Showing papers on "Friedmann–Lemaître–Robertson–Walker metric published in 2003"
TL;DR: A solution of the (4+n)-dimensional vacuum Einstein equations is found for which spacetime is compactified on an n-dimensional compact hyperbolic manifold to a flat four-dimensional Friedmann-Lemaitre-Robertson-Walker cosmology undergoing a period of accelerated expansion in the Einstein conformal frame.
Abstract: A solution of the $(4+n)$-dimensional vacuum Einstein equations is found for which spacetime is compactified on an $n$-dimensional compact hyperbolic manifold ($n\ensuremath{\ge}2$) of time-varying volume to a flat four-dimensional Friedmann-Lemaitre-Robertson-Walker cosmology undergoing a period of accelerated expansion in the Einstein conformal frame. This shows that the ``no-go'' theorem forbidding acceleration in ``standard'' (time-independent) compactifications of string or M theory does not apply to ``cosmological'' (time-dependent) hyperbolic compactifications.
289 citations
TL;DR: In this paper, a semiclassical Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmological model was proposed to predict an increase of 10-20% in the value of Ω Λ at redshifts z = 1-1.5 perfectly reachable by SNAP.
207 citations
TL;DR: In this paper, it was shown that 3-branes can be added to the background in such a way that the effective four-dimensional cosmological constant is completely independent of the brane tensions.
Abstract: We consider solutions of six-dimensional Einstein equations with two compact dimensions. It is shown that one can introduce 3-branes in this background in such a way that the effective four-dimensional cosmological constant is completely independent of the brane tensions. These tensions are completely arbitrary, without requiring any fine tuning. We must, however, fine tune bulk parameters in order to obtain a sufficiently small value for the observable cosmological constant. We comment on the effective four-dimensional description of this effect at energies below the compactification scale.
170 citations
TL;DR: In this article, the authors present a systematic study of accelerating cosmologies obtained from M/string theory compactifications of hyperbolic spaces with time-varying volume.
Abstract: We present a systematic study of accelerating cosmologies obtained from M/string theory compactifications of hyperbolic spaces with time-varying volume. A set of vacuum solutions where the internal space is a product of hyperbolic manifolds is found to give qualitatively the same accelerating four-dimensional FLRW universe behavior as a single hyperbolic space. We also examine the possibility that our universe is a hyperbolic space and provide exact Milne type solutions, as well as intersecting S-brane solutions. When both the usual 4D spacetime and the m-dimensional internal space are hyperbolic, we find eternally accelerating cosmologies for m ≥ 7, with and without form field backgrounds. In particular, the effective potential for a magnetic field background in the large 3 dimensions is positive definite with a local minimum and thus enhances the eternally accelerating expansion.
153 citations
TL;DR: In this paper, the first-order and second-order modified Friedmann equations are presented and the upper redshift bounds for the SNe Ia data are derived. But they are not valid for the cosmological predictions involving only the Hubble parameter.
Abstract: Recently, corrections to the Einstein-Hilbert action that become important at small curvature have been proposed. We discuss the first-order and second-order approximations to the field equations derived by the Palatini variational principle. We work out the first- and second-order modified Friedmann equations and present the upper redshift bounds when these approximations are valid. We show that the second-order effects can be neglected in the cosmological predictions involving only the Hubble parameter, e.g. the various cosmological distances, but the second-order effects cannot be neglected in the predictions involving the derivatives of the Hubble parameter. Furthermore, the modified Friedmann equations fit the SNe Ia data at an acceptable level.
137 citations
TL;DR: In this article, the authors present a systematic study of accelerating cosmologies obtained from M/string theory compactifications of hyperbolic spaces with time-varying volume.
Abstract: We present a systematic study of accelerating cosmologies obtained from M/string theory compactifications of hyperbolic spaces with time-varying volume. A set of vacuum solutions where the internal space is a product of hyperbolic manifolds is found to give qualitatively the same accelerating four-dimensional FLRW universe behavior as a single hyperbolic space. We also examine the possibility that our universe is a hyperbolic space and provide exact Milne type solutions, as well as intersecting S-brane solutions. When both the usual 4D spacetime and the m-dimensional internal space are hyperbolic, we find eternally accelerating cosmologies for $m\geq 7$, with and without form field backgrounds. In particular, the effective potential for a magnetic field background in the large 3 dimensions is positive definite with a local minimum and thus enhances the eternally accelerating expansion.
111 citations
TL;DR: In this paper, M-theory compactifies on a seven-dimensional time-dependent hyperbolic or flat space to a four-dimensional FLRW cosmology undergoing a period of accelerated expansion in the Einstein conformal frame.
82 citations
TL;DR: In this article, the authors use the Friedmann equations to infer the scale factor of the cosmological equation of state at the current epoch, which is the simplest model one can consider that does not make any a priori restrictions on the nature of the Cosmological fluid.
Abstract: Taylor expanding the cosmological equation of state around the current epoch is the simplest model one can consider that does not make any a priori restrictions on the nature of the cosmological fluid. Most popular cosmological models attempt to be ``predictive'', in the sense that once somea priori equation of state is chosen the Friedmann equations are used to determine the evolution of the FRW scale factor a(t). In contrast, a retrodictive approach might usefully take observational dataconcerning the scale factor, and use the Friedmann equations to infer an observed cosmological equation of state. In particular, the value and derivatives of the scale factor determined at the current epoch place constraints on the value and derivatives of the cosmological equation of state at the current epoch. Determining the first three Taylor coefficients of the equation of state at the current epoch requires a measurement of the deceleration, jerk, and snap -- the second, third, and fourth derivatives of the scale factor with respect to time. Higher-order Taylor coefficients in the equation of state are related to higher-order time derivatives of the scale factor. Since the jerk and snap are rather difficult to measure, being related to the third and fourth terms in the Taylor series expansion of the Hubble law, it becomes clear why direct observational constraints on the cosmological equation of state are so relatively weak; and are likely to remain weak for the foreseeable future.
77 citations
TL;DR: In this article, a cosmological model with a phenomenological model was considered and the minimum age of the universe was found to be H − 1 0,w hereH 0 is the Hubble constant.
Abstract: We have considered a cosmological model with a phenomenological model for the cosmological constant of the form � = β ¨ R R where β is a constant. For age an parameter consistent with observational data, the universe must be accelerating in the presence of a positive cosmological constant. The minimum age of the universe is H −1 0 ,w hereH0 is th ep resent Hubble constant. The cosmological constant is found to decrease as t −2 .A llowing the gravitational constant to change with time leads to an ever-increasing gravitational constant ¨ ¨ �
69 citations
TL;DR: These shock-wave solutions indicate a cosmological model in which the big bang arises from a localized explosion occurring inside the black hole of an asymptotically flat Schwarzschild spacetime.
Abstract: We construct a class of global exact solutions of the Einstein equations that extend the Oppeheimer–Snyder model to the case of nonzero pressure, inside the black hole, by incorporating a shock wave at the leading edge of the expansion of the galaxies, arbitrarily far beyond the Hubble length in the Friedmann–Robertson–Walker (FRW) spacetime. Here the expanding FRW universe emerges be-hind a subluminous blast wave that explodes outward from the FRW center at the instant of the big bang. The total mass behind the shock decreases as the shock wave expands, and the entropy condition implies that the shock wave must weaken to the point where it settles down to an Oppenheimer–Snyder interface, (bounding a finite total mass), that eventually emerges from the white hole event horizon of an ambient Schwarzschild spacetime. The entropy condition breaks the time symmetry of the Einstein equations, selecting the explosion over the implosion. These shock-wave solutions indicate a cosmological model in which the big bang arises from a localized explosion occurring inside the black hole of an asymptotically flat Schwarzschild spacetime.
69 citations
TL;DR: In this paper, the cosmological constant with respect to the velocity of light, Planck and Newton gravitational constants has been derived from distant supernovae observations, and it is shown that the current value remarkably agrees with the value indicated by distant supernova observations, i.e. of the order of the critical density.
Abstract: We advance the viewpoint that, only relevant modes of the vacuum fluctuations, namely, with wavelengths conditioned by the size, homogeneity, geometry and topology of the Universe, do contribute to the cosmological constant. A formula is derived which relates the cosmological constant with the size of the Universe and the three fundamental constants: the velocity of light, Planck and Newton gravitational constants. Then the current value of the cosmological constant remarkably agrees with the value indicated by distant supernovae observations, i.e. of the order of the critical density. Thus the cosmological constant had to be smaller than the matter density in the past and will be bigger in the future.
01 Jul 2003
TL;DR: The Cardassian universe as mentioned in this paper is a proposed modification to the Friedmann Robertson Walker equation (FRW) in which the universe is flat, matter dominated, and accelerating, and specific examples are presented.
Abstract: The Cardassian universe is a proposed modification to the Friedmann Robertson Walker equation (FRW) in which the universe is flat, matter dominated, and accelerating. In this presentation, we generalize the original Cardassian proposal to include additional variants on the FRW equation, specific examples are presented. In the ordinary FRW equation, the right hand side is a linear function of the energy density, H2 ∼ ϱ. Here, instead, the right hand side of the FRW equation is a different function of the energy density, H2 ∼ g(ϱ). This function returns to ordinary FRW at early times, but modifies the expansion at a late epoch of the universe. The only ingredients in this universe are matter and radiation: in particular, there is NO vacuum contribution. Currently the modification of the FRW equation is such that the universe accelerates; we call this period of acceleration the Cardassian era. The universe can be flat and yet consist of only matter and radiation, and still be compatible with observations. The energy density required to close the universe is much smaller than in a standard cosmology, so that matter can be sufficient to provide a flat geometry. The new term required may arise, e.g., as a consequence of our observable universe living as a 3-dimensional brane in a higher dimensional universe. The Cardassian model survives several observational tests, including the cosmic background radiation, the age of the universe, the cluster baryon fraction, and structure formation. As will be shown in future work, he predictions for observational tests of the generalized Cardassian models can be very different from generic quintessence models, whether the equation of state is constant or time dependent.
TL;DR: An exact solution of the Einstein equations for a Bianchi-I universe in the presence of dust, stiff matter and cosmological constant, generalising the well-known Heckmann-Schucking solution is presented in this paper.
Posted Content•
23 Sep 2003
TL;DR: In this paper, the authors use the Friedmann equations to infer the scale factor of the cosmological equation of state at the current epoch, which is the simplest model one can consider that does not make any a priori restrictions on the nature of the Cosmological fluid.
Abstract: Taylor expanding the cosmological equation of state around the current epoch is the simplest model one can consider that does not make any a priori restrictions on the nature of the cosmological fluid. Most popular cosmological models attempt to be ``predictive'', in the sense that once somea priori equation of state is chosen the Friedmann equations are used to determine the evolution of the FRW scale factor a(t). In contrast, a retrodictive approach might usefully take observational dataconcerning the scale factor, and use the Friedmann equations to infer an observed cosmological equation of state. In particular, the value and derivatives of the scale factor determined at the current epoch place constraints on the value and derivatives of the cosmological equation of state at the current epoch. Determining the first three Taylor coefficients of the equation of state at the current epoch requires a measurement of the deceleration, jerk, and snap -- the second, third, and fourth derivatives of the scale factor with respect to time. Higher-order Taylor coefficients in the equation of state are related to higher-order time derivatives of the scale factor. Since the jerk and snap are rather difficult to measure, being related to the third and fourth terms in the Taylor series expansion of the Hubble law, it becomes clear why direct observational constraints on the cosmological equation of state are so relatively weak; and are likely to remain weak for the foreseeable future.
TL;DR: In this paper, the authors studied the late-time evolution of flat and negatively curved FRW models with a perfect fluid matter source and a scalar field having an arbitrary non-negative potential function.
Abstract: We study the late-time evolution of flat and negatively curved FRW models with a perfect fluid matter source and a scalar field having an arbitrary non-negative potential function V(). We prove, using the approach of dynamical systems, four general results for a large class of non-negative potentials and show that almost always the universe ever expands. In particular, for potentials having a local zero minimum, flat and negatively curved FRW models are ever expanding and the energy density asymptotically approaches zero. We investigate the conditions under which the scalar field asymptotically approaches the minimum of the potential. We discuss the question of whether a closed FRW with ordinary matter can avoid recollapse due to the presence of a scalar field with a non-negative potential.
TL;DR: In this paper, the authors investigated the dynamics of U(1) and scalar fields on unstable D-branes with rolling tachyons and derived the equations of motion for these fields.
Abstract: We investigate the dynamics of gauge and scalar fields on unstable D-branes with rolling tachyons. Assuming an FRW metric on the brane, we find a solution of the tachyon equation of motion which is valid for arbitrary tachyon potentials and scale factors. The equations of motion for a U(1) gauge field and a scalar field in this background are derived. These fields see an effective metric which differs from the original FRW metric. The field equations receive large corrections due to the curvature of the effective metric as well as the time variation of the gauge coupling. The equations of state for these fields resemble those of nonrelativistic matter rather than those of massless particles.
TL;DR: In this article, a simple FRW cosmological string model in four dimensions is presented, describing expansion in the presence of matter with $p=k \rho $, $k=(4-n)/3n).
Abstract: The $n+1$-dimensional Milne Universe with extra free directions is used to construct simple FRW cosmological string models in four dimensions, describing expansion in the presence of matter with $p=k \rho $, $k=(4-n)/3n$. We then consider the n=2 case and make SL(2,Z) orbifold identifications. The model is surprisingly related to the null orbifold with an extra reflection generator. The study of the string spectrum involves the theory of harmonic functions in the fundamental domain of SL(2,Z). In particular, from this theory one can deduce a bound for the energy gap and the fact that there are an infinite number of excitations with a finite degeneracy. We discuss the structure of wave functions and give examples of physical winding states becoming light near the singularity.
TL;DR: In this paper, the quantum Bohmian trajectories of a different class of Gaussian packets were analyzed and the relation between luminosity distance and redshift in the quantum cosmological model can be made close to the corresponding relation coming from the classical model supplemented by a cosmology constant, for z < 1.
TL;DR: In this paper, conditions for the existence of Noether symmetries in the dynamics of FRW metric, non minimally coupled with a scalar field, in the most general situation, and with nonzero spatial curvature were explored.
Abstract: We explore the conditions for the existence of Noether symmetries in the dynamics of FRW metric, non minimally coupled with a scalar field, in the most general situation, and with nonzero spatial curvature. When such symmetries are present we find a general exact solution for the Einstein equations. We also show that non Noether symmetries can be found. Finally, we present an extension of the procedure to the Kantowski-Sachs metric which is particularly interesting in the case of degenerate Lagrangian.
TL;DR: In this article, the distance redshift for partially filled-beam optics in pressure-free Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) cosmology is shown to be the Lam\'e equation.
Abstract: The differential equation governing the distance redshift for partially filled-beam optics in pressure-free Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) cosmology is shown to be the Lam\'e equation. The distance redshift $D(z)$ discussed is appropriate for observations in inhomogeneous cosmologies for which lensing by masses external to the observing beam is negligible and for which lensing by transparent matter within the beam can be approximated by a homogeneous mass density expanding with the FLRW background. Some solutions of the derived Lam\'e equation are given in terms of Weierstrass elliptic integrals. A new simplified and useful expression for filled-beam $D(z)$ in standard flat FLRW is also given.
TL;DR: The idea that the universe has zero total energy when one includes the contribution from the gravitational field is reconsidered in this article, and a Hamiltonian is proposed as an energy for the exact equations of FRW cosmology.
Abstract: The idea that the universe has zero total energy when one includes the contribution from the gravitational field is reconsidered. A Hamiltonian is proposed as an energy for the exact equations of FRW cosmology: it is then shown that this energy is constant. Thus, open and critically open FRW universes have the energy of their asymptotic state at infinite dilution, which is Minkowski space with zero energy. It is then shown that de Sitter space, the inflationary attractor, also has zero energy, and the argument is generalized to Bianchi models converging to this attractor.
01 Jul 2003
TL;DR: In this paper, the cosmological constant problem was used to distinguish quintessence from a cosmologically constant, and it was shown that a time variation of fundamental constants can be used as a way to distinguish the two.
Abstract: Quintessence — the energy density of a slowly evolving scalar field — may constitute a dynamical form of the homogeneous dark energy in the universe. We review the basic idea in the light of the cosmological constant problem. Cosmological observations or a time variation of fundamental ‘constants’ can distinguish quintessence from a cosmological constant.
TL;DR: In this article, the quasi-isotropic inhomogeneous solution of the Einstein equations near a cosmological singularity in the form of a series expansion in the synchronous system of reference, first found by Lifshitz and Khalatnikov in 1960, is generalized to the case of a two-fluid Cosmological model.
Abstract: The quasi-isotropic inhomogeneous solution of the Einstein equations near a cosmological singularity in the form of a series expansion in the synchronous system of reference, first found by Lifshitz and Khalatnikov in 1960, is generalized to the case of a two-fluid cosmological model. This solution describes non-decreasing modes of adiabatic and isocurvature scalar perturbations and gravitational waves in the regime when deviations of a spacetime metric from the homogeneous isotropic Friedmann–Robertson–Walker (FRW) background are large while locally measurable quantities like Riemann tensor components are still close to their FRW values. The general structure of the perturbation series is presented and the first coefficients of the series expansion for the metric tensor and the fluid energy densities and velocities are calculated explicitly.
TL;DR: In this article, the back-reaction effect of the neutrino field at finite temperature in the background of the static Einstein universe is investigated, and a relationship between the temperature of the universe and its radius is found.
Abstract: The back-reaction effect of the neutrino field at finite temperature in the background of the static Einstein universe is investigated. A relationship between the temperature of the universe and its radius is found. As in previously studied cases of the massless scalar field and the photon field, this relation exhibits a minimum radius below which no self-consistent solution for the Einstein field equation can be found. A maximum temperature marks the transition from a vacuum-dominated state to the radiation-dominated state universe. In light of the results obtained for the scalar, neutrino and photon fields, the role of the back reaction of quantum fields in controlling the value of the cosmological constant is briefly discussed.
TL;DR: In this article, the exact solutions for cosmological models in higher dimensions based on Lyra geometry were obtained for a homogeneous perfect fluid withρ =ρ(t) and p =p(t), where m is a constant.
Abstract: Assuming a homogeneous perfect fluid withρ =ρ(t) andp =p(t), we have obtained exact solutions for cosmological models in higher-dimension based on Lyra geometry. Depending on the form of metric chosen, the model is similar to FRW type. The explicit solutions of the scale factor are found via the assumption of an equation of statep =mρ, where m is a constant. Some astrophysical parameters are also calculated.
TL;DR: In this article, logarithmic terms (which play the role of effective cosmological constant) change the behavior of 4D spherical brane in dS, SdS or Nariai bulk.
Abstract: Thermodynamics of 5d SdS black hole is considered. Thermal fluctuations define the (sub-dominant) logarithmic corrections to black hole entropy and then to Cardy–Verlinde formula and to FRW brane cosmology. We demonstrate that logarithmic terms (which play the role of effective cosmological constant) change the behavior of 4d spherical brane in dS, SdS or Nariai bulk. In particularly, bounce Universe occurs or 4d dS brane expands to its maximum and then shrinks. The entropy bounds are also modified by next-to-leading terms. Out of braneworld context the logarithmic terms may suggest slight modification of standard FRW cosmology.
TL;DR: In this paper, the authors studied the late time evolution of positively curved FRW models with a scalar field which arises in the conformal frame of the R+αR2 theory.
Abstract: We study the late time evolution of positively curved FRW models with a scalar field which arises in the conformal frame of the R+αR2 theory. The resulted three-dimensional dynamical system has two equilibrium solutions corresponding to a de Sitter space and an ever expanding closed universe. We analyze the structure of the first equilibrium with the methods of the center manifold theory and, for the second equilibrium, we apply the normal form theory to obtain a simplified system, which we analyze with special phase plane methods. It is shown that an initially expanding closed FRW space–time avoids recollapse.
TL;DR: In this article, the cosmological dynamics of Randall-Sundrum braneworld type scenarios in which the five-dimensional Weyl tensor has a non-vanishing projection onto the three-brane where matter fields are confined are studied.
Abstract: In this paper we study the cosmological dynamics of Randall-Sundrum braneworld type scenarios in which the five-dimensional Weyl tensor has a non-vanishing projection onto the three-brane where matter fields are confined. Using dynamical systems techniques, we study how the state space of Friedmann-Lemaitre-Robertson-Walker (FLRW) and Bianchi type I scalar field models with an exponential potential is affected by the bulk Weyl tensor, focusing on the differences that appear with respect to standard general relativity and also Randall-Sundrum cosmological scenarios without the Weyl tensor contribution.
TL;DR: In this article, a covariant characterisation of the Penrose plane wave limit is given, where the plane wave profile matrix is defined as the restriction of the null geodesic deviation matrix (curvature tensor) of the original spacetime metric to the null geometry, evaluated in a comoving frame.
Abstract: We give a covariant characterisation of the Penrose plane wave limit: the plane wave profile matrix $A(u)$ is the restriction of the null geodesic deviation matrix (curvature tensor) of the original spacetime metric to the null geodesic, evaluated in a comoving frame. We also consider the Penrose limits of spacetime singularities and show that for a large class of black hole, cosmological and null singularities (of Szekeres-Iyer ``power-law type''), including those of the FRW and Schwarzschild metrics, the result is a singular homogeneous plane wave with profile $A(u)\sim u^{-2}$, the scale invariance of the latter reflecting the power-law behaviour of the singularities.
TL;DR: In this article, the authors proposed two methods of reduction of dynamics to the form of planar Hamiltonian dynamical systems for models with a time dependent equation of state, where the solutions are analyzed on two-dimensional phase space in the variables $(x, \dot{x})$ where $x$ is a function of a scale factor.
Abstract: Methods of dynamical systems have been used to study homogeneous and isotropic cosmological models with a varying speed of light (VSL). We propose two methods of reduction of dynamics to the form of planar Hamiltonian dynamical systems for models with a time dependent equation of state. The solutions are analyzed on two-dimensional phase space in the variables $(x, \dot{x})$ where $x$ is a function of a scale factor $a$. Then we show how the horizon problem may be solved on some evolutional paths. It is shown that the models with negative curvature overcome the horizon and flatness problems. The presented method of reduction can be adopted to the analysis of dynamics of the universe with the general form of the equation of state $p=\gamma(a)\epsilon$. This is demonstrated using as an example the dynamics of VSL models filled with a non-interacting fluid. We demonstrate a new type of evolution near the initial singularity caused by a varying speed of light. The singularity-free oscillating universes are also admitted for positive cosmological constant. We consider a quantum VSL FRW closed model with radiation and show that the highest tunnelling rate occurs for a constant velocity of light if $c(a) \propto a^n$ and $-1 < n \le 0$. It is also proved that the considered class of models is structurally unstable for the case of $n < 0$.