Dynamics of locally rotationally symmetric Bianchi type VIII cosmologies with anisotropic matter

This paper is a study of the effects of anisotropic matter sources on the qualitative evolution of spatially homogenous cosmologies of Bianchi type VIII. The analysis is based on a dynamical system approach and makes use of an anisotropic matter family developed by Calogero and Heinzle which generalises perfect fluids and provides a measure of deviation from isotropy. Thereby the role of perfect fluid solutions is put into a broader context. The results of this paper concern the past and future asymptotic dynamics of locally rotationally symmetric solutions of type VIII with anisotropic matter. It is shown that solutions whose matter source is sufficiently close to being isotropic exhibit the same qualitative dynamics as perfect fluid solutions. However a high degree of anisotropy of the matter model can cause dynamics to differ significantly from the vacuum and perfect fluid case.     

A class of new LRS Bianchi type-I perfect fluid universes with decaying vacuum energy density Λ

A class of new LRS Bianchi type-I cosmological models with a variable cosmological term is investigated in presence of perfect fluid. A procedure to generate new exact solutions to Einstein’s field equations is applied to LRS Bianchi type-I space-time. Starting from some known solutions a class of new perfect fluid solutions of LRS Bianchi type-I are obtained. The cosmological constant Λ is found to be positive and a decreasing function of time which is supported by results from recent supernovae Ia observations. The physical and geometric properties of spatially homogeneous and anisotropic cosmological models are discussed.     

Phantom Appearance of Non-phantom Matter in Anisotropic Cosmological Model

Two cosmological models with non-phantom matter having the same expansion of the universe as phantom cosmologies are constructed in anisotropic Bianchi type-V universe. The exact solutions to the corresponding Einstein field equations have been obtained. The statefinder diagnostic pair i.e. {r,s} parameters have been obtained for disordered radiation i.e. γ=1/3. We have also discussed the well-known astrophysical phenomena, namely the look-back time, luminosity distance and event horizon with redshift.     

Anisotropic Bianchi VIII/IX cosmological models with matter and electromagnetic fields

We present a class of cosmological solutions of Einstein equations, with matter and electromagnetic field, which are anisotropic and spatially homogeneous of Bianchi types VIII and IX.     

The Bianchi IX cosmological models

Two cosmological models for the Bianchi IX metric are constructed. These include the following sources of gravitation: 1) a co-moving anisotropic liquid, non-comoving dust, and a scalar field; 2) an anisotropic liquid, pure radiation, and a scalar field. The kinematic parameters of the models are found.     

Phantom Appearance of Non-phantom Matter in Bianchi Type-I Cosmological Model

Two cosmological models with non-phantom matter having the same expansion of the universe as phantom cosmologies are constructed in Bianchi type-I universe. The exact solutions to the corresponding Einstein field equations have been obtained. The cosmological parameters have been obtained in two interesting cases (i) γ=0 and (ii) γ=1/3. We have also discussed the well-known astrophysical phenomena, namely the look-back time, luminosity distance and event horizon with redshift.     

Gravitational fields with space-times of Bianchi type IX

Spatially homogeneous space-times of Bianchi type IX are considered. A general scheme for the derivation of exact solutions of Einstein’s equations corresponding to perfect fluid plus pure radiation fields is outlined. Some simple rotating Bianchi type IX cosmological models are presented. The details of these solutions are also discussed. The authors felicitate Prof. D S Kothari on his eightieth birthday and dedicate this paper to him on this occasion.     

Cosmological models with rotation

Nonstationary and stationary cosmological models with rotation and the Bianchi IX metric are constructed within the general relativity theory. A comoving anisotropic liquid and non-comoving “dust-like liquid” are the sources of gravitation in one case, while a comoving anisotropic, non-comoving “dust-like liquid”, and pure radiation - in the other. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 33–37, August, 2008.     

Ancient Dynamics in Bianchi Models: Approach to Periodic Cycles

We consider cosmological models of Bianchi type. In particular, we are interested in the α-limit dynamics near the Kasner circle of equilibria for Bianchi classes VIII and IX. They correspond to cosmological models close to the big-bang singularity.     

Qualitative magnetic cosmology

The technique of phase plane analysis, which was used in a previous paper [4] to study the behaviour of a class of perfect-fluid anisotropic cosmological models, is applied to some simple anisotropic models that contain a uniform magnetic field. A formal correspondence is established between these magnetic models (of Bianchi type I) and certain perfect fluid models (of Bianchi type II), and new exact solutions are consequently discovered.     

Asymptotics of LRS Bianchi type I cosmological models with elastic matter

In this paper, we report on results in the study of spatially homogeneous cosmological models with elastic matter. We show that the behavior of elastic solutions is fundamentally different from that of perfect fluid solutions already in the case of locally rotationally symmetric Bianchi type I models; this is true even when the elastic material resembles a perfect fluid very closely. In particular, the approach to the initial singularity is characterized by an intricate oscillatory behavior of the scale factors, while the future asymptotic behavior is described by isotropization rates that differ significantly from those of perfect fluids.     

Perfect fluid quantum anisotropic universe: merits and challenges

The present paper deals with quantization of perfect fluid anisotropic cosmological models. Bianchi type V and IX models are discussed following Schutz’s method of expressing fluid velocities in terms of six potentials. The wave functions are found for several examples of equations of state. In one case a complete wave packet could be formed analytically. The initial singularity of a zero proper volume can be avoided in this case, but it is plagued by the usual problem of non-unitarity of anisotropic quantum cosmological models. It is seen that a particular operator ordering alleviates this problem.     

Isotropization of solutions of the Einstein–Vlasov system with Bianchi V symmetry

Using the methods developed for different Bianchi class A cosmological models we treat the simplest Bianchi class B model, namely Bianchi type V. The future non-linear stability for solutions of the Einstein–Vlasov system is demonstrated and it is shown that these solutions are asymptotically stable to the Milne solution. Within the isotropic solutions of the Einstein–Vlasov system the spatially flat Friedmann solution is unstable within this class, and expanding models tend also to the Milne solution.     

Isotropization of Bianchi Models and a New FRW Solution in Brans–Dicke Theory

Using scaled variables we are able to integrate an equation valid for isotropic and anisotropic Bianchi type I, V, IX models in Brans–Dicke (BD) theory. We analyze known and new solutions for these models in relation with the possibility that anisotropic models asymptotically isotropize, and/or possess inflationary properties. In particular, a new solution of curved (k 0) Friedmann–Robertson–Walker (FRW) cosmologies in Brans–Dicke theory is analyzed.     

LRS Bianchi type I perfect fluid solutions generated from known solutions

Some LRS Bianchi type I perfect fluid solutions are generated from known solutions of this type. The solutions represent spatially homogeneous and anisotropic cosmological models which would give essentially empty space for large time. The physical and kinematic properties of the models are discussed.     

Quantum fluctuations near the classical space-time singularity

The method of path integration is used to study the effects of quantum fluctuations in the space-time geometry near the classical singularity of general relativity. It is shown that in certain special cases explicit Feynman propagators can be constructed which enable us to evaluate these fluctuationsquantitatively. The cases discussed are (i) the gravitational collapse of a uniform dust ball, (ii) the Friedmann cosmologies, (iii) the axisymmetric Bianchi type I cosmological model, and (iv) the general anisotropic Bianchi type I cosmological model. In all cases discussed here the quantum uncertainty grows to infinity as the classical space-time singularity is approached. In this wider regime of quantum gravitation nonsingular solutions can occur with finite probabilities.     

Bianchi Type I Universe Models with Irreversible Matter Creation

The effects of matter creation on the evolution and dynamics of an anisotropic Bianchi type I space–time is investigated in the framework of open thermodynamic systems theory. For a cosmological fluid obeying a Zel'dovich type equation of state =p and with particle creation rate proportional to the square of the mean Hubble function and to the energy density of matter, respectively, the general solution of the gravitational field equations can be expressed in an exact parametric form. Generically all models start from a non-singular state. In the large time limit anisotropic cosmological models with particle creation rate proportional to the square of the Hubble function end in an isotropic flat (inflationary or non–inflationary) phase while models with particle source function proportional to the energy density of matter do not isotropize, ending in a Kasner–type geometry.     

Some rotating,time-dependent Bianchi type-IX cosmologies with heat flow

It is reported on an investigation of cosmologies which constitute explicit, rotating, and expanding solutions of Einstein's field equations, with spacelike, timelike, or null-like homogeneous hypersurfaces of Bianchi type IX, and the source of which is a non-thermalized perfect fluid.     

Homogeneous Bianchi type VI0 perfect fluid space-times

An algorithm is presented for generating new exact solutions of the Einstein equations for spatially homogeneous cosmological models of Bianchi type VI₀. The energy-momentum tensor is of perfect fluid type. Starting from Dunn and Tupper's dust-filled universe, new classes of solutions are obtained. The solutions represent anisotropic universes filled with perfect fluid not satisfying the equation of state. Some of their physical properties are studied.