Showing papers on "Friedmann–Lemaître–Robertson–Walker metric published in 1996"
TL;DR: This work finds nonsingular solutions which interpolate between a contracting universe and an expanding universe, and shows that these solutions provide a mechanism for removing the initial conditions problem peculiar to spatially closed FRW cosmologies.
Abstract: We study the cosmological implications of the one-loop terms in string expansion. In particular, we find nonsingular solutions which interpolate between a contracting universe and an expanding universe, and show that these solutions provide a mechanism for removing the initial conditions problem peculiar to spatially closed FRW cosmologies. In addition, we perform numerical calculations to show that the nonsingular cosmologies do not require a careful choice of initial conditions, and estimate the likely magnitude of higher order terms in string expansion.
106 citations
TL;DR: In this paper, the authors show that the recent observational data on Hubble's constant and the age of the universe are consistent with a recently proposed cosmological model based on general relativity with non-vanishing divergence for the energy-momentum tensor.
96 citations
TL;DR: In this paper, the flat inflationary dust universe with matter creation was generalized and its dynamical properties were re-examined and it was shown that the starting point of these models depends critically on a dimensionless parameter closely related to the matter creation rate.
Abstract: The flat inflationary dust universe with matter creation proposed by Prigogine and co-workers is generalized and its dynamical properties are re-examined. It is shown that the starting point of these models depends critically on a dimensionless parameter , closely related to the matter creation rate . For bigger or smaller than unity flat universes can emerge, respectively, either like a big-bang FRW singularity or as a Minkowski spacetime at . The case corresponds to a de Sitter-type solution, a fixed point in the phase diagram of the system, supported by the matter creation process. The curvature effects have also been investigated. The inflating de Sitter is a universal attractor for all expanding solutions regardless of the initial conditions as well as of the curvature parameter.
91 citations
TL;DR: It is shown that the average effect of the inhomogeneity behaves like a negative spatial curvature term and thus has a tendency to extend the age of the universe.
Abstract: We present an averaging scheme in general relativity which allows us to study the effect of local inhomogeneity on the global behavior of the universe. The scheme uses 3+1 splitting of spacetime and introduces Isaacson averaging on the spatial hypersurface to get the averaged geometry. As a result of the averaging, the Friedmann-Robertson-Walker (FWR) geometry is derived in the first-order approximation for a wide class of inhomogeneous nonlinear matter distribution. The deviation from the FRW expansion is derived to the next order in terms of the anisotropic distribution of an effective stress-energy tensor. Using a simple model of inhomogeneity we show that the average effect of the inhomogeneity behaves like a negative spatial curvature term and thus has a tendency to extend the age of the universe. \textcopyright{} 1996 The American Physical Society.
85 citations
TL;DR: Several isotropic, homogeneous cosmological models containing a self-interacting minimally coupled scalar field, a perfect fluid source and a constant constant are solved in this article.
Abstract: Several isotropic, homogeneous cosmological models containing a self-interacting minimally coupled scalar field, a perfect fluid source and cosmological constant are solved. New exact, asymptotically stable solutions with an inflationary regime or a final Friedmann stage are found for some simple, interesting potentials. It is shown that the fluid and the curvature may determine how these models evolve for large times.
74 citations
Posted Content•
TL;DR: In this paper, a brief summary of the present theoretical understanding regarding the value of the cosmological constant is given, and the probability distribution of the observed cosmology constant in theories with a large number of subuniverses (i.e., different expanding regions, or different terms in the wave function of the universe).
Abstract: This is a talk given at the conference ``Critical Dialogues in Cosmology'' at Princeton University, June 24-- 27, 1996. It gives a brief summary of our present theoretical understanding regarding the value of the cosmological constant, and describes how to calculate the probability distribution of the observed cosmological constant in cosmological theories with a large number of subuniverses (i. e., different expanding regions, or different terms in the wave function of the universe) in which this constant takes different values.
43 citations
TL;DR: In this paper, the field equations are reduced to a single first-order ODE in observational variables on the past light cone, completing the observational integration scheme, leading naturally to an explicit exact solution which is locally nearly homogeneous (i.e. FRW), but at larger redshift develops an inhomogeneity.
Abstract: Isotropic inhomogeneous dust universes are analysed via observational coordinates based on the past light cones of the observer's galactic worldline. The field equations are reduced to a single first-order ODE in observational variables on the past light cone, completing the observational integration scheme. This leads naturally to an explicit exact solution which is locally nearly homogeneous (i.e. FRW), but at larger redshift develops an inhomogeneity. New observational characterizations of homogeneity (FRW universes) are also given.
42 citations
01 Nov 1996
TL;DR: In this paper, an extension of the 1+3 decomposition formalism is presented, partially in fully covariant form, and partially on the basis of choice of an arbitrary Minkowskian orthonormal reference frame, the timelike direction of which is aligned with u=c.
Abstract: 1 + 3 “threading” decomposition methods of the pseudo-Riemannian spacetime manifold (M;g) and all itsgeometrical objects and dynamical relations with respect to an invariantly defined preferred timelike referencecongruence u=chave been useful tools in general relativistic cosmological modelling for more than three decades.In this thesis extensions of the 1+3 decomposition formalism are developed, partially in fully covariant form, andpartially on the basis of choice of an arbitrary Minkowskian orthonormal reference frame, the timelike directionof which is aligned with u=c. After introductory remarks, in Chapter 2 first an exposition is given of the general1 + 3 covariant dynamical equations for the fluid matter and Weyl curvature variables, which arise from the Ricciand second Bianchi identities for the Riemann curvature tensor of (M;g;u=c). New evolution equations arethen derived for all spatial derivative terms of geometrical quantities orthogonal to u=c. The latter are used todemonstrate in 1 + 3 covariant terms that the spatial constraints restricting relativistic barotropic perfect fluidspacetime geometries are preserved along the integral curves of u=c. The integrability of a number of differentspecial subcases of interest can easily be derived from this general result.In Chapter 3, 1 + 3 covariant representations of two classes of well-known cosmological models with abarotropic perfect fluid matter source are obtained. These are the families of the locally rotationally symmetric(LRS) and the orthogonally spatially homogeneous (OSH) spacetime geometries, respectively. Subcases arisingfrom either dynamical restrictions or the existence of higher symmetries are systematically discussed. For exam-ple, models of purely “magnetic” Weyl curvature and, in the LRS case, a transparent treatment of tilted spatialhomogeneity can be obtained. The 1 + 3 covariant discussion of the OSH models requires completion.Chapter 4 reviews the complementary 1 + 3 orthonormal frame (ONF) approach and extends it to includethe second Bianchi identities, which provide dynamical relations for the physically interesting Weyl curvaturevariables. Then, possible choices of local coordinates within the 1+3 ONF framework are introduced, taking boththe 1 + 3 threading and the ADM 3 + 1 slicing perspectives.The 1 + 3 ONF method is employed in Chapter 5 to investigate the integrability of the dynamical equationsdescribing “silent” irrotational dust spacetime geometries, for which the “magnetic” part of the Weyl curvature isrequired to vanish. Evidence is obtained that these equations may not be consistent in the generic case, but thatonly either algebraically special or spatially homogeneous classes of solutions may be covered. Furthermore, thischapter uses the extended 1 + 3 ONF dynamical equations to describe LRS models with an imperfect fluid mattersource and contrasts the perfect fluid subcase with the results obtained in Chapter 3.In Chapter 6, a brief detour is taken into considering those classical theories of gravitation in which the La-grangean density of the gravitational field is assumed to be proportional to a general differentiable function f(R)in the Ricci curvature scalar. The generalisations of the relativistic 1 + 3 covariant dynamical equations to thef(R) case are derived and a few examples of applications are commented on.Finally, Chapter 7 investigates in detail features of the dynamical evolution of the cosmological density pa-rameter in anisotropic inflationary models of Bianchi Type–I and Type–V and points out important qualitativechanges as compared to the idealised standard FLRW situation. A related analysis employing the same spacetimegeometries addresses the occurrence of restrictions on the permissible functional form of the inflationary expansionlength scale parameter Sas a consequence of the so-called reality condition for Einstein–Scalar-Field configura-tions. Again, the effect of the (exact) anisotropic perturbations on the FLRW case is thoroughly studied and foundto have significant effects. Both cases can be treated as examples of structural instability.This thesis ends with concluding remarks and an appendix section containing the conventions employed andmathematical relations relevant to derivations given in various chapters.
41 citations
TL;DR: This is the first time that a ST theory is found to be compatible both with primordial nucleosynthesis and solar-system experiments while implying cosmological models significantly different from the standard FRW ones.
Abstract: We present a detailed calculation of the light element production in the framework of Scalar-Tensor (ST) theories of gravitation. The coupling function \omega has been described by an appropriate form which reproduces all the possible asymptotic behaviors at early times of viable ST cosmological models with a monotonic \omega(\Phi). This form gives an exact representation for most of the particular theories proposed in the literature, but also a first-order approximation to many other theories. In most of ST theories, the nucleosynthesis bounds lead to cosmological models which do not significantly differ from the standard FRW ones. We have found however a particular class of ST theories where the expansion rate of the universe during nucleosynthesis can be very different from that found in GR, while the present value of \omega is high enough to ensure compatibility with solar-system experiments. In the framework of this class of theories, right primordial abundances can be obtained for a baryon density range much wider (2.8 \lesssim \eta_{10} \lesssim 58.7) than in GR. Consequently, the usual constraint on the baryon contribution to the density parameter of the universe can be drastically relaxed (0.01 \lesssim \Omega_{b0} \lesssim 1.38) by considering these gravity theories. This is the first time that a ST theory is found to be compatible both with primordial nucleosynthesis and solar-system experiments while implying cosmological models significantly different from the FRW ones.
39 citations
TL;DR: In this paper, the existence of smooth hyperboloidal initial data sets for the vacuum Einstein equations with non-zero cosmological constant was studied and it was shown that there is a correspondence between the solutions of the vacuum constraints with and without cosmologically constant.
Abstract: The existence of smooth hyperboloidal initial data sets for the vacuum Einstein equations with non-zero cosmological constant is studied. Supposing that the trace of the (physical) second fundamental form of the initial hypersurface is constant, there is a correspondence between the solutions of the vacuum constraints with and without cosmological constant, respectively. This enables us to extend the results proved by Andersson and Chrusciel about the smoothness of the initial data with zero cosmological constant to the case .
35 citations
TL;DR: An alternative procedure to construct local supersymmetric quantum cosmological models is presented, performed by introducing a superfield formulation and is applied here to the FRW model, which has the advantage of being more simple than models proposed based on full supergravity.
Abstract: An alternative procedure to construct local supersymmetric quantum cosmological models is presented. This is performed by introducing a superfield formulation and is applied here to the FRW model. It has the advantage of being more simple than models proposed based on full supergravity and gives, by means of this local symmetry procedure, in a direct manner, the corresponding fermionic partners. It also permits the inclusion of matter in a systematic way. \textcopyright{} 1996 The American Physical Society.
TL;DR: In this article, the exact equality of the path integral of the general renormalizable fourth order gravitational action to the PPI of the Einstein action coupled with a massive spin-0 field and a ghost-like field with non-polynomial interactions was shown.
TL;DR: In this article, the Friedmann-Robertson-Walker field equations of a dissipative fluid described by both truncated and non-truncated causal transport equations are analyzed using techniques from dynamical systems theory.
Abstract: The Einstein’s field equations of Friedmann–Robertson–Walker universes filled with a dissipative fluid described by both the truncated and non‐truncated causal transport equations are analyzed using techniques from dynamical systems theory. The equations of state, as well as the phase space, are different from those used in the recent literature. In the de Sitter expansion both the hydrodynamic approximation and the non‐thermalizing condition can be fulfilled simultaneously. For Λ=0 these expansions turn out to be stable provided a certain parameter of the fluid is lower than 1/2. The more general case Λ≳0 is studied in detail as well.
TL;DR: In this article, the geometry of possible wavefronts is analyzed in detail in all three types of FRW models and exact solutions are given which describe gravitational waves propagating into the FRW universes with a fluid with a stiff equation of state.
TL;DR: In this article, the authors consider the question of whether the viscosity/creation concepts describe after all one and the same physical process and conclude that they do not, and show that it is possible to account for the large non-dimensional entropy in the universe (σ∼109) by ignoring viscoity altogether, and allowing for a particle sink (Ψ < 0) of large magnitude being operative during a brief time period.
Abstract: Mechanical and thermodynamic aspects of the early universe are discussed. Adopting an isotropic and imperfect fluid model, we can introduce one single viscosity coefficient, viz. the bulk viscosity ζ. Allowing for particle creation or annihilation there is room for one additional coefficient, viz. the creation rate Ψ. Specializing to the FRW metric we consider the question, discussed in the recent literature, whether the viscosity/creation concepts describe after all one and the same physical process. We conclude that they do not. Thereafter considering the limitations on Ψ set by the second law of thermodynamics, we find that it is possible to account for the large nondimensional entropy in the universe (σ∼109) by ignoring viscosity altogether, and allowing for a particle sink (Ψ<0) of large magnitude being operative during a brief time period. Numerical examples are given.
TL;DR: In this article, the motion of test particles around cosmic strings connected to black holes is analyzed and both the geodesic equations and the Hamilton-Jacobi formalism are used to determine the trajectories.
Abstract: We first analyse the motion of test particles around cosmic strings connected to black holes. We study both the geodesic equations and the Hamilton - Jacobi formalism to determine the trajectories. We have also discussed the FRW cosmological model containing a cosmic string and finally the behaviour of particles in the gravitational field of a domain wall crossed by cosmic strings. In most of the cases we show that the particles cannot be trapped by the cosmic strings.
TL;DR: In this article, the theory of N = 2 supergravity is applied to Bianchi class A models and their canonical formulation is addressed for two cases: when the O(2) internal symmetry is (a) global or (b) local.
Abstract: The theory of N=2 supergravity is applied to Bianchi class A models. Their canonical formulation is addressed for two cases: when the O(2) internal symmetry is (a) global or (b) local. A cosmological constant and mass-like term for the gravitinos are required in the latter but are absent in the former. For the case of global O(2) symmetry, it is shown that the presence of a Maxwell field in the supersymmetry constraints is sufficient to imply a non-conservation of the fermionic number. This effect corresponds to a mixing between different Lorentz invariant fermionic sectors in the wave function of the universe. It is similar to what a cosmological constant term would have caused but considerably different from what occurs in FRW and Bianchi models in N=1 supergravity with scalar fields and fermionic partners. The nonconservation effect is interpreted from the point of view of N=2 supergravity theory. For case (b), we obtain the more general solution of the gauge constraint. Possible quantum physical states are then discussed regarding previous works where Ashtekar variables have been used. These states can be obtained from an N=2 supersymmetric Chern-Simons functional. Some comments concerning the physical validity of the Chern-Simons solution and its transformation into metric representation variables are included.
TL;DR: In this article, the flat inflationary dust universe with matter creation was generalized and its dynamical properties were reexamined, and it was shown that the starting point of these models depends critically on a dimensionless parameter, closely related to the matter creation rate.
Abstract: The flat inflationary dust universe with matter creation proposed by Prigogine and coworkers is generalized and its dynamical properties are reexamined. It is shown that the starting point of these models depends critically on a dimensionless parameter $\Sigma$, closely related to the matter creation rate $\psi$. For $\Sigma$ bigger or smaller than unity flat universes can emerge, respectively, either like a Big-Bang FRW singularity or as a Minkowski space-time at $t=-\infty$. The case $\Sigma=1$ corresponds to a de Sitter-type solution, a fixed point in the phase diagram of the system, supported by the matter creation process. The curvature effects have also been investigated. The inflating de Sitter is a universal attractor for all expanding solutions regardless of the initial conditions as well as of the curvature parameter.
Posted Content•
TL;DR: In this article, the authors give conditions to obtain cosmological asymptotic freedom in scalar-tensor theories of gravity and show that this feature can be achieved in FRW flat spacetimes since they obtain singularity free solutions where the effective gravitational constant is the Newton constant.
Abstract: We give conditions to obtain cosmological asymptotic freedom in scalar-tensor theories of gravity. We show that this feature can be achieved in FRW flat spacetimes since we obtain singularity free solutions where the effective gravitational constant $G_{eff}\rightarrow 0$ for $t\rightarrow -\infty$ and, for some of them, $G_{eff}\rightarrow G_{N}$ for $t\rightarrow\infty$, where $G_{N}$ is the Newton constant.
TL;DR: In this paper, the authors suggest that a natural resolution of this paradox lies with the re-introduction of Einstein's cosmological constant, and that sentiment against this constant fails to take into account its connection with quantum field theory.
Abstract: Recent astronomical observations have re-opened the old paradox that the universe appears to be younger than some of the objects within it. I suggest that a natural resolution of this paradox lies with the re-introduction of Einstein’s cosmological constant, and that sentiment against this constant fails to take into account its connection with quantum field theory.
TL;DR: In this article, the classical tests of cosmology are applied to a simple cosmological model based on the Kantowski-Sachs metric and the results compared with those obtained for the standard model, based on FRW metric.
Abstract: The classical tests of cosmology are applied to a simple cosmological model based on the Kantowski-Sachs metric and the results compared with those obtained for the standard model, based on the FRW metric. It is seen that for a large class of KS models the observations will not be able to distinguish between these models and the standard model. Some comments are also made with respect to the possibility of other tests, those involving the primordial nucleosynthesis and the generation of large scale structure, to constrain the acceptable KS models.
TL;DR: In this paper, it was shown that the spacetime singularity cannot be avoided and that turning points are absent in the decrumpling FRW cosmology model with turning points.
Abstract: It is argued that when the dimension of space is a constant integer the full set of Einstein's field equations has more information than the spatial components of Einstein's equation plus the energy conservation law. Applying the former approach to the decrumpling FRW cosmology recently proposed, it is shown that the spacetime singularity cannot be avoided and that turning points are absent. This result is in contrast to the decrumpling nonsingular spacetime model with turning points previously obtained using the latter approach.
Dissertation•
01 Jan 1996
TL;DR: In this article, the role of shear in inhomogeneous spherically symmetric spacetimes in the field of general relativity is examined, and two classes of nonaccelerating solutions are obtained for the Einstein field equations.
Abstract: This thesis examines the role of shear in inhomogeneous spherically symmetric spacetimes in the field of general relativity. The Einstein field equations are derived for a perfect fluid source in comoving coordinates. By assuming a barotropic equation of state, two classes of nonaccelerating solutions are obtained for the Einstein field equations. The first class has equation of state p = ~It and the second class, with equation of state p = It, generalises the models of Van den Bergh and Wils (1985). For a particular choice of a metric potential a new class of solutions is found which is expressible in terms of elliptic functions of the first and third kind in general. A class of nonexpanding cosmological models is briefly studied. The method of Lie symmetries of differential equations generates a self-similar variable which reduces the field and conservation equations to a system of ordinary differential equations. The behaviour of the gravitational field in this case is governed by a Riccati equation which is solved in general. Another class of solutions is obtained by making an ad hoc choice for one of the gravitational potentials. It is demonstrated that for a stiff fluid a particular case of the generalised Emden-Fowler equation arises. To Shamla Govender For her constant encouragement, infinite patience and unending inspiration.
TL;DR: This paper carries the Hamiltonian treatment of the perturbed FRW cosmology to its full extent by advancing one step further and employing the quantum optics formalism to solve the Schr\"odinger equation and obtain all relevant quantities in this framework.
Abstract: In two previous papers we have undertaken an analysis of the scalar, vectorial, and tensorial perturbations in Friedmann-Robertson-Walker (FRW) universes. A method which involved only observable, gauge-independent perturbed quantities, considered in the framework of quasi-Maxwellian equations of gravitation, was derived. This method made it possible to obtain a Hamiltonian treatment of the perturbed FRW cosmology without the entailed ambiguities regarding gauge choices. Now we carry this Hamiltonian treatment to its full extent by advancing one step further in order to perform the quantization of all three perturbation types. This is done by following the standard semiclassical procedure and employing the quantum optics formalism to solve the Schr\"odinger equation and obtain all relevant quantities in this framework.
TL;DR: For large comoving time, the equation of state "oscillates" around that for cold matter, and it follows that a matter-dominated FRW cosmology is a self-consistent solution to the Einstein equations with string sources.
Abstract: Using the string perturbation series approach, developed by de Vega and S\'anchez, we solve the classical string equations of motion and constraints up to second order in string perturbations around the string center of mass in ordinary nonaccelerated power-expanding FRW universes. For large comoving time we find, for all initial configurations, that the comoving string size goes to zero while the proper string size becomes constant. In the era just after the big bang, on the other hand, we find different kinds of string evolution depending on the string mass and momentum. The evolution of strings just after the big bang essentially depends on the initial string configurations, which are of course unknown. However, by tracing backwards the string evolution towards the big bang, we find that just after the big bang strings can have arbitrary proper size (even zero proper size or infinitely large proper size). The zero proper size strings are understood as a consequence of the scale factor being zero at the big bang, while the very large proper size strings (proper size much larger than the horizon size) are interpreted as results of the high density and high temperature, supporting very long but extremely wiggly strings. We also compute energy and pressure for a gas of strings. For large comoving time, the equation of state "oscillates" around that for cold matter, and it follows that a matter-dominated FRW cosmology is a self-consistent solution to the Einstein equations with string sources.
TL;DR: The dynamics of particle creation in the slowly rotating Robertson-Walker universe is studied by use of the Brans-Dicke theory, and four interesting solutions are obtained.
Abstract: The dynamics of particle creation in the slowly rotating Robertson-Walker universe is studied by use of the Brans-Dicke theory, and four interesting solutions are obtained. Along with the discussion of the nature of the ‘gravitational constant’ and other physical parameters in these model universes, the behaviour of these solutions with respect to Dirac's hypotheses are investigated. Also it is found that the expansion law is determined by the particles created by the expansion itself. Except for the case of a flat universe, the metric rotation as well as the matter rotation is found to have a damping effect on the creation of particles.
TL;DR: Starting out with new deenitions for the gauge-invariant perturbations in energy density and particle number density, evolution equations for these quantities are derived which are manifestly gauge- Invariant.
Abstract: Starting out with new definitions for the gauge-invariant perturbations in energy density and particle number density, evolution equations for these quantities are derived which are manifestly gauge invariant. In the case of vanishing pressure, these equations are identical to Poisson's equation. This fact is in contrast with what is found in earlier treatments based on other definitions.
TL;DR: In this article, a cosmological model is defined as an Einstein-inextendible spacetime, which is a generalization of the spacetime of spacetime spacetimes.
Abstract: In this paper a theory of models of the universe is proposed. We refer to such models ascosmological models, where a cosmological model is defined as an Einstein-inextendible Einstein spacetime. A cosmological model isabsolute if it is a Lorentz-inextendible Einstein spacetime,predictive if it is globally hyperbolic, andnon-predictive if it is nonglobally-hyperbolic. We discuss several features of these models in the study of cosmology. As an example, any compact Einstein spacetime is always a non-predictive absolute cosmological model, whereas a noncompact complete Einstein spacetime is an absolute cosmological model which may be either predictive or non-predictive. We discuss the important role played by maximal Einstein spacetimes. In particular, we examine the possible proper Lorentz-extensions of such spacetimes, and show that a spatially compact maximal Einstein spacetime is exclusively either a predictive cosmological model or a proper sub-spacetime of a non-predictive cosmological model. Provided that the Strong Cosmic Censorship conjecture is true, a generic spatially compact maximal Einstein spacetime must be a predictive cosmological model. It isconjectured that the Strong Cosmic Censorship conjecture isnot true, and converting a vice to a virtue it is argued that the failure of the Strong Cosmic Censorship conjecture would point to what may be general relativity's greatest prediction of all, namely,that general relativity predicts that general relativity cannot predict the entire history of the universe.
TL;DR: In this paper, a general view is given of the Petrov type II metric with a cosmological constant to an accuracy of two complex functions of three variables which are related by four differential equations.
Abstract: A general view is given of the Petrov type II metric with a cosmological constant to an accuracy of two complex functions of three variables which are related by four differential equations. As a consequence the form of the metric is obtained for types III and N which are specified by one complex function satisfying three differential equations. A particular solution is given as an example of an accurate solution of type II with a cosmological constant.