Gravitational effect on effective potential

Abstract

We study effective potentials to see the possibility of symmetry breaking in general curved space-time. The one-loop effective potential is computed to first order in the scalar curvature $R$ in $\ensuremath{\lambda}{\ensuremath{\varphi}}^{4}$ theory and for scalar electrodynamics. In particular, in the case of negative curvature the phase structure depends on the magnitude of the curvature in scalar electrodynamics.