A new class of inhomogeneous cosmological models with Yang-Mills fields

Exact solutions corresponding to spherically symmetric inhomogeneous nonstationary Tolman metrics are obtained for the self-consistent system of Einstein-Yang-Mills equations for the gauge group SO ₃ . Pis’ma Zh. éksp. Teor. Fiz. 64, No. 2, 65–70 (25 July 1996)     

New exact solutions of the Yang-Mills field equations

In this paper new exact solutions of the Yang-Mills SU(2) gauge field equations are obtained using the Carmeli-Charach-Kaye null-tetrad formalism. The solutions are classified and briefly discussed.     

Properties of exact solutions for a massive classical Yang-Mills field

Exact solutions for a massive Yang-Mills field are found and solutions of classical Wong equations and quantum Dirac equations are discussed for the field configurations obtained. A procedure for constructing constant fields is given and transition to solutions of the Yang-Mills equations in the case of a massless field is discussed.Translated from Izvestriya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 96–100, May, 1986.In conclusion, the authors express their gratitude to V. Ch. Zhukovskii and V. R. Khalilov for valuable remarks and discussions.     

Inflationary stages in cosmological models with a scalar field

Homogeneous isotropic cosmological models with a massive scalar field are studied. It is shown that inflationary stages of evolution are characteristic of most solutions in these models.     

Higher symmetries in a class of cosmological models

A particular class of solutions of Einstein's field equations, in which the source is a perfect fluid and the geometry admits a two-parameter Abelian isometry group with spacelike orbits, is examined for the possible admission of higher symmetries. It is shown that in certain cases the geometry is spatially homogeneous, being either of the orthogonal Bianchi type I or of the tilted Bianchi-Behr type VIU_h withh = –4, and that no other cases of higher symmetry (in the sense of isometry groups) are possible. The global behaviour of the Bianchi-Behr type VIU_h, models is studied, and conformal diagrams are given. This investigation is extended to the case when additional homothetic vectors are admitted, and a parallel study of the global behaviour, complete with conformal diagrams, is provided. A brief argument also shows that, within the class considered, whenever the fluid flow-lines possess identical thermal histories, the geometry is necessarily spatially homogeneous.     

Discrete isotropies in a class of cosmological models

It is shown that a certain class of cosmological models admits discrete isotropies. These models are solutions of Einsteins field equations, characterised by: (1) the matter is described as a perfect fluid, and (2) there exists a group of motions simply transitive on three-surfaces orthogonal to the fluid flow vector.     

A class of homogeneous cosmological models

Einstein's field equations are studied under the assumptions that (1) the source of the gravitational field is a perfect fluid, and (2) there exists a group of motions simply transitive on three-surfaces orthogonal to the fluid flow vector. There are two classes of solutions; these are studied in detail. Three special families of solutions examined include all analytic solutions of the field equations obeying (1) and (2) of which the authors are aware. The relation of these solutions to various vacuum solutions is indicated.     

A class of inhomogeneous cosmological models

All solutions of Einstein's field equations representing irrotational dust and possessing a metric of the formds ²=dt ²?e ^2α dr ²?e ^2β(dy ²+dz ²) are found. The new metrics generalize the earlier Bondi-Tolman, Eardley-Liang-Sachs, and Kantowski-Sachs cosmological models.     

A class of homogeneous cosmological models

This paper discusses the application of geometric optics to the study of observational properties of cosmological models examined in a previous paper. A number of results concerning these properties are derived, the most interesting of which is the invariance of observational relations under certain discrete isotropy groups. Closed form expressions are obtained in certain cases.     

Inflation in cosmological models with a non-minimally coupled, massless scalar field

A homogeneous, spatially flat cosmological model induced by a massless scalar field is investigated. The parameter ξ of coupling of the field with the curvature can take any value. It is shown that the range of values of ξ is divided into three regions, ξ<0, 0<ξ<1/6, and ξ>1/6, each of which is characterized by the behavior of the scale factor in it. The points ξ=0 and ξ=1/6 are singular. Stages with exponential and power-law inflation are found in the ranges 0<ξ<1/6 and ξ>1/6. An exponential inflationary stage with acceptable cosmological consequences can occur for small positive ξ. Kazan’ State Pedagogical University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 53–57, March, 1997.     

An exact bianchi type-V tilted cosmological model with matter and an electromagnetic field

We present a cosmological solution of the source-free Einstein-Maxwell equations with stiff matter and an electromagnetic null field, which is a locally rotationally symmetric tilted Bianchi type-V universe.     

A class of stationary rotating string cosmological models

We obtain a one parameter class of stationary rotating string cosmological models of which the well-known Gödel universe is a particular case. By suitably choosing the free parameter function, it is always possible to satisfy the energy conditions. The rotation of the model hinges on the cosmological constant which turns out to be negative. String-dust distribution in Gödel-type universes is also briefly discussed.     

The existence of Newtonian analogs of a class of 5D Wesson's cosmological models

The conditions for the existence of Newtonian analogs of a five dimensional (5D) generalization of the Friedman-Robertson-Walker (FRW) cosmological models in Wesson's gravitational theory are re-analyzed. Contrarily to other claims, we show that classical analogs can be obtained for non-null cosmological constant and negative or null spatial curvature.     

New exact solutions of the Yang-Mills equation

New exact classical solutions of the Euclidean Yang-Mills equation are constructed. The exact solutions presented here are characterized by infinite values of topological charges and therefore they are in striking contrast to the well-known instanton and meron solutions which have finite topological charges.     

Homogeneous anisotropic cosmological models with viscous fluid and magnetic field

The paper presents some exact solutions of Bianchi types I and III and Kantowski-Sachs cosmological models consisting of a dissipative fluid along with an axial magnetic field. A barytropic equation of state (p=), together with a pair of linear relations between the matter density (), the shear scalar (), and the expansion scalar () have been assumed for simplicity. The solutions are basically of two different types, one for the Bianchi I and the other for III and Kantowski-Sachs type. The presence of the magnetic field, however, does not change the fundamental nature of the initial singularity.