Quadratic, Higgs and hilltop potentials in Palatini gravity

Abstract

In this work, we study the theory of inflation with the non-minimally coupled quadratic, standard model Higgs, and hilltop potentials, through ξϕ2R term in Palatini gravity. We first analyze observational parameters of the Palatini quadratic potential as functions of ξ for the high-N scenario. In addition to this, taking into account that the inflaton field ϕ has a non-zero vacuum expectation value v after inflation, we display observational parameters of well-known symmetry-breaking potentials. The types of potentials considered are the Higgs potential and its generalizations, namely hilltop potentials in the Palatini formalism for the high-N scenario and the low-N scenario. We calculate inflationary parameters for the Palatini Higgs potential as functions of v for different ξ values, where inflaton values are both ϕ > v and ϕ < v during inflation, as well as calculating observational parameters of the Palatini Higgs potential in the induced gravity limit for high-N scenario. We illustrate differences between the Higgs potential’s effect on ξ versus hilltop potentials, which agree with the observations for the inflaton values for ϕ < v and ξ, in which v ≪ 1 for both these high and low N scenarios. For each considered potential, we also display ns − r values fitted to the current data given by the Keck Array/BICEP2 and Planck collaborations.