$\beta$-function formalism for inflationary models with a non minimal coupling with gravity

TL;DR

This paper extends the $eta$-function formalism to include non-minimal coupling between the inflaton and gravity, showing how to reduce to minimal coupling and exploring the universal attractor at strong coupling.

Contribution

It introduces a method to incorporate non-minimal coupling into the $eta$-function formalism and analyzes conditions for the universal attractor to be evaded.

Findings

Reduction to minimally coupled theories via field redefinition

Universal attractor at strong coupling explained through a new field

Potential to evade the universal attractor in generalized models

Abstract

We discuss the introduction of a non minimal coupling between the inflaton and gravity in terms of the recently proposed $\beta$-function formalism for inflation\cite{Binetruy:2014zya}. Via a field redefinition we reduce to the case of minimally coupled theories. The universal attractor at strong coupling has a simple explanation in terms of the new field. Generalizations are discussed and the possibility of evading the universal attractor is shown.