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

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