Showing papers on "Friedmann–Lemaître–Robertson–Walker metric published in 1988"

On the Degree of Generality of Inflation in Friedmann Cosmological Models with a Massive Scalar Field

Abstract: Friedmann cosmological models with a massive minimally coupled scalar field are investigated by numerical methods. It is indicated that the majority of the solutions undergo the inflationary stage in flat and open models. In a closed model the ratio of the number of solutions without adequate inflation to the number of the total solutions are obtained numerically. I ) One oL the questions concerning this model is a generality of the inflationary solutions. We investigate this problem studying classical solutions of a homogeneous model with a massive scalar field. Among all solutions in this model some are inflationary and the others are not. If it is found that a fraction of the inflationary solutions (the ratio of the number of the inflationary solutions to the total number of solutions in some measure) is large enough, it becomes very reasonable to take such solutions for the model of our universe. For the flat Friedmann-Robertson-Walker (FRW) models, this problem was treated in the paper by Belinsky, Grishchuk, Zel'dovich and Khalatnikov. 2 ) Analyz­ ing the behavior of trajectories in the phase space of this dynamical system, they have shown that a fraction of the non-inflationary solution is the order of m/mp, mp and m being the Planck mass and a mass of the scalar field respectively. In fact, in order for the density fluctuation generated during the inflation to be small, the ratio m/mp is restricted to be smalI"such as m/mp~ 1O-5~ 10- 6 • 4 ) Therefore, at least for the flat FRW model, the overwhelming majority of the solutions are found to be inflationary. N ow, as for the open and closed FRW models, the problem was treated by the analytic method in the paper by Belinsky and Khalatnikov. 5 ) For the open model, the result is not so different from the flat model. However, for the closed model, the result is quite different: Due to the curvature effect, the expansion tends to turn into collapse. In the previous work, it was shown that the fra<;:tion of the non-inflationary solution is about 1/4 in some measure. In this paper, we investigate the evolution of the universe.modelsby an.explicit numerical computation of the phase space trajectories and have confirmed the.results of the previous work. The phase space for open and closed models is three dimen­ sional and the trajectories start from the two dimensional surface called "Quantum

Perfect-fluid cosmologies with extra dimensions.

Abstract: We give an analysis of the solutions of the n-dimensional vacuum Einstein equations with a metric in the form of a direct sum of a Friedmann-Robertson-Walker (FRW) metric and a Kasner-type Euclidean metric. The solutions are interpreted as four-dimensional perfect-fluid cosmological FRW models, using the simple ansatz proposed by Ib\'an\ifmmode \tilde{}\else \~{}\fi{}ez and Verdaguer. We first obtain the general solution for flat models. These are perfect-fluid solutions that can be made compatible with contraction of all the extra dimensions. The general compatibility of the field equations is then discussed. It is found that for ng5 both open and closed models admit a range of perfect-fluid solutions whose qualitative behavior is analyzed.

Inhomogeneous two-fluid cosmologies

Abstract: A new class of expanding cosmological solutions is derived. The matter content of these models is a mixture of two interacting simple fluids: the first one, homogeneous and isotropic with equation of statep = (γ-1)ρ, the dynamics of which is given by the FRW equation and the second one an inhomogenous dust. The limiting case of two dusts corresponds to the Szekeres' universes of class II. A large subclass of the models evolve to a FRW phase for all physically meaningful values of the polytropic indexγ and the curvature parameterk. A gauge condition, under which the metric is invariant, is shown to exist for k≠0. In particular, it explains why the parabolic model is a peculiar solution in the class found by Szekeres.

Cosmic strings in an expanding spacetime.

Abstract: We investigate the stability of a static, infinitely long and straight vacuum string solution under inhomogeneous axisymmetric time-dependent perturbations. We find it to be perturbatively stable. We further extend our work by finding a string solutions in an expanding Universe. The back reaction of the string on the gravitational field has been ignored. The background is assumed to be a Friedman-Robertson-Walker (FRW) cosmology. By numerically integrating the field equations in a radiation and matter dominated models, we discover oscillatory solutions. The possible damping of these oscillations is discussed. For late times the solution becomes identical to the static one studied in the first part of the paper. 19 refs., 8 figs.

Open and closed Robertson-Walker-type Lyttleton-Bondi universes

Abstract: The exterior field of the Robertson-Walker-type metric in the Lyttleton-Bondi universe is studied and exact solutions are obtained for closed and open universes. Only the flat space solution was previously known.

Quantum effects in homogeneous multidimensional cosmologies.

Abstract: In the present paper we determine quantum distribution functions for a wide class of multidimensional cosmological models. The exact formulas for quantum distribution functions are given and their universal character at high and low temperatures shown. The obtained formulas provide us with the possibility to investigate the metric back reaction and to discuss the dimensional reduction problem. The assumption of the low-temperature approximation gives us the possibility to discuss the dynamics by using the methods of dynamical systems. Stable solutions, within the class FRW x S/sup 3/ x S/sup 3/ models, where FRW denotes Friedmann, Robertson and Walker, are discussed, and it is shown that only a zero-measure set of trajectories in the phase space leads to a solution with a static microspace. This analysis shows that, insofar as quantum effects lead to solutions with a static microspace, these solutions are unstable.

Thermodynamics and two-fluid cosmological models

Abstract: Exact solutions of Einstein's field equations and the laws of thermodynamics are presented in which both a comoving radiative perfect fluid (modelling the cosmic microwave background) and a non-comoving imperfect fluid (modelling the observed material content of the Universe) act as the source of the gravitational field as represented by the flat FRW line element. The tilting velocity of the imperfect fluid is associated with the peculiar velocity of our local cluster of galaxies relative to the cosmic microwave background. In these relativistic two-fluid cosmological models the temperatures of the radiation and matter fields are equal until hydrogen recombines at 4000 K, after which time thermal contact between the two fluids is broken. The models presented are physically acceptable cosmologies that are shown to give rise to numerical predictions consistent with current observations.

Exact solutions of the Einstein field equations for a topologically nontrivial metric

Abstract: Two exact solutions of the Einstein field equations are presented, each having a Finkelstein–Misner kink. The first of these has a perfect fluid interior and a vacuum exterior. The equation of state is ρ=−p=C (where C is a constant), which is the same as that found in inflationary models.

Bianchi type VI0 space‐times with perfect fluid source

Abstract: An analytic solution to Einstein’s field equations is presented for the Bianchi type VI0 class of models. The energy‐momentum tensor is of the perfect fluid type. The solution corresponds to a locally rotationally symmetric and expanding cosmological universe which would give an essentially empty universe for large time. Some kinematical properties of the solution are discussed.

Slowly rotating cosmological viscous fluid Universe

Abstract: The perturbation by a spherical rotating shell is investigated in a homogeneous and isotropic cosmological model of viscous fluid distribution to first order in angular velocity ω(r, t) of matter and the metric rotation function Ω(r, t) which is uniform and non-uniform the exact solutions for Ω(r, t) are obtained for all cosmological models. The physical properties of these solutions are discussed.

Slow rotational perturbations of Robertson-Walker universes

Abstract: A slow rotation perturbation of Robertson-Walker universes filled with perfect fluid has been investigated. It is found that the unit-four vector of perfect fluid hasno angular velocity in the perturbed cosmological models. The slow rotation which is related to the dragging of the local inertial frames, is compatible only with the cases of positive and negative curvatures of the cosmological universe. The intrinsic velocity vector field of the Universe isexpanding as well asshearing.

The Vaidya–Patel solution with Robertson–Walker metric as a rotating inflationary scenario

Abstract: The Vaidya–Patel solution of a rotating homogeneous fluid in the presence of a Maxwellian source‐free electromagnetic field is interpretated as an inflationary scenario with a gauge field with local U(1) symmetry, a vacuum energy, and a rotating perfect fluid. An explicit solution is found to be expressible in terms of known solutions representing the radiation filled Robertson–Walker universe with a cosmological term. In the case that the rotating fluid is radiation, the discussion of the model is considerably simplified. How the time scale of transition into a pseudo‐de Sitter stage, as observed by an observer following the rotating fluid, is affected by vorticity is also studied.

Massive scalar field interacting with viscous fluid distribution in cosmological models

Abstract: The study of Einstein's field equations describing Robertson-Walker cosmological models with massive scalar field and viscous fluid representing the matter has been made. The problem has been investigated with and without the source density in the wave equation. Corresponding exact solutions of the field equations have been obtained under different physical equations of state: namely, (i) dust distribution, (ii) Zeldovich fluid distribution, (iii) disordered distribution of radiation subject to physically realistic conditions. The physical interpretations of the physically realistic solutions has been investigated. It has been found that physically realistic solutions has been obtained for closed cosmological models only.

Phase transitions in perturbed stiff fluid Friedmann-Robertson-Walker cosmological models

Abstract: The authors consider one-soliton perturbations of a flat Friedmann-Robertson-Walker (FRW) cosmological model, with an ideal fluid with pressure equal to energy density (stiff fluid), in the case where the 'pole trajectory' parameter is negative, thereby introducing singularities along certain null hypersurfaces. Starting with a metric that approaches asymptotically the FRW background, they show that it is possible to construct extensions through these hypersurfaces such that the energy-momentum tensor Tmu nu is finite and satisfies the energy conditions. One of the extensions is Cinfinity and displays a smooth transformation where the stiff fluid becomes 'tachyonic' (and vice versa), similar to one already discussed by Tabensky and Taub (1973). The other extension is only C1, providing a sort of 'shock front', with continuity in Tmu nu , that has an associated 'null dust to stiff fluid phase transformation' of the form described by Chandrasekhar and Xanthopoulos (1986).

Self-similar cosmological models

Abstract: The Universe today is observed to be extremely homogeneous and isotropic on large scales. The dipole anisotropy of the microwave background, due to the relative motion of the Earth, is measured to be less than one part in 10 4. The quadropole component, due to intrinsic anisotropies, is even smaller. Thus, any viable mathematical or physical description of the large scale properties of the Universe must encompass the observational evidence and reflect this large degree of uniformity. The most popular, and certainly the most successful, description of the Universe at the present epoch is provided by the Friedmann-Robertson-Walker (FRW) cosmological models. These spherically symmetric models consider the Universe as an isotropic, spatially homogeneous, perfect fluid matter distribution, which is in a state of dynamic evolution. All of the FRW cosmologies exhibit an expansion, i. e. the volume of the spatial sections varies with time, during some stage of their evolution, in agreement with the observed expansion of the Universe. An important consequence of this behaviour is that it leads to a singularity at a finite time in the past when the volume of the spatial sections becomes zero and matter becomes infinitely dense and infinitely hot (the hot Big Bang scenario). The isotropy and homogeneity of the Universe at the present epoch, cannot necessarily be extrapolated back to these earlier times. Certainly, there must exist inhomogeneities on small scales at all epochs in order to produce the observed structure, such as galaxies, clusters and superclusters. This raises the question of the effect of anisotropy on the initial stages of the evolution of the Universe. In this thesis we consider cosmological models which differ significantly from the FRW descriptions. We consider the effect of a large cosmological constant (vacuum energy term) on the behaviour of a spherically symmetric anisotropic universe, characterised by different expansion rates in the radial and transverse directions. The analysis is simplified considerably by imposing the condition that the model admits a self-similar symmetry. The techniques of similarity and dimensional analysis are employed to obtain a class of spatially inhomogeneous solutions to the Einstein field equations with a non-zero cosmological term. These solutions are found to contain some which tend asymptotically to a de-Sitter FRW solution and thereby extend the cosmological "no-hair" theorems, which state that under certain restrictions any model containing a large positive cosmological term will evolve to a de-Sitter cosmology at late times. Such models are attractive since they tend to isotropic spacetimes. Similarity methods are also applied to the study of an anisotropic spacetime with an imperfect fluid as source. The fluid description of the cosmology is chosen to include the dissipative processes of shear and bulk viscosity but to neglect the effects due to the existence of magnetic fields, heat conduction or acceleration along the flow lines. In order to obtain a self-similar description of such a fluid we must impose certain conditions on the form of the viscous coefficients of bulk and shear. This allows a degree of tractability but restricts the physical significance of the models. Solutions are found for which the matter distribution acts as (i) a 'presureless fluid' with an equation of state given by T11=0 and (ii) a 'stiff' fluid with equation of state, T1 1=-T0 0. The conditions under which the Universe may attain either of these extreme properties are discussed in relation to the physical processes occurring in the matter distribution at different epochs. It is found that the presence of viscosity has a marked effect on the dynamics of the Universe, particularly at early times. The self-similar viscous models with a stiff equation of state are then considered with respect to the formation of black holes in the early Universe. The difficulties of obtaining a smooth continuation of the viscous solutions from the Universe particle horizon to a black hole event horizon are discussed in view of the limitations encountered in the non-viscous black hole solutions. Finally, the possibility of future investigations inspired by the considerations of this thesis are discussed. In particular, the determination of a geometric symmetry corresponding to self-symmetry of the second kind and the formation of a self-consistent similarity treatment of imperfect fluid cosmologies are deemed important. Possible lines of research to these ends are considered.

Brans-Dicke solitons as finite perturbations on perfect-fluid FRW models in general relativity

Abstract: The authors consider the relation between a class of vacuum solutions in the Brans-Dicke theory of gravitation and perfect barotropic fluid Friedmann-Robertson-Walker cosmologies which can be related to five-dimensional vacuum solutions of Einstein's equations. They present a family of solitonic solutions of the Einstein equations obtained by the application of the inverse scattering technique in five dimensions followed by a subsequent Kaluza-Klein dimensional reduction procedure and a conformal rescaling. The effective energy-momentum tensor that appears is equivalent to that of the Brans-Dicke theory of gravitation. For large time values the metric approaches that of a flat FRW universe with a barotropic perfect fluid as material content. The solutions are a particular case of a family previously presented, together with a new renormalisation procedure for the inverse scattering technique.

An inflationary cosmological model in Dunn's scalar-tensor theory of gravitation

Abstract: The gravitational field equations in Dunn's scalar-tensor theory of gravitation are generalized by including a cosmological constant The resulting equations are solved for a Robertson-Walker line-element with flat three-space The solution represents a cosmological model that develops into an inflationary era

Helium Formation in a Class of Radiative Cosmological Models

Abstract: Helium formation is studied in a class of exact radiation-filled cosmological models in which the space-time geometry is represented by the Friedmann-Robertson-Walker metric and the source of the gravitational field is a non-co-moving imperfect fluid. Using the methods described by Barrow (1984) we find it possible to calculate the predicted helium-4 abundance in the class of radiative models analytically in terms of the results in the corresponding standard model. It is found that different amounts of helium-4 are produced at different space-time locations in the models. It is also found that while there is less helium-4 produced than in the standard model, the models give rise to predictions for the primordial helium-4 abundance within the observed range. In view of current estimates for the pre-galactic helium abundance and the predictions obtained from the standard model, models in which less helium is produced are of particular interest. The techniques employed in the calculation are discussed, and the assumptions and approximations that have been made are described in some detail.

Phase transitions in perturbed stiff‐fluid Friedmann‐Robertson‐Walker cosmological models

Abstract: We consider one-soliton perturbations of a flat Friedmann-Robertson-Walker (FRW) cosmological model, with an ideal fluid with pressure equal to the energy density (stiff fluid), in the case where the “pole trajectory” parameter is negative, introducing thereby singularities along certain null hypersurfaces Starting with a metric that approaches asymptotically the FR W background, we show that it is possible to construct an extension through these hypersurfaces such that the energy momentum tensor Tab is finite and satisfies the energy conditions The extension is only C1, providing a sort of “shock front” with continuity in Tab, that has an associated phase transition from null dust to stiff fluid, the transition being of the form described by CHANDRASEKHAR and XANTHOPOULOS

Quantum conformal fluctuations revisited

Abstract: The conformal quantization method of Narlikar and Padmanabhan is reformulated with a view to take into account theexact propagator and to provide explicitnumerical estimates of various predictions for dust cosmologies. It is found that in spite of the divergence of quantum fluctuations at the big-bang epoch it is possible to construct wave packets which remain sharp fromt=10−70s, say, up to the present epoch provided the present state is finely tuned to the classical one. Also, if the transition probability from the Minkowski to the FRW metric is calculated using Gaussian wave functions (with zero mean) then thet2/3 models withk = 0, ± 1 cannot be distinguished, i.e., a fine tuning to the flat (k=0) model does not seem to result if the conformal factor depends on time only.