Functional evaluation of spontaneous symmetry breaking in an open Universe.

In many applications of gauge theories the phenomenon of spontaneous symmetry breaking is utilized to account for the masses which various particles may acquire. The present investigation is concerned with the determination of the vacuum expectation value of a conformally invariant self-interacting scalar field in an open Friedmann universe. The scalar field phi, with conformal invariance, in a cosmological space is considered. It is shown that the functional approach, associated with the method of the stationary phase and the dimensional regularization, makes it possible to determine the vacuum expectation value of the field phi up to at least one loop.