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

TL;DR

This paper investigates slow-roll inflation within Palatini $F(R)$ gravity, introducing a new method to compute inflationary observables and analyzing specific models, revealing how certain $F(R)$ forms influence tensor-to-scalar ratios.

Contribution

It presents a novel approach to analyze inflation in Palatini $F(R)$ gravity, especially for complex $F(R)$ functions, and explores the impact of different $F(R)$ forms on inflationary predictions.

Findings

Large $eta$ suppresses tensor-to-scalar ratio $r$.

Models with $F(R)$ growing faster than $R^2$ face issues.

The method effectively handles complex $F(R)$ functions in inflation analysis.

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.