The symmetric tensor field in the relativistic theory of gravitation

The system of a self-gravitating scalar field is frequently used in inflationary cosmological models. In the present paper we study a more complicated system containing an extra linear tensor field _ik=_ki with minimal coupling. We determine five of the six free parameters that occur in the most general expression for the actionS of this field. In doing so we assume that in flat space-time the field _ik must be invariant under gauge transformations. In a special case theS found becomes a known expression for the action of a massless tensor field _ik. We compute the metric energy-momentum tensor that determines the contribution of _ik to the Einstein equations. We also exhibit the equations of motion of _ik in curved space-time.Translated fromAstrofizika, Vol. 38, No. 3, 1995.