Showing papers on "Friedmann–Lemaître–Robertson–Walker metric published in 2002"
TL;DR: Evidence for quantum stability of the cosmological constant is illustrated in a number of examples including bulk descriptions in terms of delocalized degrees of freedom, boundary screen descriptions on stretched horizons, and nonsupersymmetric conformal field theories as dual descriptions of anti-de Sitter space.
Abstract: Gravitational holography is argued to render the cosmological constant stable against divergent quantum corrections, thus providing a technically natural solution to the cosmological constant problem Evidence for quantum stability of the cosmological constant is illustrated in a number of examples including bulk descriptions in terms of delocalized degrees of freedom, boundary screen descriptions on stretched horizons, and nonsupersymmetric conformal field theories as dual descriptions of anti--de Sitter space In an expanding universe, holographic quantum contributions to the stress-energy tensor are argued to be at most of order the energy density of the dominant matter component
339 citations
TL;DR: In this paper, the authors consider the evolution of FRW cosmological models and linear perturbations of tachyon matter rolling towards a minimum of its potential, and show that this linear stage changes to a strongly nonlinear one very early, so that the usual quasi-linear stage observed at sufficiently large scales in the present Universe may not be realized in the absence of the usual particle-like cold dark matter.
315 citations
TL;DR: In this article, Friedmann-Robertson-Walker (FRW) brane equations are considered from the point of view of their representation in the form similar to two-dimensional CFT entropy, the Cardy-Verlinde (CV) formula.
Abstract: In the first part of this work we review the equations of motion for the brane presented in Friedmann–Robertson–Walker (FRW) form, when the bulk is five-dimensional (A)dS Black Hole. The spacelike (timelike) FRW brane equations are considered from the point of view of their representation in the form similar to two-dimensional CFT entropy, the so-called Cardy–Verlinde (CV) formula. The following five-dimensional gravities are reviewed: Einstein, Einstein–Maxwell and Einstein with brane quantum corrections. The second part of the work is devoted to the study of FRW brane equations and their representation in CV form, brane induced matter and brane cosmology in Einstein–Gauss–Bonnet (GB) gravity. In particular, we focus on the inflationary brane cosmology. The energy conditions for brane matter are also analyzed. We show that for some values of GB coupling constant (bulk is AdS BH) the brane matter is not CFT. Its energy density and pressure are not always positive. The appearance of logarithmic corrections in brane cosmology is discussed.
191 citations
Posted Content•
TL;DR: A cosmological model with an exotic fluid is investigated in this paper, and it is shown that the equation of state of this modified Chaplygin gas can describe the current accelerated expansion of the universe.
Abstract: A cosmological model with an exotic fluid is investigated. We show that the equation of state of this ``modified Chaplygin'' gas can describe the current accelerated expansion of the universe. We then reexpress it as FRW cosmological model containing a scalar field $\phi$ and find its self--interacting potential. Moreover motivated by recent works of Sen [sen1, sen2] and Padmanbhan [pad] on tachyon field theory, a map for this exotic fluid as a normal scalar field $\phi$ with Lagrangian ${\cal L}_{\phi} = \frac{\dot{\phi}^2}{2} - U (\phi)$ to the tachyonic field $T$ with Lagrangian ${\cal L}_{T} = - V(T) \sqrt{1 - \dot{T}^2}$ is obtained.
167 citations
TL;DR: Higher-dimensional braneworld models which contain both bulk and brane curvature terms in the action admit cosmological singularities of rather unusual form and nature as mentioned in this paper, which can occur both during the contracting as well as the expanding phase.
Abstract: Higher-dimensional braneworld models which contain both bulk and brane curvature terms in the action admit cosmological singularities of rather unusual form and nature. These 'quiescent' singularities, which can occur both during the contracting as well as the expanding phase, are characterized by the fact that while the matter density and Hubble parameter remain finite, all higher derivatives of the scale factor ( etc) diverge as the cosmological singularity is approached. The singularities are the result of the embedding of the (3 + 1)-dimensional brane in the bulk and can exist even in an empty homogeneous and isotropic (FRW) universe. The possibility that the present universe may expand into a singular state is discussed.
157 citations
TL;DR: In this paper, a mathematical toy model is proposed for the analytical nonsingular extension of FRW solutions, which is obtained for a class of nonlinear generalizations of the electromagnetic theory.
Abstract: Maxwell electrodynamics, considered as a source of the classical Einstein field equations, leads to the singular isotropic Friedmann solutions. We show that this singular behavior does not occur for a class of nonlinear generalizations of the electromagnetic theory. A mathematical toy model is proposed for which the analytical nonsingular extension of FRW solutions is obtained.
152 citations
TL;DR: In this paper, a static Friedmann brane with zero cosmological constant and 3-curvature, but satisfying p > 0 and p + 3p > 0, is shown to have a different relation between the density, pressure, curvature and cosmology constant than in the case of the general relativistic Einstein static universe.
Abstract: A static Friedmann brane in a five-dimensional bulk (Randall-Sundrum-type scenario) can have a very different relation between the density, pressure, curvature and cosmological constant than in the case of the general relativistic Einstein static universe. In particular, static Friedmann branes with zero cosmological constant and 3-curvature, but satisfying p > 0 and p + 3p > 0, are possible. Furthermore, we find static Friedmann branes in a bulk that satisfies the Einstein equations but is not Schwarzschild-anti-de Sitter or its specializations. In the models with negative bulk cosmological constant, a positive brane tension leads to negative density and 3-curvature.
87 citations
TL;DR: In this article, the energy density measured by an observer living on a brane embedded in a charged black-hole spacetime was calculated using the Weyl tensor, and it was shown that this tensor gives rise to nonlinear terms in the energy densities and pressure in the FRW equations for the brane.
Abstract: We use a new, exact approach in calculating the energy density measured by an observer living on a brane embedded in a charged black-hole spacetime. We find that the bulk Weyl tensor gives rise to nonlinear terms in the energy density and pressure in the FRW equations for the brane. Remarkably, these take exactly the same form as the 'unconventional' terms found in the cosmology of branes embedded in pure AdS, with extra matter living on the brane. Black-hole-driven cosmologies have the benefit that there is no ambiguity in splitting the braneworld energy momentum into tension and additional matter. We propose a new, enlarged relationship between the two descriptions of braneworld cosmology. We also study the exact thermodynamics of the field theory and present a generalized Cardy–Verlinde formula in this set-up.
69 citations
TL;DR: In this article, the authors consider cosmological consequences of a conformal-invariant formulation of Einstein's General Relativity where instead of the scale factor of the spatial metrics in the action functional, a massless scalar field occurs which scales all masses including the Planck mass.
65 citations
TL;DR: For the case of arbitrary hydrodynamical matter, the authors generalize the quasi-isotropic solution of Einstein equations near the cosmological singularity, found by Lifshitz and Khalatnikov in 1960, to the special case of the radiation-dominated universe.
Abstract: For the case of arbitrary hydrodynamical matter, we generalize the quasi-isotropic solution of Einstein equations near the cosmological singularity, found by Lifshitz and Khalatnikov in 1960 for the case of the radiation-dominated universe. It is shown that this solution always exists, but dependence of terms in the quasi-isotropic expansion acquires a more complicated form.
52 citations
Abstract: We examine the status of various dark energy models in light of the recently observed SN 1997ff at z 1.7. The modified data still fit a pure cosmological constant A or a quintessence with an equation of state similar tothat of A. The kinematical A models, Λ ∼ S - 2 and Λ ∼ H 2 , also fit the data reasonably well and require less dark energy density (hence more matter energy density) than is required by the constant A model. However, the model Λ ∼ S - 2 with low energy density becomes unphysical as it cannot accommodate higher redshift objects. We also examine an alternative explanation of the data, namely the absorption by the intervening whisker-like dust, and find that the quasi-steady state (QSS) model and the Friedmann-Robertson-Walker (FRW) model Ω m 0 = 0.33 without any dark energy also fit the data reasonably well. We notice that the addition of SN 1997ff to the old data has worsened the fit to most of the models, except a closed FRW model with a constant A and a closed quintessence model with ω Φ = -0.82, and the models have started departing from each other as we go above z = 1. However, to make a clear discrimination possible, a few more supernovae with z > 1 are required. We have also calculated the age of the Universe in these models and find that, in the models with a constant A, the expansion age is uncomfortably close to the age of the globular clusters. Quintessence models show even lower age. The kinematical A models are, however, interesting in this connection (especially the model A ∼ H 2 ), as they give a remarkably large age of the Universe.
TL;DR: Higher-dimensional braneworld models which contain both bulk and brane curvature terms in the action admit cosmological singularities of rather unusual form and nature as discussed by the authors, which can occur both during the contracting as well as the expanding phase.
Abstract: Higher-dimensional braneworld models which contain both bulk and brane curvature terms in the action admit cosmological singularities of rather unusual form and nature. These `quiescent' singularities, which can occur both during the contracting as well as the expanding phase, are characterised by the fact that while the matter density and Hubble parameter remain finite, all higher derivatives of the scale factor ($\stackrel{..}{a}$, $\stackrel{...}{a}$ etc.) diverge as the cosmological singularity is approached. The singularities are the result of the embedding of the (3+1)-dimensional brane in the bulk and can exist even in an empty homogeneous and isotropic (FRW) universe. The possibility that the present universe may expand into a singular state is discussed.
TL;DR: In this paper, the authors generalize the results of hep-th/0008140 to the case of the (n+1)-dimensional closed FRW universe satisfying a general equation of state of the form p = wρ.
TL;DR: In this article, the energy density measured by an observer living on a brane embedded in a charged black hole spacetime was calculated using the Weyl tensor, and it was shown that this tensor gives rise to non-linear terms in the FRW equations for the brane.
Abstract: We use a new, exact approach in calculating the energy density measured by an observer living on a brane embedded in a charged black hole spacetime. We find that the bulk Weyl tensor gives rise to non-linear terms in the energy density and pressure in the FRW equations for the brane. Remarkably, these take exactly the same form as the ``unconventional'' terms found in the cosmology of branes embedded in pure AdS, with extra matter living on the brane. Black hole driven cosmologies have the benefit that there is no ambiguity in splitting the braneword energy momentum into tension and additional matter. We propose a new, enlarged relationship between the two descriptions of braneworld cosmology. We also study the exact thermodynamics of the field theory and present a generalised Cardy-Verlinde formula in this set up.
TL;DR: In this article, an exact solution of the Friedmann-Robertson field equation with the appropriate matter density for generic values of the cosmological constant Λ and curvature constant K was derived and a formal expression for the Hubble constant was 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 spacetime line elements with a non-zero 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 spacetime 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 Λ and curvature constant K. A formal expression for the Hubble constant is derived. The cosmological implications of the resulting nonlinear solutions are systematically investigated. Two particularly interesting solutions: (i) the case of a flat universe K = 0, Λ ≠ 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 nonlinear solutions of general relativity are expressed in terms of theta functions associated with Riemann-surfaces is discussed.
TL;DR: In this paper, the group of symmetry transformations under which the Einstein equations for the spatially flat Friedmann-Robertson-Walker universe are form invariant was studied. But the symmetry transformation rule for the spectrum and spectral index of the curvature perturbations was not considered.
Abstract: We find the group of symmetry transformations under which the Einstein equations for the spatially flat Friedmann-Robertson-Walker universe are form invariant. They relate the energy density and the pressure of the fluid to the expansion rate. We show that inflation can be obtained from nonaccelerated scenarios by a symmetry transformation. We derive the transformation rule for the spectrum and spectral index of the curvature perturbations. Finally, the group is extended to investigate inflation in the anisotropic Bianchi type-I spacetime and the brane-world cosmology.
TL;DR: In this article, the cosmological evolution equations of de Sitter braneworlds sandwiched in between two n -dimensional AdS-Schwarzschild spacetimes are examined.
TL;DR: In this paper, the field equations of the Lagrangian theory were derived from a cosmological model described by the FRW metric, and the resulting field equations were put into the form of General Relativity with cosmology constant and coupling constant that are curvature depending.
Abstract: In the present work we consider those theories that are obtained from a Lagrangian density ℒ
T
(R) = f(R)√{-g} + ℒ
M
, that depends on the curvature scalar and a matter Lagrangian that does not depend on the connection, and apply Palatini's method to obtain the field equations. We start with a brief discussion of the field equations of the theory and apply them to a cosmological model described by the FRW metric. Then, we introduce an auxiliary metric to put the resultant equations into the form of GR with cosmological constant and coupling constant that are curvature depending. We show that we reproduce known results for the quadratic case. We find relations among the present values of the cosmological parameters q
0, H
0,
$$\mathop {(G/G)}\limits^ \circ _0$$
and
$$\mathop {(G/G)}\limits^{ \circ \circ } _0 $$
. Next we use a simple perturbation scheme to find the departure in angular diameter distance with respect to General Relativity. Finally, we use the observational data to estimate the order of magnitude of what is essentially the departure of f(R) from linearity. The bound that we find for f″ (0) is so huge that permit almost any f(R). This is in the nature of things: the effect of higher order terms in f(R) are strongly suppressed by power of Planck's time 8πG
0. In order to improve these bounds more research on mathematical aspects of these theories and experimental consequences is necessary.
Posted Content•
11 Apr 2002
TL;DR: Higher-dimensional braneworld models which contain both bulk and brane curvature terms in the action admit cosmological singularities of rather unusual form and nature as mentioned in this paper, which can occur both during the contracting as well as the expanding phase.
Abstract: Higher-dimensional braneworld models which contain both bulk and brane curvature terms in the action admit cosmological singularities of rather unusual form and nature. These `quiescent' singularities, which can occur both during the contracting as well as the expanding phase, are characterised by the fact that while the matter density and Hubble parameter remain finite, all higher derivatives of the scale factor ($\stackrel{..}{a}$, $\stackrel{...}{a}$ etc.) diverge as the cosmological singularity is approached. The singularities are the result of the embedding of the (3+1)-dimensional brane in the bulk and can exist even in an empty homogeneous and isotropic (FRW) universe. The possibility that the present universe may expand into a singular state is discussed.
TL;DR: In this paper, three solutions of the Brans-Dicke theory with a self-interacting quartic potential and perfect fluid distribution are presented for a spatially flat FRW geometry.
Abstract: Three solutions of the Brans-Dicke theory with a self-interacting quartic potential and perfect fluid distribution are presented for a spatially flat FRW geometry. The physical behavior is consistent with the recent cosmological scenario favored by supernova type-Ia observations, indicating an accelerated expansion of the Universe.
Journal Article•
TL;DR: In this article, the authors studied the physics of a general (n − 2)-brane of arbitrary tension, embedded in some n-dimensional bulk, and showed that the geometry on a brane near the AdS boundary is just that of a radiation dominated universe.
Abstract: This thesis is devoted to studying two important aspects of braneworld physics: their cosmology and their holography. We examine the Einstein equations induced on a general (n - 2)-brane of arbitrary tension, embedded in some n-dimensional bulk. The brane energy-momentum tensor enters these equations both linearly and quadratically. From the point of view of a homogeneous and isotropic brane we see quadratic deviations from the FRW equations of the standard cosmology. There is also a contribution from a bulk Weyl tensor. We study this in detail when the bulk is AdS-Schwarzschild or Reissner-Nordstrom AdS. This contribution can be understood holographically. For the AdS-Schwarzschild case, we show that the geometry on a brane near the AdS boundary is just that of a radiation dominated FRW universe. The radiation comes from a field theory that is dual to the AdS bulk. We also develop a new approach which allows us to consider branes that are not near the AdS boundary. This time the dual field theory contributes quadratic energy density/pressure terms to the FRW equations. Remarkably, these take exactly the same form as for additional matter placed on the brane by hand, with no bulk Weyl tensor. We also derive the general equations of motion for a braneworld containing a domain wall. For the critical brane, the induced geometry is identical to that of a vacuum domain wall in (n-l)-dimensional Einstein gravity. We develop the tools to construct a nested Randall-Sundrum scenario whereby we have a "critical" domain wall living on an anti-de Sitter brane. We also show how to construct instantons on the brane, and calculate the probability of false vacuum decay.
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 of 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.
TL;DR: In this article, the authors consider the evolution of FRW cosmological models and linear perturbations of tachyon matter rolling towards a minimum of its potential, and show that this linear stage changes to a strongly non-linear one very early, so that the usual quasi-linear stage observed at sufficiently large scales in the present Universe may not be realized in the absence of the usual particle-like cold dark matter.
Abstract: We consider the evolution of FRW cosmological models and linear perturbations of tachyon matter rolling towards a minimum of its potential. The tachyon coupled to gravity is described by an effective 4d field theory of string theory tachyon. In the model where a tachyon potential $V(T)$ has a quadratic minimum at finite value of the tachyon field $T_0$ and $V(T_0)=0$, the tachyon condensate oscillates around its minimum with a decreasing amplitude. It is shown that its effective equation of state is $p=-\epsilon/3$. However, linear inhomogeneous tachyon fluctuations coupled to the oscillating background condensate are exponentially unstable due to the effect of parametric resonance. In another interesting model, where tachyon potential exponentially approaches zero at infinity of $T$, rolling tachyon condensate in an expanding universe behaves as pressureless fluid. Its linear fluctuations coupled with small metric perturbations evolve similar to these in the pressureless fluid. However, this linear stage changes to a strongly non-linear one very early, so that the usual quasi-linear stage observed at sufficiently large scales in the present Universe may not be realized in the absence of the usual particle-like cold dark matter.
TL;DR: In this paper, the Friedmann-Robertson-Walker (FRW) brane equations are considered from the point of view of their representation in the form similar to two-dimensional CFT entropy, so-called Cardy-Verlinde (CV) formula.
Abstract: In the first part of this work we review the equations of motion for the brane presented in Friedmann-Robertson-Walker (FRW) form, when bulk is five-dimensional (A)dS Black Hole. The spacelike (timelike) FRW brane equations are considered from the point of view of their representation in the form similar to two-dimensional CFT entropy, so-called Cardy-Verlinde (CV) formula. The following five-dimensional gravities are reviewed: Einstein, Einstein-Maxwell and Einstein with brane quantum corrections. The second part of the work is devoted to study FRW brane equations and their representation in CV form, brane induced matter and brane cosmology in Einstein-Gauss-Bonnet (GB) gravity. In particular, we focus on the inflationary brane cosmology. The energy conditions for brane matter are also analyzed. We show that for some values of GB coupling constant (bulk is AdS BH) the brane matter is not CFT. Its energy density and pressure are not always positive.
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 are 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 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 paper, 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.
20 Feb 2002
TL;DR: In this article, the numerical value of the cosmological constant is calculated using a recently suggested cosmology model and found to be Λ=2.036×10−35 s−2.
Abstract: The numerical value of the cosmological constant is calculated using a recently suggested cosmological model and found to be Λ=2.036×10−35 s−2. This value of Λ is in excellent agreement with the measurements recently obtained by the High-Z Supernova Team and the Supernova Cosmology Project.
TL;DR: In this paper, the evolution of perturbations on a moving probe D3-brane coupled to a 4-form field in an AdS$_5$-Schwarzschild bulk was studied.
Abstract: We study the evolution of perturbations on a moving probe D3-brane coupled to a 4-form field in an AdS$_5$-Schwarzschild bulk. The unperturbed dynamics are parametrised by a conserved energy $E$ and lead to Friedmann-Robertson-Walker `mirage' cosmology on the brane with scale factor $a(\tau)$. The fluctuations about the unperturbed worldsheet are then described by a scalar field $\phi(\tau,\vec{x})$. We derive an equation of motion for $\phi$, and find that in certain regimes of $a$ the effective mass squared is negative. On an expanding BPS brane with E=0 superhorizon modes grow as $a^4$ whilst subhorizon modes are stable. When the brane contracts, all modes grow. We also briefly discuss the case when $E>0$, BPS anti-branes as well as non-BPS branes. Finally, the perturbed brane embedding gives rise to scalar perturbations in the FRW universe. We show that $\phi$ is proportional to the gauge invariant Bardeen potentials on the brane.
TL;DR: In this paper, a cosmological model with perfect fluid and self-interacting quintessence field is considered in the framework of the spatially flat Friedmann-Robertson-Walker (FRW) geometry.
Abstract: A cosmological model with perfect fluid and self-interacting quintessence field is considered in the framework of the spatially flat Friedmann–Robertson–Walker (FRW) geometry. By assuming that all physical quantities depend on the volume scale factor of the Universe, the general solution of the gravitational field equations can be expressed in an exact parametric form, with the volume taken as the parameter, and with the quintessence field as a free parameter. With an appropriate choice of the scalar field a class of exact parametric solutions is obtained, with an exponential type scalar field potential fixed via the gravitational field equations. The general physical behavior of the model is consistent with the recent cosmological scenario favored by supernova type Ia observations, indicating an accelerated expansion of the Universe.
TL;DR: In this paper, the authors investigate the back reaction of cosmological perturbations on the evolution of the universe using the renormalization group method and derive the evolution equation for the effective scale factor which includes back reaction due to inhomogeneities of the Universe.
Abstract: We investigate the back reaction of cosmological perturbations on the evolution of the Universe using the renormalization group method. Starting from the second order perturbed Einstein's equation, we renormalize a scale factor of the Universe and derive the evolution equation for the effective scale factor which includes back reaction due to inhomogeneities of the Universe. The resulting equation has the same form as the standard Friedman-Robertson-Walker equation with the effective energy density and pressure which represent the back reaction effect.