Natural Inflation with a periodic non-minimal coupling

Abstract

Natural inflation is an attractive model for primordial inflation, since the potential for the inflaton is of the pseudo Nambu-Goldstone form, $V(\varphi )={\Lambda }^4[1+\cos (\varphi /f)]$, and so is protected against radiative corrections. Successful inflation can be achieved if $f\gtrsim \mathrm{few}{M}_P$ and $\Lambda \sim m_{GUT}$ where $\Lambda$ 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 ${\gamma }^2(\varphi )R$, that respects the symmetry $\varphi \to \varphi +2\pi f$ 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 $M_p$.

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