Natural inflation in Palatini $F(R)$

TL;DR

This paper explores how embedding natural inflation within Palatini $F(R)$ gravity, specifically with $F(R) = R + eta R^n$, can reconcile the model with observational data, highlighting the significance of the parameter $n$ for viability.

Contribution

It demonstrates that natural inflation's compatibility with observations improves when formulated in Palatini $F(R)$ gravity with specific $n$ values, especially near $n=2$.

Findings

Models with $7/4 \, extless \, n \, extless \, 2$ fit observational data well.

Models with $n > 2$ only partially agree with data, approaching $n=2$.

Embedding in Palatini $F(R)$ gravity extends the viability of natural inflation models.

Abstract

$F(R)$ Palatini gravity provides a robust framework for constructing viable inflationary potentials. In this study, we examine natural inflation and show that its consistency with observational data can be restored when the model is embedded within $F(R)$ Palatini gravity, specifically for $F(R) = R + \alpha R^n$ with $7/4 \lesssim n \leq 2$. For completeness, we also demonstrate that models with $n > 2$ do not yield comparable improvements, achieving partial agreement with the data only in the limit $n \rightarrow 2$.