Cosmological aspects of the gravitational interaction of a scalar field in the affine-metric theory of gravitation

Abstract

The gravitational interaction of a scalar field, with allowance for the possible influence of the torsional and nonmetric nature of space-time, is investigated within the framework of the affine-metric theory of gravitation. The equations of the theory are derived from the variational principle. It is shown that in an affine-metric space, the combined Lagrangian of the gravitational and scalar fields with conformal coupling is reduced to the Lagrangian of the system of gravitational and axion fields in the general theory of relativity. All of the exact general solutions of the consistent system of equations of gravitational and scalar (massless) fields in the affine-metric space under consideration are obtained for all types of homogeneous Friedmann cosmological models, with the initial singularity being removed from some of them. Homogeneous, anisotropic cosmological models, for which all of the exact general solutions are also obtained, are investigated. Some of these models are nonsingular, and the effect of isotropization due to the torsional and nonmetric nature of space-time occurs for many of them.