Showing papers on "Friedmann–Lemaître–Robertson–Walker metric published in 2000"

Cosmology of brane models with radion stabilization

Abstract: We analyze the cosmology of the Randall-Sundrum model and that of compact brane models in general in the presence of a radius stabilization mechanism. We find that the expansion of our Universe is generically in agreement with the expected effective four dimensional description. The constraint (which is responsible for the appearance of nonconventional cosmologies in these models) that must be imposed on the matter densities on the two branes in the theory without a stabilized radius is a consequence of requiring a static solution even in the absence of stabilization. Such constraints disappear in the presence of a stablizing potential, and the ordinary Friedmann-Robertson-Walker (FRW) equations are reproduced, with the expansion driven by the sum of the physical values of the energy densities on the two branes and in the bulk. For the case of the Randall-Sundrum model we examine the kinematics of the radion field, and find that corrections to the standard FRW equations are small for temperatures below the weak scale. We find that the radion field has renormalizable and unsuppressed couplings to standard model particles after electroweak symmetry breaking. These couplings may have important implications for collider searches. We comment on the possibility that matter off the TeV brane could serve as a dark matter candidate.

LETTER TO THE EDITOR: Cosmic holography + Cosmic holography

Abstract: A version of holographic principle for the cosmology is proposed, which dictates that the particle entropy within the cosmological apparent horizon should not exceed the gravitational entropy associated with the apparent horizon. It is shown that, in the Friedmann-Robertson-Walker (FRW) cosmology, the open Universe as well as a restricted class of flat cases are compatible with the principle, whereas closed Universe is not. It is also found that inflationary universe after the big-bang is incompatible with the cosmic holography.

On the Holographic Principle in a Radiation Dominated Universe

Abstract: The holographic principle is studied in the context of a $n+1$ dimensional radiation dominated closed Friedman-Robertson-Walker (FRW) universe. The radiation is represented by a conformal field theory with a large central charge. Following recent ideas on holography, it is argued that the entropy density in the early universe is bounded by a multiple of the Hubble constant. The entropy of the CFT is expressed in terms of the energy and the Casimir energy via a universal Cardy formula that is valid for all dimensions. A new purely holographic bound is postulated which restricts the sub-extensive entropy associated with the Casimir energy. Unlike the Hubble bound, the new bound remains valid throughout the cosmological evolution. When the new bound is saturated the Friedman equation exactly coincides with the universal Cardy formula, and the temperature is uniquely fixed in terms of the Hubble parameter and its time-derivative.

An Example of a New Type of Cosmological Solutions of Einstein's Field Equations of Gravitation

Abstract: Kurt Gödel became interested in general relativity theory while he and Einstein were both on staff of the Institute for Advanced Studies in Princeton, and saw a lot of each other (Ref. 25, p.7, Ref. 19, p.157). Gödel’s resultant two technical papers were highly original, and had a major impact. Indeed (see Ref. 38, p.111-112, Refs. 29,8) the beginning of the modern studies of singularities in general relativity in many ways had its seeds in the presentation by Gödel in 1949 [10] of an exact solution of Einstein’s equations for pressure-free matter, which could be thought of as a singularity-free rotating but non-expanding cosmological model. This was one of the papers presented in a special issue of Reviews of Modern Physics dedicated to Einstein on his 70th birthday. Gödel used this space-time as an example helping to clarify the nature of time in general relativity, for it is an exact solution of the Einstein equations in which there are closed timelike lines. He shortly thereafter published a further paper [12] discussing a family of exact solutions of Einstein’s equations representing rotating and

Effective Gauss-Bonnet interaction in Randall-Sundrum compactification

Abstract: The effective gravitational interaction below the Planck scale in the Randall-Sundrum world is shown to be the Gauss-Bonnet term. In this theory we find that there exists another static solution with a positive bulk cosmological constant. Also, there exist solutions for a positive visible sector cosmological constant, which is needed for a later Friedmann-Robertson-Walker universe.

Cosmological perturbations on a magnetized Bianchi I background

Abstract: Motivated by the isotropy of the CMB spectrum, all existing studies of magnetized cosmological perturbations employ FRW backgrounds However, it is important to know the limits of this approximation and the effects one loses by neglecting the anisotropy of the background magnetic field We develop a new treatment, which fully incorporates the anisotropic magnetic effects by allowing for a Bianchi I background universe The anisotropy of the unperturbed model facilitates the closer study of the coupling between magnetism and geometry The latter leads to a curvature stress, which accelerates positively curved perturbed regions and balances the effect of magnetic pressure gradients on matter condensations We argue that the tension carried along the magnetic force lines is the reason behind these magneto-curvature effects For a relatively weak field, we also compare with the results of the almost-FRW approach We find that some of the effects identified by the FRW treatment are in fact direction-dependent, where the key direction is that of the background magnetic field vector Nevertheless, the FRW-based approach to magnetized cosmological perturbations remains an accurate approximation, particularly on large scales, when one looks at the lowest-order magnetic impact on gravitational collapse On small scales, however, the accuracy of the perturbed Friedmann framework may be compromised by extra shear effects

The dynamical system approach to scalar field cosmology

Abstract: A spatially flat FLRW universe (motivated by inflation) is studied; by a dimensional reduction of the dynamical equations of scalar field cosmology, it is demonstrated that a spatially flat universe cannot exhibit chaotic behaviour. The result holds when the source of gravity is a non-minimally coupled scalar field, for any self-interaction potential and for arbitrary values of the coupling constant with the Ricci curvature. The phase space of the dynamical system is studied, and regions inaccessible to the evolution are found. The topology of the forbidden regions, their dependence on the parameters, the fixed points and their stability character, and the asymptotic behaviour of the solutions are studied. New attractors are found, in addition to those known from the minimal coupling case, certain exact solutions are presented and the implications for inflation are discussed. The equation of state is not prescribed a priori , but rather is deduced self-consistently from the field equations.

Microwave background polarization in cosmological models

Abstract: We introduce a new multipole formalism for polarized radiative transfer in general spacetime geometries. The polarization tensor is expanded in terms of coordinate-independent, projected symmetric trace-free (PSTF) tensor-valued multipoles. The PSTF representation allows us to discuss easily the observer dependence of the multipoles of the polarization, and to formulate the exact dynamics of the radiation in convenient 1+3 covariant form. For the case of an almost-Friedmann-Robertson-Walker (FRW) cosmological model we recast the Boltzmann equation for the polarization in to a hierarchy of multipole equations. This allows us to give a rigorous treatment of the generation and propagation of the polarization of the cosmic microwave background in almost-FRW models (with open, closed or flat geometries) without recourse to any harmonic decomposition of the perturbations. We also show how expanding the intensity and polarization multipoles in derivatives of harmonic functions gives a streamlined derivation of the mode-expanded multipole hierarchies. Integral solutions to these hierarchies are provided, and the relation of our formalism to others in the literature is discussed.

Quintessential adjustment of the cosmological constant

Abstract: We construct a time dependent adjustment mechanism for the cosmological ``constant'' which could be at work in a late Friedmann-Robertson-Walker universe dominated by quintessence and matter. It makes use of a Brans-Dicke field that couples to the evolving standard-model vacuum energy density. Our explicit model possesses a stable late-time solution with a fixed ratio of matter and field energy densities. No fine-tuning of model parameters or initial conditions is required.

Einstein's mistake and the cosmological constant

Abstract: A brief history of the cosmological constant in the equations of general relativity is presented. Particular attention is paid to (a) a misunderstanding by Einstein of both its function as a repulsive force and new vacuum state rather than the relativistic analog of an exponential potential cutoff he thought he had introduced and to (b) a common misunderstanding of the function of the cosmological constant.

Undermining the cosmological principle: almost isotropic observations in inhomogeneous cosmologies

Abstract: We challenge the widely held belief that the cosmological principle is an obvious consequence of the observed isotropy of the cosmic microwave background radiation (CMB), combined with the Copernican principle. We perform a detailed analysis of a class of inhomogeneous perfect fluid cosmologies admitting an isotropic radiation field, with a view to assessing their viability as models of the real universe. These spacetimes are distinguished from FLRW universes by the presence of inhomogeneous pressure, which results in an acceleration of the fluid (fundamental observers). We examine their physical, geometrical and observational characteristics for all observer positions in the spacetimes. To this end, we derive exact, analytic expressions for the distance-redshift relations and anisotropies for any observer, and compare their predictions with available observational constraints. As far as the authors are aware, this work represents the first exact analysis of the observational properties of an inhomogeneous cosmological model for all observer positions. Considerable attention is devoted to the anisotropy in the CMB. The difficulty of defining the surface of last scattering in exact, inhomogenous cosmological models is discussed; several alternative practical definitions are presented, and one of these is used to estimate the CMB anisotropy for any model. The isotropy constraints derived from `local' observations (redshift 1) are also considered, qualitatively. A crucial aspect of this work is the application of the Copernican principle: for a specific model to be acceptable we demand that it must be consistent with current observational constraints (especially anisotropy constraints) for all observer locations. The most important results of the paper are presented as exclusion plots in the two-dimensional parameter space of the models. We show that there is a region of parameter space not ruled out by the constraints we consider and containing models that are significantly inhomogeneous. It follows immediately from this that the cosmological principle cannot be assumed to hold on the basis of present observational constraints.

On the varying speed of light in a brane-induced FRW universe

Abstract: We investigate a string/M theoretic realization of the varying speed of light scenario. We consider a (3+1)-dimensional probe-brane universe in the background of a black hole in the bulk formed by a stack of branes, in the spirit of Kiritsis (hep-th/9906206). We generalize the dynamics of the system at hand by including rotation and Hubble damping of the bulk space-time and show that this may lead to a mechanism to stabilize the brane-universe and hence fix the speed of light at late times.

Cosmological perturbations in a Friedmann-Robertson-Walker model with a scalar field and false vacuum decay

Abstract: The unconstrained reduced action corresponding to the dynamics of scalar fluctuations about the Friedmann-Robertson-Walker (FRW) background is derived using Dirac's method of description of singular Lagrangian systems. The results are applied to the so-called negative mode problem in the description of tunneling transitions with gravity. With our special choice of physical variable, the kinetic term of the reduced action has a conventional signature for a wide class of models. In this representation, the existence of a negative mode justifying the false vacuum decay picture turns out to be manifest. We also explain how the present result becomes consistent with the previously proved ``no negative mode (supercritical supercurvature mode) theorem.''

Dynamical Casimir effect and quantum cosmology

Abstract: We apply the background field method and the effective action formalism to describe the four-dimensional dynamical Casimir effect. Our picture corresponds to the consideration of quantum cosmology for an expanding FRW universe (the boundary conditions act as a moving mirror) filled by a quantum massless GUT which is conformally invariant. We consider cases in which the static Casimir energy is attractive and repulsive. Inserting the simplest possible inertial term, we find, in the adiabatic (and semiclassical) approximation, the dynamical evolution of the scale factor and the dynamical Casimir stress analytically and numerically [for SU(2) super Yang-Mills theory]. Alternative kinetic energy terms are explored in the Appendix. (c) 2000 The American Physical Society.

Distance-Redshift in Inhomogeneous $Omega_0=1$ Friedmann-Lemaitre-Robertson-Walker Cosmology

Abstract: Distance--redshift relations are given in terms of associated Legendre functions for partially filled beam observations inspatially flat Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmologies. These models are dynamically pressure-free, flat FLRW on large scales but, due to mass inhomogeneities, differ in their optical properties. The partially filled beam area-redshift equation is a Lame$^{\prime}$ equation for arbitrary FLRW and is shown to simplify to the associated Legendre equation for the spatially flat, i.e. $\Omega_0=1$ case. We fit these new analytic Hubble curves to recent supernovae (SNe) data in an attempt to determine both the mass parameter $\Omega_m$ and the beam filling parameter $ u$. We find that current data are inadequate to limit $ u$. 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.

Distance-Redshift Relations in Inhomogeneous Friedmann-Lemaître-Robertson-Walker Cosmology

Abstract: We give distance-redshift relations in terms of elliptic integrals for three different mass distributions of the Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmology. These models are dynamically pressure-free FLRW cosmology on large scales but, due to mass inhomogeneities, differ in their optical properties. They are the filled-beam model (standard FLRW), the empty-beam model (no mass density exists in the observing beams), and the 2/3 filled-beam model. For special Ωm-ΩΛ values, the elliptic integrals reduce to more familiar functions. These new expressions for distance-redshift significantly reduce computer evaluation times.

Gravitational lensing statistical properties in general FRW cosmologies with dark energy component(s): Analytic results

Abstract: Various astronomical observations have been consistently making a strong case for the existence of a component of dark energy with negative pressure in the universe. It is now necessary to take the dark energy component(s) into account in gravitational lensing statistics and other cosmological tests. By using the comoving distance we derive analytic but simple expressions for the optical depth of multiple image, the expected value of image separation and the probability distribution of image separation caused by an assemble of singular isothermal spheres in general FRW cosmological models with dark energy component(s). We also present the kinematical and dynamical properties of these kinds of cosmological models and calculate the age of the universe and the distance measures, which are often used in classical cosmological tests. In some cases we are able to give formulae that are simpler than those found elsewhere in the literature, which could make the cosmological tests for dark energy component(s) more convenient.

How Do Nonlinear Voids Affect Light Propagation

Abstract: Propagation of light in a clumpy universe is examined. As an inhomogeneous matter distribution, we take a spherical void surrounded by a dust shell, where the “lost mass” in the void is compensated by the shell. We study how the angular-diameter distance behaves when such a structure exists. The angular-diameter distance is calculated by integrating the Raychaudhuri equation including the shear. An explicit expression for the junction condition for the massive thin shell is calculated. We apply these results to a dust shell embedded in a Friedmann universe and determine how the distance-redshift relation is modified compared with that in the purely Friedmann universe. We also study the distribution of distances in a universe filled with voids. We show that the void-filled universe gives a larger distance than the FRW universe by ∼ 5% at z ∼ 1 if the size of the void is ∼ 5% of the Horizon radius.

Renormalization of the nonequilibrium dynamics of fermions in a flat FRW universe

Abstract: We derive the renormalized equations of motion and the renormalized energy-momentum tensor for fermions coupled to a spatially homogeneous scalar field (inflaton) in a flat FRW geometry. The fermion back reaction to the metric and to the inflaton field is formulated in the one-loop approximation. Having determined the infinite counterterms in a $\overline{\mathrm{MS}}$ scheme we formulate the finite terms in a form suitable for numerical computation. We comment on the trace anomaly which is inferred from the standard analysis. We also address the problem of initial singularities and determine the Bogoliubov transformation by which they are removed.

Non-singular cosmological models in string gravity with constant dilaton and second-order curvature corrections

Abstract: We investigate FRW cosmological solutions in the theory of a modulus field coupled to gravity through a Gauss-Bonnet term. The explicit analytical forms of non-singular asymptotics are presented for power-law and exponentially steep modulus coupling functions. We study the influence of a modulus field potential on these asymptotic regimes and find some forms of the potential which do not destroy the non-singular behaviour. In particular, we obtain that exponentially steep coupling functions arising from the string theory do not allow non-singular past asymptotic unless the modulus field potential tends to zero for a modulus field ψ→±∞. Finally, the modification of the chaotic dynamics in the closed FRW universe due to presence of the Gauss-Bonnet term is discussed.

Dynamical properties of the conformally coupled flat FRW model

Abstract: In this paper we study the dynamical behaviour of a simple cosmological model defined by a spatially flat Robertson-Walker geometry, conformally coupled with a massive scalar field. We determine a Lyapunov-like function for the non-linear evolution equations. From this function we prove that all the stationary solutions are unstable. We also show that all initial conditions, different from the stationary points, originate an expanding universe in the asymptotic regime, with a scale parameter $a(t)$ that goes to infinity and the scalar field $\phi (t)$ that goes to zero in an oscillatory way . We also find two asymptotic solutions, valid for sufficiently large values of time. These solutions correspond to a radiation dominated phase and to a matter dominated phase, respectively.

The Covariant Perturbative Approach to Cosmic Microwave Background Anisotropies

Abstract: The Ehlers–Ellis 1+3 formulation of covariant hydrodynamics, when supplemented with covariant radiative transport theory, gives an exact, physically transparent description of the physics of the cosmic microwave background radiation (CMB). Linearisation around a Friedmann–Robertson–Walker (FRW) universe provides a very direct and seamless route through to the linear, gauge-invariant perturbation equations for scalar, vector and tensor modes in an almost-FRW model. In this contribution we review covariant radiative transport theory and its application to the perturbative method for calculating and understanding the anisotropy of the CMB. Particular emphasis is placed on the inclusion of polarization in a fully covariant manner. With this inclusion, the covariant perturbative approach offers a complete description of linearised CMB physics in an almost-FRW universe.

Letter: Spatial Metrics Which are Static in Many Ways

Abstract: We consider Riemannian 3-metrics which can form the spatial part of vacuum solutions of the Einstein equations, possibly with a cosmological constant, in more than one way (in a sense made precise). The locally rotationally symmetric (LRS) Kasner metric gives the simplest example, and we find that the resulting space-time metrics are always of Petrov type D.

Cosmological Models with Bulk Viscosity in the Presence of Adiabatic Matter Creation and with Variable G, c, and Λ

Abstract: Some properties of cosmological models with a time variable bulk viscous coefficient in the presence of adiabatic matter creation and variable G, c, Λ are investigated in the framework of a specifically flat FRW line element. We trivially find a set of solutions through Dimensional Analysis. In all the studied cases it is found that the behaviour of these "constants" is inversely proportional to the cosmic time. It is found that with the solution obtained our model verifies the principles of general covariance and Lorentz invariance. Finally we emphasize that the envisaged models are free of the horizon and entropy problem.

Chaos in Closed Isotropic Cosmological Models with Steep Scalar Field Potential

Abstract: The dynamics of closed scalar field FRW cosmological models is studied for several types of exponentially and more than exponentially steep potentials. The parameters of scalar field potentials which allow a chaotic behaviour are found from numerical investigations. It is argued that analytical studies of equation of motion at the Euclidean boundary can provide an important information about the properties of chaotic dynamics. Several types of transition from chaotic to regular dynamics are described.

A no-chaos theorem for non-minimally coupled scalar field cosmology and a new cosmogenesis scenario

Abstract: A general dynamical system approach to classical self-consistent scalar field cosmology is presented in the framework of spatially flat FLRW space–times, for arbitrary potentials and arbitrary non-minimal coupling. We show that these universes cannot undergo chaotic behaviors, thus suggesting a possible new role of inflation in cosmology. An unexpectedly involved topology of the phase-portrait of the cosmological dynamics is exhibited: Dynamically forbidden regions, playing a crucial dynamical role, appear. A new exact critical solution, a heteroclinic orbit, connects two de Sitter inflationary regimes. We suggest a novel intriguing semiclassical cosmogenesis scenario in which the quantized scalar field could tunnel through the classically forbidden region, from the Minkowski space–time towards the nearest classically allowed solution: The critical one.