  The classical observational cosmological tests (Hubble diagram, count of
sources, etc.) are considered for a homogeneous and isotropic model of the
Universe in the framework of the five-dimensional Projective Unified Field
Theory in which gravitation is described by both space-time curvature and some
hypothetical scalar field (sigma-field). It is shown that the presence of the
sigma-field can essentially affect conclusions obtained from the cosmological
tests. The surface brightness-redshift relation can be used as a critical test
for sigma-field effects. It seems reasonable to say that the available
experimental data testify that the sigma-field decreases with time. It is
concluded that the spatial curvature is positive or negative depending on
whether the mass density is larger or smaller than some critical parameter
which is smaller than the critical density and can even take negative values.
It is shown that the increase in the number of the observational cosmological
parameters as compared to the standard Friedmann model can essentially
facilitate coordination of the existing observational data.
