Reheating in $R^2$ Palatini inflationary models

TL;DR

This paper investigates $R^2$ inflation within Palatini gravity, analyzing scalar field models and their constraints from scalar power spectrum data, highlighting the fine-tuning needed for high reheating temperatures.

Contribution

It extends $R^2$ Palatini inflation analysis to monomial and Higgs models, revealing tight constraints and fine-tuning requirements for reheating temperatures.

Findings

Scalar power spectrum constrains inflationary models.

High reheating temperature (~10^{15} GeV) requires fine-tuning.

Viable models exist within narrow parameter ranges.

Abstract

We consider $R^2$ inflation in the Palatini gravity assuming the existence of scalar fields, coupled to gravity in the most general manner. These theories, in the Einstein frame, and for one scalar field $h$, share common features with $K$ - inflation models. We apply this formalism for the study of popular inflationary models, whose potentials are monomials, $ V \sim h^{n} $, with $ n $ a positive even integer. We also study the Higgs model non-minimally coupled to gravity. Although these have been recently studied, in the framework of the Palatini approach, we show that the scalar power spectrum severely constrains these models. Although we do not propose a particular reheating mechanism, we show that the quadratic $ \sim h^2$ and the Higgs model can survive these constraints with a maximum reheating temperature as large as $ \sim 10^{15} \, GeV$, when reheating is instantaneous. However, this can be only attained at the cost of a delicate fine-tuning of couplings. Deviations from this fine-tuned values can still yield predictions compatible with the cosmological data, for couplings that lie in very tight range, giving lower reheating temperatures.