Renormalization-Group Improved Effective Potential for Finite Grand   Unified Theories in Curved Spacetime
  The renormalization-group improved effective potential ---to leading-log and in the linear curvature approximation--- is constructed for ``finite'' theories in curved spacetime. It is not trivial and displays a quite interesting, exponential-like structure ---in contrast with the case of flat spacetime where it coincides with the classical potential. Several possible cosmological applications, as curvature-induced phase transitions and modifications of the values of the gravitational and cosmological constants, are briefly discussed. 
E. Elizalde and S.D. Odintsov