Natural in ation with a periodic non-minimal coupling to gravity

Abstract

Natural Inflation is a model for inflation where the potential of the inflaton is V (φ) = ∧4[1 + cos(φ/ ∫ )] and thus exhibits a discrete shift symmetry φ - φ + 2π∫ . Successful inflation can be chieved if ∫ > ∼ few MPl and ∧ ∼ mGUT ∼ 1016 GeV. However, the latest observational constraints put Natural Inflation in tension with data. We propose in this letter the introduction of a non-minimal coupling to gravity Υ2(φ)R that respects the characteristic shift symmetry and the periodicity of the potential. We show that the agreement with cosmological data can be substantially improved, obtaining a scale ∧ ∼ 1015 ∼ 1016 GeV, and furthermore, in certain cases, successful inflation can be achieved even for a periodicity scale smaller than the Planck scale