Natural Inflation with a periodic non-minimal coupling

Guillem Simeon, Alessio Notari, Ricardo Z Ferreira

Abstract: Natural inflation is an attractive model for primordial inflation, since the potential for the inflaton is of the pseudo Nambu-Goldstone form, V(ϕ)=Λ4[1+cos(ϕ/f)], and so is protected against radiative corrections. Successful inflation can be achieved if f≳fewMP and Λ∼mGUT where Λ can be seen as the strong coupling scale of a given non-abelian gauge group. However, the latest observational constraints put natural inflation in some tension with data. We show here that a non-minimal coupling to gravity γ2(ϕ)R, that respects the symmetry ϕ→ϕ+2πf and has a simple form, proportional to the potential, can improve the agreement with cosmological data. Moreover, in certain cases, satisfactory agreement with the Planck 2018 TT, TE, EE and low P data can be achieved even for a periodicity scale of approximately Mp.