  The unification of the Einstein theory of gravity with a conformal invariant
version of the standard model for electroweak interaction without the Higgs
potential is considered. In this theory, a module of the Higgs field is
absorbed by the scale factor component of metric so that the evolution of the
Universe and the elementary particle masses have one and the same cosmological
origin and the flat space limit corresponds to the $\sigma$-model version of
the standard model. The red shift formula and Hubble law are obtained under the
assumption of homogeneous matter distribution. We show that the considered
theory leads to a very small vacuum density of the Higgs field
$\rho_\phi^{Cosmic}=10^{-34}\rho_{cr}$ in contrast with the theory with the
Higgs potential $\rho_\phi^{Higgs}=10^{54}\rho_{cr}$.
