Issues in Palatini ${\mathcal{R}}^2$ inflation: Bounds on the Reheating Temperature

Abstract

We consider ${\mathcal{R}}^2$-inflation in Palatini gravity, in the presence of scalar fields coupled to gravity. 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 single-field 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. With ${\mathcal{R}}^2$-terms coupled to gravity as $\sim \alpha {\mathcal{R}}^2$, with $\alpha$ constant, the instantaneous reheating temperature $T_{ins}$, is bounded by $T_{ins}\le 0.290m_{Planck}/{\alpha }^{1/4}$, with the upper bound being saturated for large $\alpha$. For such large $\alpha$ need go beyond slow-roll to calculate reliably the cosmological parameters, among these the end of inflation through which $T_{ins}$ is determined. In fact, as inflaton rolls towards the end of inflation point, the quartic in the velocity terms, unavoidable in Palatini gravity, play a significant role and can not be ignored. The values of $\alpha$, and other parameters, are constrained by cosmological data, setting bounds on the inflationary scale $M_s\sim 1/\sqrt{\alpha }$ and the reheating temperature of the Universe.

arXiv comment35 pages, 18 figures, PDFLaTeX, text and references added, typos corrected

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