On Non-Minimal Couplings to Gravity and Axion Isocurvature Bounds

For axions present during inflation, it has been shown that a non-minimal coupling ${\xi }_{\sigma }$ of the inflaton to gravity worsens isocurvature bounds, while a non-minimal coupling ${\xi }_{\rho }$ of the radial Peccei-Quinn field can alleviate them. We analyze the simultaneous presence of both couplings and determine when one effect dominates the other, in both the metric and Palatini formulations of gravity. The two tendencies interpolate smoothly, but introducing a non-minimal inflaton coupling reduces the viable interval of ${\xi }_{\rho }$ in which isocurvature bounds can be alleviated while avoiding backreaction on the inflationary dynamics. We illustrate our findings in Palatini Higgs inflation and Starobinsky inflation.