Slow-roll inflation in Palatini $F(R)$ gravity

Abstract

We study single field slow-roll inflation in the presence of $F(R)$ gravity in the Palatini formulation. In contrast to metric $F(R)$, when rewritten in terms of an auxiliary field and moved to the Einstein frame, Palatini $F(R)$ does not develop a new dynamical degree of freedom. However, it is not possible to solve analytically the constraint equation of the auxiliary field for a general $F(R)$. We propose a method that allows us to circumvent this issue and compute the inflationary observables. We apply this method to test scenarios of the form $F(R)=R+\alpha R^n$ and find that, as in the previously known $n=2$ case, a large $\alpha$ suppresses the tensor-to-scalar ratio $r$. We also find that models with $F(R)$ increasing faster than $R^2$ for large $R$ suffer from numerous problems.

arXiv comment20 pages, 5 figures, 1 table, matches the published version

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• Non-minimal Coupling Inflation and Dark Matter under the ${\mathbb{Z}}_3$ Symmetry
• Slow-roll inflation in $f\left(R,T,R_{ab}{T}^{ab}\right)$ gravity