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

Understand

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.