with the current observation of cosmic acceleration. The model predict an increasing value for the effective cosmological constant.
1,923 citations
TL;DR: In this article, Friedmann's equations governing the expansion factor of spatially averaged portions of inhomogeneous cosmologies are derived for general relativistic spacetimes filled with an irrotational perfect fluid.
Abstract: For general relativistic spacetimes filled with an irrotational perfect fluid a generalized form of Friedmann's equations governing the expansion factor of spatially averaged portions of inhomogeneous cosmologies is derived. The averaging problem for scalar quantities is condensed into the problem of finding an "effective equation of state" including kinematical as well as dynamical "backreaction" terms that measure the departure from a standard FLRW cosmology. Applications of the averaged models are outlined including radiation-dominated and scalar field cosmologies (inflationary and dilaton/string cosmologies). In particular, the averaged equations show that the averaged scalar curvature must generically change in the course of structure formation, that an averaged inhomogeneous radiation cosmos does not follow the evolution of the standard homogeneous-isotropic model, and that an averaged inhomogeneous perfect fluid features kinematical "backreaction" terms that, in some cases, act like a free scalar field source. The free scalar field (dilaton) itself, modelled by a "stiff" fluid, is singled out as a special inhomogeneous case where the averaged equations assume a simple form.
342 citations
TL;DR: In this paper, a general model of multidimensional gravity including a Riemann tensor square term (nonzero c case) was considered and the number of brane-worlds in such a model was constructed (mainly in five dimensions).
Abstract: A general model of multidimensional ${R}^{2}$ gravity including a Riemann tensor square term (nonzero c case) is considered. The number of brane-worlds in such a model is constructed (mainly in five dimensions) and their properties are discussed. The thermodynamics of a Schwarzschild--anti-deSitter (S-AdS) BH (with boundary) is presented when perturbation on c is used. The entropy, free energy, and energy are calculated. For a nonzero c the entropy (energy) is not proportional to the area (mass). The equation of motion of the brane in a BH background is presented as a FRW equation. Using a dual CFT description it is shown that the dual field theory is not a conformal one when c is not zero. In this case the holographic entropy does not coincide with the BH entropy (they coincide for Einstein gravity or $c=0$ HD gravity where the AdS/CFT description is well applied). An asymmetrically warped background (an analogue of a charged AdS BH) where Lorentz invariance violation occurs is found. The cosmological 4D dS brane connecting two dS bulk spaces is formulated in terms of the parameters of ${R}^{2}$ gravity. Within the proposed dS/CFT correspondence the holographic conformal anomaly from five-dimensional higher derivative gravity in a de Sitter background is evaluated.
220 citations
TL;DR: In this article, the authors considered a brane-universe in the background of an anti-de-Sitter/Schwarzschild geometry and showed that the induced geometry of the brane is exactly given by that of a standard radiation dominated FRWuniverse.
174 citations
TL;DR: In this article, cosmological perturbations of kinetic components based on relativistic Boltzmann equations in the context of generalized gravity theories are considered. But they are not considered in this paper.
Abstract: 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 with the accompanying polarizations. We also include direct interactions among fluids and fields. The background FLRW model includes the general 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 have implemented four different gauge conditions in a gauge-ready manner where two of them are new. By comparing solutions solved separately in different gauge conditions we can naturally check the numerical accuracy.
141 citations
TL;DR: In this paper, the authors consider a variant of the brane-world model in which the universe is the direct product of a Friedmann-Robertson-Walker (FRW) space and a compact hyperbolic manifold of dimension $dg~2.$ Cosmology in this space is particularly interesting.
Abstract: We consider a variant of the brane-world model in which the universe is the direct product of a Friedmann-Robertson-Walker (FRW) space and a compact hyperbolic manifold of dimension $dg~2.$ Cosmology in this space is particularly interesting. The dynamical evolution of the space-time leads to the injection of a large entropy into the observable (FRW) universe. The exponential dependence of surface area on distance in hyperbolic geometry makes this initial entropy very large, even if the CHM has a relatively small diameter (in fundamental units). The very large statistical averaging inherent in the collapse of the initial entropy onto the brane acts to smooth out initial inhomogeneities. This smoothing is then sufficient to account for the current homogeneity of the universe. With only mild fine-tuning, the current flatness of the universe can also then be understood. Finally, recent brane-world approaches to the hierarchy problem can be readily realized within this framework.
103 citations
TL;DR: In this paper, the role of 2D brane cosmological constant is played by effective tension due to two-dimensional conformal anomaly and the dynamical equations to describe 4D FRW universe with the account of quantum effects produced by conformal anomalies are obtained.
Abstract: The role of conformal anomaly in AdS/CFT and related issues is clarified. The comparison of holographic and QFT conformal anomalies (with the account of brane quantum gravity contribution) indicates the possibility for brane quantum gravity to occur within the AdS/CFT setup. Three-dimensional quantum induced inflationary (or hyperbolic) brane-world is shown to be realized in the frames of AdS3/CFT2 correspondence where the role of 2d brane cosmological constant is played by effective tension due to two-dimensional conformal anomaly. The dynamical equations to describe 4d FRW universe with the account of quantum effects produced by conformal anomaly are obtained. The quantum corrected energy, pressure and entropy are found. The dynamical evolution of entropy bounds in the inflationary universe is estimated and its comparison with quantum corrected entropy is done. It is demonstrated that entropy bounds for quantum corrected entropy are getting the approximate ones and occur for some limited periods of evolution of the inflationary universe.
76 citations
TL;DR: In this article, an isotropic homogeneous FRW universe in the presence of a bulk viscous fluid within the framework of Lyra's geometry was studied and exact solutions of the Sen equations were obtained assuming the deceleration parameter to be constant.
Abstract: We have studied an isotropic homogeneous FRW universe in the presence of a bulk viscous fluid within the framework of Lyra's geometry. We have obtained exact solutions of the Sen equations assuming the deceleration parameter to be constant. The coefficient of bulk viscosity has been assumed to be a power function of the mass density. With this assumption, we have considered the behavior of the displacement field and the energy density for both power-law and exponential expansions of the universe. We show that our models are generalised and we obtain the results of previous works by considering k=0 and k=-1.
74 citations
TL;DR: In this paper, higher derivative bulk gravity (without Riemann tensor square term) admits AdS-Schwarzschild black hole as an exact solution, and induced brane geometry on such background is open, flat or closed FRW radiation dominated universe.
Abstract: Higher derivative bulk gravity (without Riemann tensor square term) admits AdS–Schwarzschild black hole as an exact solution. It is shown that induced brane geometry on such background is open, flat or closed FRW radiation dominated universe. Higher derivative terms contributions appear in the Hawking temperature, entropy and Hubble parameter via the redefinition of five-dimensional gravitational constant and AdS scale parameter. These higher derivative terms do not destroy the AdS-dual description of radiation represented by strongly-coupled CFT. The Cardy–Verlinde formula which expresses cosmological entropy as the square root from other parameters and entropies is derived in R2 gravity. The corresponding cosmological entropy bounds are briefly discussed.
49 citations
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TL;DR: In this article, the cosmological relativity theory has been shown to determine the value of Lambda = 1.934 x 10^-35 s^-2 for the Cosmological constant.
Abstract: It is shown that the cosmological relativity theory prdicts the value Lambda = 1.934 x 10^-35 s^-2 for the cosmological constant. This value of Lambda is in exellent agreement with the measurements recently obtained by the High-Z Supernova Team and the Supernova Cosmology Project.
47 citations
TL;DR: In this paper, the authors derived the distance-redshift relation in terms of associated Legendre functions for partially filled beam observations in spatially flat Friedmann-Lemaitre-Robertson-Walker cosmologies.
Abstract: Distance-redshift relations are given in terms of associated Legendre functions for partially filled beam observations in spatially flat Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmologies. These models are dynamically pressure-free and flat FLRW on large scales but, because of mass inhomogeneities, differ in their optical properties. The partially filled beam area-redshift equation is a Lame equation for arbitrary FLRW models and is shown to simplify to the associated Legendre equation for the spatially flat, i.e., Ω0 = 1, case. We fit these new analytic Hubble curves to recent supernovae (SNe) data in an attempt to determine both the mass parameter Ωm and the beam-filling parameter ν. We find that current data are inadequate for limiting ν. However, we are able to estimate what limits are possible when the number of observed SNe is increased by factor of 10 or 100, sample sizes achievable in the near future with the proposed SuperNova Acceleration Probe satellite.
TL;DR: In this article, the authors studied brane-world solutions of 5D supergravity in singular spaces and obtained a self-tuned four-dimensional cosmological constant when five-dimensional supergravity is broken by an arbitrary tension on the brane world.
TL;DR: In this article, the evolution of a flat Friedmann-Robertson-Walker universe, filled with a causal bulk viscous cosmological fluid, in the presence of variable gravitational and cosmology constants is considered.
Abstract: We consider the evolution of a flat Friedmann-Robertson-Walker Universe, filled with a causal bulk viscous cosmological fluid, in the presence of variable gravitational and cosmological constants. The basic equation for the Hubble parameter, generalizing the evolution equation in the case of constant gravitational coupling and cosmological term, is derived, under the supplementary assumption that the total energy of the Universe is conserved. By assuming that the cosmological constant is proportional to the square of the Hubble parameter and a power law dependence of the bulk viscosity coefficient, temperature and relaxation time on the energy density of the cosmological fluid, two classes of exact solutions of the field equations are obtained. In the first class of solutions the Universe ends in an inflationary era, while in the second class of solutions the expansion of the Universe is non-inflationary for all times. In both models the cosmological "constant" is a decreasing function of time, while the gravitational "constant" increases in the early period of evolution of the Universe, tending in the large time limit to a constant value.
TL;DR: In this article, the authors recall the Newtonian derivation of the Friedmann equations which govern the dynamics of our universe and discuss the validity of such a derivation, and study the equations of evolution of the universe in terms of a dynamical system.
Abstract: Cosmology is an attractive subject for students but it is usually difficult if general relativity is not understood. In this article, we first recall the Newtonian derivation of the Friedmann equations which govern the dynamics of our universe and discuss the validity of such a derivation. We then study the equations of evolution of the universe in terms of a dynamical system. This sums up the different behaviours of our universe and enables us to address some cosmological problems.
TL;DR: In this paper, the authors use the integration scheme for the exact spherically symmetric Einstein field equations in observational coordinates recently developed by Araujo and Stoeger, and input data functions for area distance and galaxy number counts that would be obtained if the universe were exactly represented by nonflat Friedmann-Lemaitre-Robertson-Walker models.
Abstract: In this paper we use the integration scheme for the exact spherically symmetric Einstein field equations in observational coordinates recently developed by Araujo and Stoeger, and input data functions for area distance and galaxy number counts that would be obtained if the universe were exactly represented by nonflat Friedmann-Lemaitre-Robertson-Walker models.
TL;DR: In this article, the authors investigate the general asymptotic behavior of Friedman-Robertson-Walker (FRW) models with an inflaton field, scalar-tensor FRW cosmological models and diagonal Bianchi-IX models by means of Lyapunov's method.
Abstract: We investigate the general asymptotic behaviour of Friedman-Robertson-Walker (FRW) models with an inflaton field, scalar-tensor FRW cosmological models and diagonal Bianchi-IX models by means of Lyapunov's method. This method provides information not only about the asymptotic stability of a given equilibrium point but also about its basin of attraction. This cannot be obtained by the usual methods found in the literature, such as linear stability analysis or first-order perturbation techniques. Moreover, Lyapunov's method is also applicable to non-autonomous systems. We use this advantage to investigate the mechanism of reheating for the inflaton field in FRW models.
TL;DR: In this paper, an exact solution of the Friedmann Robertson field equation with the appropriate matter density for generic values of the Cosmological Constant %Lambda and curvature constant K is derived.
Abstract: Strong field (exact) solutions of the gravitational field equations of General Relativity in the presence of a Cosmological Constant are investigated. In particular, a full exact solution is derived within the inhomogeneous Szekeres-Szafron family of space-time line element with a nonzero Cosmological Constant. The resulting solution connects, in an intrinsic way, General Relativity with the theory of modular forms and elliptic curves. The homogeneous FLRW limit of the above space-time elements is recovered and we solve exactly the resulting Friedmann Robertson field equation with the appropriate matter density for generic values of the Cosmological Constant %Lambda and curvature constant K. A formal expression for the Hubble constant is derived. The cosmological implications of the resulting non-linear solutions are systematically investigated. Two particularly interesting solutions i) the case of a flat universe K=0, Lambda not= 0 and ii) a case with all three cosmological parameters non-zero, are described by elliptic curves with the property of complex multiplication and absolute modular invariant j=0 and 1728, respectively. The possibility that all non-linear solutions of General Relativity are expressed in terms of theta functions associated with Riemann-surfaces is discussed.
TL;DR: In this article, a canonical and quantum cosmological analysis of a spatially flat, four-dimensional Friedmann-Robertson-Walker (FRW) model that is derived from the M-theory effective action obtained originally by Billyard, Coley, Lidsey and Nilsson is presented.
Abstract: We present a canonical and quantum cosmological investigation of a spatially flat, four-dimensional Friedmann-Robertson-Walker (FRW) model that is derived from the M-theory effective action obtained originally by Billyard, Coley, Lidsey and Nilsson (BCLN). The analysis makes use of two sets of canonical variables, the Shanmugadhasan gauge-invariant canonical variables and the `hybrid' variables which diagonalize the Hamiltonian. We find the observables and discuss in detail the phase space of the classical theory. In particular, a region of phase space exists that describes a four-dimensional FRW spacetime first contracting from a strong-coupling regime and then expanding to a weak-coupling regime, while the internal space always contracts. We find the quantum solutions of the model and obtain the positive norm Hilbert space of states. Finally, the correspondence between wavefunctions and classical solutions is outlined.
TL;DR: In this article, an analysis of a n-dimensional vacuum Einstein field equation in which four-dimensional space-time is described by a Friedmann-Robertson-Walker (FRW) metric and that of extra dimensions by a Kasner-type Euclidean metric is presented.
Abstract: We present an analysis of a n-dimensional vacuum Einstein field equations in which four-dimensional space-time is described by a Friedmann-Robertson-Walker (FRW) metric and that of extra dimensions by a Kasner-type Euclidean metric. The field equations are interpreted as four-dimensional Einstein equations with effective matter properties. The effective matter is then treated as a viscous fluid. We consider the theories of imperfect fluid given by Eckart, truncated Israel-Stewart, and full Israel-Stewart theories, and obtain cosmological solutions for a flat model of the universe. The imperfect fluid assumption admits here power law inflation for the three-physical space in some cases.
TL;DR: In this paper, the problem of matching an inhomogeneous overdense region to a Friedmann-Robertson-Walker background universe in the general spherical symmetric case of pressure-free models was considered.
Abstract: Within the framework of an exact general relativistic formulation of gluing manifolds, we consider the problem of matching an inhomogeneous overdense region to a Friedmann-Robertson-Walker background universe in the general spherical symmetric case of pressure-free models. It is shown that, in general, the matching is only possible through a thin shell, a fact ignored in the literature. In addition to this, in subhorizon cases where the matching is possible, an intermediate underdense region will necessarily arise.
TL;DR: In this article, Liapunov's method is applied to Friedman-Robertson-Walker (FRW) models with an inflaton field, scalar-tensor FRW cosmological models and diagonal Bianchi-IX models.
Abstract: We investigate the general asymptotic behaviour of Friedman-Robertson-Walker (FRW) models with an inflaton field, scalar-tensor FRW cosmological models and diagonal Bianchi-IX models by means of Liapunov's method. This method provides information not only about the asymptotic stability of a given equilibrium point but also about its basin of attraction. This cannot be obtained by the usual methods found in the literature, such as linear stability analysis or first order perturbation techniques. Moreover, Liapunov's method is also applicable to non-autonomous systems. We use this advantadge to investigate the mechanism of reheating for the inflaton field in FRW models.
01 Apr 2001
TL;DR: In this paper, the basic kinematic and dynamical consequences associated to the existence of a cosmological term in Einstein's equations are discussed at a fairly elementary level. And the recent interpretation of data from Type Ia supernovae in terms of a small, positive, cosmologically constant selects a distinguished set of Friedmann-Lemaitre cosmology models.
Abstract: I review, at a fairly elementary level, the basic kinematic and dynamical consequences associated to the existence of a cosmological term in Einstein's equations. In particular, the recent interpretation of data from Type Ia supernovae in terms of a small, positive, cosmological constant selects a distinguished set of Friedmann-Lemaitre cosmological models. One of them should be the universe where we live.
TL;DR: In this article, the cosmological constant is identified with the Lorentz-invariant scalar arising by the contraction of the stress-energy tensor of ordinary matter which represents a form of the quintessence.
TL;DR: In this article, the authors consider a brane-universe in the background of an AdS-dual geometry and show that the induced geometry of the brane is exactly given by that of a standard radiation-dominated FRW-Universe.
Abstract: We consider a brane-universe in the background of an Anti-de Sitter/ Schwarschild geometry. We show that the induced geometry of the brane is exactly given by that of a standard radiation dominated FRW-universe. The radiation is represented by a strongly coupled CFT with an AdS-dual description. We show that when the brane crosses the horizon of the AdS-black hole the entropy and temperature are simply expressed in the Hubble constant and its time derivative. We present formulas for the entropy of the CFT which are generally valid, and which at the horizon coincide with the FRW equations. These results shed new light on recently proposed entropy bounds in the context of cosmology.
TL;DR: In this paper, a model for a spacetime-dependent cosmological constant is presented and a realization of this model based on a possible quantum aspects of the initial stage of the universe is made.
Abstract: We present a model for a spacetime-dependent cosmological constant. We make a realization of this model based on a possible quantum aspects of the initial stage of the universe and relate the cosmological constant to the chiral anomaly.
TL;DR: In this paper, the authors consider the cosmology of a pair of domain walls bounding a five-dimensional bulk space-time with negative cosmological constant, in which the distance between the branes is not fixed in time.
Abstract: We consider the cosmology of a pair of domain walls bounding a five-dimensional bulk space-time with negative cosmological constant, in which the distance between the branes is not fixed in time. Although there are strong arguments to suggest that this distance should be stabilized in the present epoch, no such constraints exist for the early universe and thus non-static solutions might provide relevant inflationary scenarios. We find the general solution for the standard ansatz where the bulk is foliated by planar-symmetric hypersurfaces. We show that in all cases the bulk geometry is that of anti-de Sitter (AdS_5). We then present a geometrical interpretation for the solutions as embeddings of two de Sitter (dS_4) surfaces in AdS_5, which provide a simple interpretation of the physical properties of the solutions. A notable feature explained in the analysis is that two-way communication between branes expanding away from one another is possible for a finite amount of time, after which communication can proceed in one direction only. The geometrical picture also shows that our class of solutions (and related solutions in the literature) are not completely general, contrary to some claims. We then derive the most general solution for two walls in AdS_5. This includes novel cosmologies where the brane tensions are not constrained to have opposite signs. The construction naturally generalizes to arbitrary FRW cosmologies on the branes.
TL;DR: The relationship between the entropy of de Sitter (dS) Schwarzschild space and that of the CFT, which lives on the brane, is discussed by using Friedmann-Robertson-Walker (FRW) equations and Cardy-Verlinde formula as mentioned in this paper.
Abstract: The relationship between the entropy of de Sitter (dS) Schwarzschild space and that of the CFT, which lives on the brane, is discussed by using Friedmann-Robertson-Walker (FRW) equations and Cardy-Verlinde formula. The cosmological constant appears on the brane with time-like metric in dS Schwarzschild background. On the other hand, in case of the brane with space-like metric in dS Schwarzschild background, the cosmological constant of the brane does not appear because we can choose brane tension to cancel it. We show that when the brane crosses the horizon of dS Schwarzschild black hole, both for time-like and space-like cases, the entropy of the CFT exactly agrees with the black hole entropy of 5-dimensional AdS Schwarzschild background as it happens in the AdS/CFT correspondence.
TL;DR: In this article, the general solution of the gravitational field equations in the flat Friedmann-Robertson-Walker geometry is obtained in the framework of the full Israel-Stewart-Hiscock theory for a bulk viscous stiff cosmological fluid, with bulk viscosity coefficient proportional to the energy density.
Abstract: The general solution of the gravitational field equations in the flat Friedmann-Robertson-Walker geometry is obtained in the framework of the full Israel-Stewart-Hiscock theory for a bulk viscous stiff cosmological fluid, with bulk viscosity coefficient proportional to the energy density.
TL;DR: In this article, the Darmois junction conditions are applied to a flat Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime to show that such a matching can be extended to an open FLRW spacetime.
Abstract: It is known that a flat Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime can be joined smoothly to a particular case of the Kasner vacuum spacetime. We apply the Darmois junction conditions to show that such a matching can be extended to an open FLRW spacetime. We also investigate the effect of a non-zero cosmological constant Λ on the matchings and conclude that the presence of the constant has no significant effect.