Self-consistent solutions for cosmological models with rotation

A wide spectrum of new results is obtained describing homogeneous motionless cosmological models with rotation in which causality is not violated. Exact solutions are also given for cosmological models describing an expanding and rotating universe. Sources in the obtained solutions are an anisotropic or ideal fluid, a massless complex scalar field, the electromagnetic field, a radiation field, and various combinations of these sources.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 5–10, June, 1988.     

Spontaneous symmetry breaking in cosmological models with rotation

We study the possibility of spontaneously broken gauge symmetry in the theory of a charged massive or massless scalar field for cosmological models of the Gödel and Ozsvath-Schücking types. We consider the effect of spontaneous symmetry breaking in the construction of a new cosmological solution with rotation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 22–26, February, 1989.The author thanks the participants of the seminars of Prof. A. A. Grib and Prof. D. D. Ivanenko for discussions of the results.     

Bianci-IX cosmological models with rotation in general relativity theory

Bianci-IX metrics have been used to obtain new exact solutions to the GRT equations, which may describe the early stages in the evolution of an expanding and rotating universe.Kaluga Branch, Bauman Moscow State Technical University. M. V. Lomonosov Moscow State University. Translated from Izvestiya Vysshikh Uchebnyk Zavedenii, Fizika, No. 9, pp. 122–127, September, 1994.     

Bianchi-II cosmological models with rotation in general relativity theory

We obtain a broad class of new exact solutions in Bianchi-II cosmologies with rotation and expansion. We show that within the framework of general relativity theory, we can construct realistic cosmological models in good agreement with current observational data.N. É. Bauman State Technical University, Moscow. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 54–63, October, 1994.     

Nonstationary Gödel-type cosmological model

We construct a nonstationary, rotating, causal Gödel-type cosmological model filled with a massless complex scalar field, an anisotropic fluid with distributed scalar field charge, and a radiation field, taking into account heat flow.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 62–66, January, 1990.In conclusion, the author expresses thanks to the participants in Prof. D. D. Ivanenko's seminar for discussion of the results of the work.     

Five-domensional, nonstationary cosmological solutions with rotation

Two nonstationary cosmological solutions of the five-dimensional Einstein equations are found for different metrics. In one case the sources of the gravitational field are an anisotropic fluid and a radiation field, while in the other case they are an anisotropic fluid, a radiation field, and a heat flux. Perm' State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 25–28, September, 1997.     

Inhomogeneous cosmological models with heat flux

We present a general class of inhomogeneous cosmological models filled with non-thermalized perfect fluid by assuming that the background spacetime admits two space-like commuting Killing vectors and has separable metric coefficients. The singularity structure of these models depends on the choice of the parameters and the metric functions. A number of previously known perfect fluid models follow as particular cases of this general class. Physical and geometrical features of these models are studied and the general expression for temperature distribution is given.     

Brans-Dicke models with time-dependent cosmological term

More general solutions than those presented by Bertolami are deduced in the Brans-Dicke cosmology, endowed with a time-dependent cosmological term, for a Robertson-Walker metric and a perfect fluid obeying the perfect gas law of state.     

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.     

Behavior of a bundle of rays forming the image of a source in cosmological models with rotation

Our earlier results regarding the absence of Birch anisotropy in cosmological models with rotation were obtained under the assumption that a bundle of rays forming the image of a source is nonrotating. This appears to be at variance with the rotation of space. The detailed analysis in the present paper of the behavior of rays propagating from a source to an observer shows that the congruence of the rays is, in fact, nonrotating. The doubts expressed by some authors in reference to our conclusions that the Birch effect is not attributable to cosmological rotation are thereby put to rest. Zh. éksp. Teor. Fiz. 114, 769–776 (September 1998)     

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.     

Five-dimensional cosmological models with massless scalar fields

Simple cosmologies are constructed from solutions of the five-dimensional Einstein equations with a real massless non-self-interacting scalar field source. It is demonstrated that non-trivial cosmological models occur only if the metric of the homogeneous and isotropic three-space of the universe has non-positive constant curvature. For the case of flat three-space, it is further demonstrated that two classes of solutions result - one of which has a power-law type of expansion for three-space and contraction of the one-dimensional internal space, while the other class has an exponential expansion for three-space and exponential contraction of the internal space. The exponentially expanding solutions are the limiting case of the power-law expanding solutions. Hence, our model is consistent with a simple inflationary scenario.     

Magnetized anisotropic cosmological models with varying Λ

Some anisotropic homogeneous cosmological models with electromagnetic field are obtained in presence of a perfect fluid. The source of the magnetic field is due to an electric current produced along the x-axis. Without assuming any ad hoc law, we obtain a cosmological constant as a decreasing function of time which is supported by results from recent supernovae Ia observations. The behaviour of the electromagnetic field tensor together with some physical aspects of the model are also discussed.     

Rotating quantum cosmological models with wave fields

The quantum evolution of homogeneous rotating cosmological models of the Gödel type with spinor and scalar fields is considered within the framework of the formalism of superspace quantization. De Witt's equation for a rotating cosmological model is shown to take the form of a Schrödinger equation in which the role of time is played by the phase of the spinor field, and it becomes possible to determine correctly the probability that rotating models lacking an initial singularity exist.K. D. Ushinskii Yaroslav Pedagogical Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 41–44, January, 1993.     

Quantum effects in cosmological models with singularities

The vacuum expectation values of the energy-momentum tensor of quantized scalar and spinor fields in a de Sitter space of the first kind are calculated. Limiting cases of the obtained exact expressions are considered. It is noted that the de Sitter space is a self-consistent solution of the Einstein equations with allowance for quantum vacuum fluctuations of massless fields.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 67–70, January, 1981.I thank V. M. Mostepanenko and B. N. Sharapov for numerous helpful discussions.     

Kantowski-Sachs cosmological models with anisotropic dark energy

The exact solutions of the Einstein field equations for dark energy in Kantowski-Sachs metric under the assumption on the anisotropy of the fluid are obtained for exponential and power-law volumetric expansions. The isotropy of the fluid, space and expansion are examined.     

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.