General slow-roll inflation in $f(R)$ gravity under the Palatini approach

TL;DR

This paper investigates slow-roll inflation within $f(R)$ gravity using the Palatini formalism, showing how a scalar field can drive inflation and how gravitational modifications affect observable parameters like spectral index and tensor-to-scalar ratio.

Contribution

It introduces a framework for analyzing slow-roll inflation in Palatini $f(R)$ gravity with a scalar field, deriving general slow-roll parameters and examining their impact on cosmological observables.

Findings

Inflation requires non-traceless matter in Palatini $f(R)$ gravity.

The effective potential modifies inflation dynamics and predictions.

Differences in spectral index and tensor-to-scalar ratio are identified.

Abstract

Slow-roll inflation is analyzed in the context of modified gravity within the Palatini formalism. As shown in the literature, inflation in this framework requires the presence of non-traceless matter, otherwise it does not occur just as a consequence of the non-linear gravitational terms of the action. Nevertheless, by including a single scalar field that plays the role of the inflaton, slow-roll inflation can be performed in these theories, where the equations lead to an effective potential that modifies the dynamics. We obtain the general slow-roll parameters and analyze a simple model to illustrate the differences introduced by the gravitational terms under the Palatini approach, and the modifications on the spectral index and the tensor to scalar ratio predicted by the model.