Lessons from $T_{\mu }^{\mu }$ on inflation models: two-loop renormalization of $\eta$ in the scalar QED

Abstract

A non-minimal coupling $\eta$ has been attracting growing interest particularly in the context of inflation models, though its quantum nature is not clear yet. We study the renormalization of a non-minimal coupling in the scalar quantum electrodynamics (QED). We find $no$ inhomogeneous term of the renormalization group equation (RGE) at the two-loop level. This is similar to other theories, where an inhomogeneous term of the RGE appears only at a higher-loop order: e.g., four-loop order in $\lambda {\varphi }^4$ theory.

Comments: 11+28 pages, 10 figures; massive revision, calculation corrected, conclusion changed