Inflation with $R_{(\alpha\beta)}$ terms in the Palatini formulation

TL;DR

This paper explores how general Ricci tensor terms in the Palatini formulation influence inflation, showing that such terms can suppress the tensor-to-scalar ratio without affecting the scalar spectrum, with specific results for quadratic and cubic cases.

Contribution

It introduces a method to incorporate general Ricci tensor terms into inflation models within the Palatini framework, analyzing their effects on observable inflation parameters.

Findings

Quadratic Ricci terms can suppress tensor-to-scalar ratio arbitrarily.

Cubic Ricci terms can suppress the ratio by up to 2/9.

Scalar spectral index can experience significant changes in the cubic case.

Abstract

We study inflation with the most general non-degenerate gravitational action that depends on the symmetric part of the Ricci tensor coupled to a scalar field in the Palatini formulation of gravity. We use field redefinitions to shift the effect of the Ricci terms from gravity to the scalar field, and apply the result to slow-roll inflation. As examples, we consider actions quadratic and cubic in the Ricci tensor. In the quadratic case the results are similar to the case $R+\alpha R^2$ that has been studied earlier: the tensor-to-scalar ratio $r$ can be suppressed by an arbitrary amount, while the scalar spectrum is unaffected. In the cubic case, $r$ can be suppressed by at most a factor of $2/9$, and the change in the scalar spectral index $n_s$ can be large.