Renormalization-Group Improved Effective Potential for Interacting Theories with Several Mass Scales in Curved Spacetime

TL;DR

This paper develops a method to compute the renormalization group improved effective potential for theories with multiple mass scales in curved spacetime, with applications to phase transitions and back-reaction in cosmological models.

Contribution

It introduces a way to obtain the RG improved effective potential for theories with several mass scales in curved spacetime, extending previous flat spacetime methods.

Findings

RG improved effective potential explicitly calculated for Yukawa and scalar electrodynamics.

Demonstrated curvature-induced phase transitions in the Yukawa model.

Derived effective equations for $ ext{λ} ext{ϕ}^4$-theory in De Sitter space.

Abstract

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 $\lambda \varphi^4$-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 $\lambda \varphi^4$-theory on a De Sitter background.