Quantum corrections to quartic inflation with a non-minimal coupling: metric vs. Palatini

TL;DR

This paper compares quantum corrections in quartic inflation models with non-minimal coupling between metric and Palatini gravity, showing that quantum effects do not alter the potential's flatness.

Contribution

It provides a detailed analysis of quantum corrections in both metric and Palatini formalisms, deriving beta-functions and effective potentials in curved space.

Findings

Quantum corrections depend on the formalism used.

The flatness of the inflationary potential remains unchanged by quantum effects.

Differences arise from the order of perturbation theory in the Einstein frame.

Abstract

We study models of quartic inflation where the inflaton field $\phi$ is coupled non-minimally to gravity, $\xi \phi^2 R$, and perform a study of quantum corrections in curved space-time at one-loop level. We specifically focus on comparing results between the metric and Palatini theories of gravity. Transformation from the Jordan to the Einstein frame gives different results for the two formulations and by using an effective field theory expansion we derive the appropriate $\beta$-functions and the renormalisation group improved effective potentials in curved space for both cases in the Einstein frame. In particular, we show that in both formalisms the Einstein frame depends on the order of perturbation theory but that the flatness of the potential is unaltered by quantum corrections.