Cosmological Vacuum in Unified Theories

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 $\rho_\phi^{Higgs}=10^{54}\rho_{cr}$.