Spatially homogeneous cosmological models

We study nonviscous and viscous fluids in Bianchi types II, VIII, and IX space-times under the restriction that the ratio of shear to expansion be constant.     

Self-similar cosmological models

The kinematics and dynamics of self-similar cosmological models are discussed. The degrees of freedom of the solutions of Einstein's equations for different types of models are listed. The relation between kinematic quantities and the classifications of the self-similarity group is examined. All dust local rotational symmetry models have been found.     

Spatially homogeneous and anisotropic cosmological solution in Brans-Dicke theory

An exact solution of the vacuum Brans-Dicke (BD) field equations has been obtained for the metric tensor of a spatially homogeneous and anisotropic Bianchi type-I cosmological model. The Kasner metric is shown to be a special case. Some physical properties of the model have been discussed.     

Tilted homogeneous cosmological models

We examine spatially homogeneous cosmological models in which the matter content of space-time is a perfect fluid, and in which the fluid flow vector is not normal to the surfaces of homogeneity. In such universes, the matter may move with non-zero expansion, rotation and shear; we examine the relation between these kinematic quantities and the Bianchi classification of the symmetry group. Detailed characterizations of some of the simplest such universe models are given.     

Einstein-Cartan-Maxwell-bianchi type-V cosmological models

Exact cosmological solutions of the Einstein- Cartan-Maxwell equations with spin, stiff matter and an electromagnetic field for Bianchi type-V universes are obtained. A class of nonsingular solutions is presented. The most important characteristic of these solutions is that in one case the effect of the electromagnetic field is to reduce the value of the minimum volume while in another case there exists the possibility of enlarging this value arbitrarily.     

Charge in cosmological models

The balanced field equations due to Penney are used to find solutions for cosmological models in the presence of charge. Herein, it is found that the introduction of charge adds additional terms to the Einstein conservation equation and distribution expressions. The curvature parameter is affected and it is concluded that whereas matter affects it positively, the charge does so negatively. There then arises also the possibility of an evolution of local systems against the background of a global expansion.     

Oscillatory behavior in cosmological models

Oscillatory behavior in cosmological models is investigated, motivated, in part, by the apparent periodic distribution of galaxies in deep narrow-cone red-shift surveys. In particular, oscillatory behavior in two cosmological models is studied; a qualitative analysis is performed and approximate solutions are found for a soft inflationary model and for a Friedmann-Robertson-Walker model containing a perfect fluid and a scalar field source. These two models are conformally equivalent to particular models arising from a large class of scalar-tensor theories. It is then argued that such oscillatory behavior is a generic property of scalartensor theories of gravity.     

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.     

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.     

Building analytical three-field cosmological models

A difficult task to deal with is the analytical treatment of models composed of three real scalar fields, as their equations of motion are in general coupled and hard to integrate. In order to overcome this problem we introduce a methodology to construct three-field models based on the so-called “extension method”. The fundamental idea of the procedure is to combine three one-field systems in a non-trivial way, to construct an effective three scalar field model. An interesting scenario where the method can be implemented is with inflationary models, where the Einstein–Hilbert Lagrangian is coupled with the scalar field Lagrangian. We exemplify how a new model constructed from our method can lead to non-trivial behaviors for cosmological parameters.     

Nonstationary cosmological models with rotation

Cosmological models containing rotation and expansion have become of great interest since the publication of Birch. In the present paper we obtain a wide class of exact solutions describing an expanding and rotating universe. Sources are taken to be an anisotropic or ideal fluid, a massless scalar field, and a radiation field.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 48–51, March, 1988.     

Quantum statistics in cosmological models

The properties and evolution of a Friedmann universe filled with a quantum gas of massless particles and massive dust are investigated on the basis of quantum statistics. Values are given for the critical temperature and the Fermi temperature, and the possibility of degeneracy of the neutrino gas is shown. The expressions obtained for the Fermi energy are applied for estimates of the neutrino density in the Universe.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 61–65, May, 1981.     

Friedmann-like cosmological models without singularity

The Einstein-Cartan theory of gravitation (general relativity with spin) provides a specific spin-spin contact interaction of matter, in addition to the usual long-range gravity. This new interaction enables us to prevent singularities in Cosmological models. It is shown how this mechanism works in the case when the standard Einstein-Cartan equations are valid at a microphysical level, and some spin-spin terms remain from the averaging procedure for randomly distributed spins. In contrast with the case of aligned spin distributions, it is possible to take over the isotropic and spatially homogeneous (i.e., Friedmannian) models into the Einstein-Cartan theory. These models can be made free from singularity, thanks to the self-interaction of spinning fluid.     

Bochner techniques and cosmological models

We demonstrate the possibility of applying the Bochner techniques [R. Zh. Matematika, 2A, 746 (1985)] to dynamics of an ideal fluid in a curved space-time. One example of the result of such application is that every irrotational motion of cosmological fluid with zero expansion in a closed oriented space-time obeying the energy condition is shearless.Vladimir State Pedagogical Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 82–86, June, 1993.     

Nonsingular cosmological models in Brans-Dicke theory

An attempt has been made to construct nonsingular cosmological models in Brans-Dicke theory by taking vacuum field as the long-range interacting scalar field which tends to avert the occurrence of initial singularity in a homogeneous and isotropic cosmological model. Such a model will possess an extremely small value of coupling parameter , as such they will be characteristically different from the usual Brans-Dicke models with 6. A justification for the estimated value of coupling parameter in the present paper has been given with particular reference to the helium problem. The model satisfies the initial conditions as proposed by Salam, Sinha, etc. However, it predicts a larger value of the energy density at the present epoch.     

Geometrized dynamics of multidimensional cosmological models

In the present work we reduce the dynamics of multidimensional cosmological models to the geodesics on a pseudo-Riemannian space. The significance of Killing vectors and tensors for the integrability problem is discussed. We also investigate geometric properties of the geodesics representing the evolution of cosmological models.