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 classes of exact solutions in inflationary cosmology

The problem of determining a representation of the self-interaction potential in the form of a time dependence of the field potential energy which admits the existence of an inflationary regime and the transition of evolution to a Friedmann regime of asymptotic expansion is investigated within a cosmological model with a self-interacting scalar field. A variational formulation of the slow-roll concept is introduced, and, on the basis thereof, an exact solution is constructed for the evolution of the scale factor and the form of the self-interaction potential. A method based on representing the Einstein equations in the form of a linear second-order equation is developed for constructing and analyzing exact cosmological solutions of these equations. Selected types of potentials and the corresponding evolutions of the universe are investigated. Zh. éksp. Teor. Fiz. 114, 406–417 (August 1998)     

A local criterion for Weyl modules for groups of type A

Let G be a universal Chevalley group over an algebraically closed field and U⁻ be the subalgebra of generated by all divided powers X_α,m with α<0. We conjecture an algorithm to determine if , where F∈U⁻, ω is a dominant weight and is a highest weight vector of the Weyl module Δ(ω). This algorithm does not use bases of Δ(ω) and is similar to the algorithm for irreducible modules that involves stepwise raising the vector under investigation. For an arbitrary G, this conjecture is proved in one direction and for G of type A in both.     

Cosmological Models with Fractional Derivatives and FractionalAction Functional

Cosmological models of a scalar field with dynamical equations containing fractional derivatives or derived from the Einstein-Hilbert action of fractional Order, are constructed. A number of exact solutions to those equations of fractional cosmological models in both cases is given.     

Cosmological sigma model with non-minimal coupling to the target space

A homogeneous and isotropic Universe in the framework of a nonlinear sigma model with non-minimal coupling to the target space is considered. Preliminary investigation of a two-component model of this sort is conducted. Some solutions for this model are given. Perspectives and directions of development of such a sort of models are discussed.     

T-Spaces and Their Applications

The paper is a review of recent results on T-spaces and their applications. It is proved that T-spaces over a field of zero characteristic from a large class are finitely based; this implies the positive solution of the local Specht problem. If the characteristic of the base field is positive, then similar assertions do not hold. The negative solution of Maltsev's problem on the existence of a finite basis of all identities of an associative ring is given. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 18, Algebra, 2004.     

Magnetic monopole solutions of non-Abel gauge theory in an expanding universe

The equations of motion of Yang-Mills-Higgs fields are considered within the framework of the SO(3) model against the background of the gravitational fields of an expanding universe. Static and nonstatic Bogomolov-Prasad-Sommerfield magnetic monopole solutions are found for various laws of gravitational field evolution.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 67–71, August, 1984.     

Inverse problem of dyon and magnetic monopole dynamics

The problem of finding an electromagnetic field allowing the movement of dual-charged particles on the background of an arbitrary static space-time to have a priori given properties, is considered. A solution of this problem is given, and the degree of arbitrariness of the obtained solution is found. Two particular examples of application of the general results are considered.