Inflation with $R^2$ term in the Palatini formalism

TL;DR

This paper investigates how adding an $R^2$ term in $F(R)$ gravity within the Palatini formalism influences inflation, notably reducing the tensor-to-scalar ratio without altering scalar perturbations.

Contribution

It demonstrates that in the Palatini formalism, the $R^2$ term can suppress the tensor-to-scalar ratio independently of scalar spectrum constraints.

Findings

The $R^2$ term lowers the effective inflaton potential height.

Adjusting $eta$ allows suppression of tensor-to-scalar ratio $r$.

Scalar perturbation spectrum remains unaffected.

Abstract

We study scalar field inflation in $F(R)$ gravity in the Palatini formulation of general relativity. Unlike in the metric formulation, in the Palatini formulation $F(R)$ gravity does not introduce new degrees of freedom. However, it changes the relations between existing degrees of freedom, including the inflaton and spacetime curvature. Considering the case $F(R)=R+\alpha R^2$, we find that the $R^2$ term decreases the height of the effective inflaton potential. By adjusting the value of $\alpha$, this mechanism can be used to suppress the tensor-to-scalar ratio $r$ without limit in any scalar field model of inflation without affecting the spectrum of scalar perturbations.