Anisotropic cosmological models of Bianchi types III and V in Lyra's geometry

Exact solutions to Einstein's equations are presented in vacuum and in the presence of stiff matter for spatially homogeneous cosmological models of Bianchi types type III and V in the normal gauge for Lyra's geometry. Solutions represent anisotropic cosmological universes which contract from infinite volume at the initial time singularityT=0 to zero volume asT. Some physical properties of the models are also discussed.     

Rotating cosmological models of Bianchi type VIII

We find cosmological solutions with rotation of Bianchi type VIII for the energy-momentum tensor of a perfect fluid with heat flow.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 98–103, May, 1989.In conclusion the author expresses thanks to the participants in Professor D. D. Ivanenko's seminar for helpful discussions.     

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.     

Bianchi type III and Kantowski-Sachs cosmological models in Lyra geometry

Cosmological models for Bianchi type III and Kantowski-Sachs space-times within the framework of Lyra geometry are obtained. The physical behavior of the models is also discussed.     

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.     

Geodesic Bianchi type cosmological models

Some perfect fluid solutions of Einstein's field equations are obtained in spacetimes with two hypersurface orthogonal space-lika commuting Killing vectors. The flow is assumed to be geodesic. The solutions depend on an arbitrary function of time which determines the equation of state. In the models derived one additional Killing vector exists and the solutions are actually Bianchi-type cosmological models.     

Ricci collineations of the Bianchi type II,VIII, and IX space-times

Ricci and contracted Ricci collineations of the Bianchi type II, VIII, and IX space-times, associated with the vector fields of the form (i) one component of ^a (x ^b ) is different from zero and (ii) two components of ^a (x ^b ) are different from zero, fora, b=1, 2, 3, 4, are presented. In subcase (i.b), which is ^a = (0, ¹(x ^a ),0,0), some known solutions are found, and in subcase (i.d), which is ^a =(0, 0, 0, ⁴(x ^a )), choosingS(t) = const.×R(t), the Bianchi type II, VIII, and IX spacetime is reduced to the Robertson-Walker metric.     

Bianchi type IX string cosmological model in general relativity

We have investigated Bianchi type IX string cosmological models in general relativity. To get a determinate solution, we have assumed a condition ρ=λ i.e. rest energy density for a cloud of strings is equal to the string tension density. The various physical and geometrical aspects of the models are also discussed.     

Anisotropic Bianchi type V perfect fluid cosmological models in Lyra’s geometry

The law of variation for mean Hubble’s parameter with average scale factor, in an anisotropic Bianchi type V cosmological space–time, is discussed within the frame work of Lyra’s manifold. The variation of Hubble’s parameter, which gives a constant value of deceleration parameter, generates two types of solutions for the average scale factor; one is the power-law and the other one is of exponential form. Using these two forms, new classes of exact solutions of the field equations have been found for a Bianchi type V space–time filled with perfect fluid in Lyra’s geometry by considering a time-dependent displacement field. The physical and kinematical behaviors of the singular and non-singular models of the universe are examined. Exact expressions for look-back time, luminosity distance and event horizon versus redshift are also derived and their significance are discussed in detail. It has been observed that the solutions are compatible with the results of recent observations.     

Classical and quantum aspects of Bianchi type IX cosmological model

A detailed study of the Bianchi type IX cosmological model is done. Classical field equations are discussed with a massive scalar field. The Wheeler-DeWitt quantum equation is formed and is solved using a Born-Oppenheimer type of approximation.     

Energy distribution of the universe in the Bianchi type II cosmological models

Using the energy‐momentum complexes of Tolman, Papapetrou and Weinberg, the total energy of the universe in Locally Rotationally Symmetric (LRS) Bianchi type II models is calculated. The total energy is found to be zero due to the matter plus field. This result supports the viewpoint of Tryon, Rosen and Albrow.     

Bianchi type I cosmological models with variableG and A

Einstein's equations with variableG and A scalars are considered for a Bianchi type I metric. A solution is found in which the cosmological term varies inversely with the square of time. As in the case of the flat Friedmann-Lemaître-Robertson-Walker (flrw) models discussed recently, there is then no dimensional constant associated with A. However, it is shown that the time behaviour of Bianchi type I inflationary solutions cannot be of the pure de Sitter type. This shows that if the flat FLRW inflationary solutions previously considered are perturbed by the introduction of Bianchi type I anisotropy, then the time evolution may be perturbed from the pure exponential form.     

Cosmic strings in Bianchi II,VIII and IX spacetimes: Integrable cases

We investigate the integrability of cosmic strings in Bianchi II, VIII and IX space-times using a Lie symmetry analysis. The behaviour of the gravitational field is governed by solutions of a single second order nonlinear differential equation. We demonstrate that this equation is integrable and admits an infinite family of physically reasonable solutions. Particular solutions obtained by other authors are shown to be special cases of our class of solutions.     

Bianchi Type-I cosmological mesonic stiff fluid models in Lyra’s geometry

Bianchi Type-I cosmological models in Lyra’s geometry are obtained when the source of gravitational field is a perfect fluid coupled with massless mesonic scalar field. Some physical and kinematical properties of the models are also discussed.      

A new class of LRS Bianchi type-I cosmological models in Lyra geometry

LRS Bianchi type-I models have been studied in the cosmological theory based on Lyra’s geometry. A new class of exact solutions has been obtained by considering a time dependent displacement field for constant deceleration parameter models of the universe. The physical behaviour of the models is examined in vacuum and in the presence of perfect fluids.     

Quark matter coupled to domain walls in Bianchi types II,VIII and IX Universes

In this study of Bianchi types II, VIII and IX Universes, quark matter coupled to domain walls in the context of general relativity are explored. To obtain deterministic solution of the Einstein’s field equations, various techniques are adopted. The features of the obtained solution are discussed.     

Generation of massless fermions in cosmological models of first Bianchi type

Generation of massless fermions in a general case of the anisotropic metric of first Bianchi type is considered. A regularized energy-momentum tensor of the generated particles is constructed. The absence of a conformal anomaly is shown for the initially massless quantum theory of a spinor field in an external gravitational field.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 35–40, January, 1984.The author thanks A. A. Grib and A. V. Nesteruk for useful discussions.     

Stationary cosmological Bianchi II solutions

Stationary cosmological solutions for the Bianchi metric II are derived. In the models, use is made of a scalar field with a vacuum-averaged energy-momentum tensor, a cosmological constant, and ideal co-moving or not co-moving liquids as sources of gravitations.