Renormalization-group improved effective potential for interacting theories with several mass scales in curved spacetime

The renormalization group (RG) is used in order to obtain the RG improved effective potential in curved spacetime. This potential is explicitly calculated for the Yukawa model and for scalar electrodynamics, i.e. theories with several (namely, more than one) mass scales, in a space of constant curvature. Using the λφ-theory on a general curved spacetime as an example, we show how it is possible to find the RG improved effective Lagrangian in curved spacetime. As specific applications, we discuss the possibility of curvature induced phase transitions in the Yukawa model and the effective equations (back-reaction problem) for the λφ-theory on a De Sitter background. E-mail: eli @ ebubecm1.bitnet E-mail: odintsov @ ebubecm1.bitnet. On leave from: Tomsk Pedagogical Institute, 634041 Tomsk, Russian Federation.