(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 spaceborne 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 R2 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.