Conformal symmetry and cosmological vacuum in unified theories

The emergence of elementary-particle masses in Weinberg-Salam theory is con sidered for the case in which the interactions of matter fields with gravit y possess conformal symmetry. The Lagrangian of gravitation theory, with a Penrose-Chernikov-Tagirov term, plays the role of a Higgs potential for a s calar field. The value of a uniform sca;ar field is found from the Friedman n equations for the homogeneous universe. It is shown that this cosmologica l mechanism solves the problem of the vacuum density of a scalar field (rho (phi)(cosm) = 10(-34) rho(cr) is obtained instead of rho(phi)(Higgs) = 10(5 4) rho(cr)). The sigma-model version of Weinberg-Salam theory is obtained i n the flatspace limit.