(Multi-field) Natural Inflation and Gravitational Waves

We provide a detailed study of natural inflation with a periodic non-minimal coupling, which is a well-motivated inflationary model that admits an explicit UV completion. We demonstrate that this construction can satisfy the most recent observational constraints from Planck and the BICEP/Keck collaborations. We also compute the corresponding relic gravitational wave background due to tensor perturbations and show that future space-borne interferometers, such as DECIGO, BBO and ALIA, may be able to detect it. Next, we extend this analysis and establish the validity of these results in a multi-field model featuring an additional $R^2$ term in the action, which allows us to interpolate between natural and scalaron (a.k.a.~Starobinsky) inflation. We investigate the conditions under which the aforementioned future interferometers will have the capability to differentiate between pure natural inflation and natural-scalaron inflation. The latter analysis could open the door to distinguishing between single-field and multi-field inflation through gravitational wave observations in more general contexts.