  A homogeneous and isotropic model of the Universe is considered in the
framework of the five-dimensional Projective Unified Field Theory in which the
gravitation is described by both space-time curvature and some hypothetical
scalar field (sigma-field). We propose a generation method for obtaining exact
solutions. New exact Friedmann-like solutions for a dust model and inflationary
solutions are found. It is shown that in the framework of exponential type
inflation we obtain a natural explanation of why at present we do not observe
sigma-field effects or why these effects are negligible.
