  The renormalization-group improved effective potential for an arbitrary
renormalizable massless gauge theory in curved spacetime is found,thus
generalizing Coleman-Weinberg's approach corresponding to flat space.Some
explicit examples are considered,among of them:scalar self-interacting
theory,scalar electrody namics,the asymptotically-free SU(2) gauge model,and
the SU(5) GUT theory. The possibility of curvature-induced phase transitions is
analyzed.It is shown that such a phase transition may take place in a SU(5)
inflationary universe.The inclusion of quantum gravity effects isbriefly
discussed.
