Dynamical symmetry breaking due to radiative corrections in cosmology

Dynamical symmetry breaking in massless ^4 theory in curved spacetime with non-conformal coupling to the curvature is investigated. It is shown that in general the one-loop self-energy for such a field will involve a term of the form Rln|R^-2|, where R is the scalar curvature, and is a mass. This term can give rise to symmetry breaking. Two models, the Einstein universe and a spatially flat Robertson-Walker universe with a power-law expansion, are considered where this term is the sole contribution to the one-loop self-energy. In both cases a phase transition will occur at a critical value of the curvature. The form of the two-loop corrections to the self-energy and the limits of validity of the one-loop approximation are discussed.