  We use the $\zeta$-function regularization method to evaluate the finite
temperature 1-loop effective potential for $\phi^4$ theory in the Godel
spacetime. It is used to study the effects of temperature and curvature
coupling on the cosmological phase transition in the rotational spacetime. From
our results the critical temperature of symmetry restoration, which is a
function of curvature coupling and magnitude of spacetime rotation, can be
determined.
