Scalar Field Assisted $f(R)$ Gravity Inflation

TL;DR

This paper explores how a scalar field can assist $f(R)$ gravity models, specifically modified $R^2$ gravity, to produce inflation consistent with observational data, with a focus on spectral index and tensor-to-scalar ratio.

Contribution

It demonstrates that scalar field assisted $f(R)$ gravity can achieve inflationary predictions compatible with observations, extending the $R^2$ inflation model.

Findings

Spectral index matches that of $R^2$ gravity.

Scalar-to-tensor ratio is reduced compared to $R^2$ inflation.

Model aligns with Planck 2015 and BICEP2/Keck-Array data.

Abstract

In this paper we investigate the inflationary dynamics of an $f(R)$ gravity in the presence of a canonical scalar field. We specifically choose the cosmological evolution to be a quasi-de Sitter evolution and also the $f(R)$ gravity is assumed to be a modified version of the $R^2$ gravity. We investigate which scalar field potential can produce the quasi-de Sitter evolution for the choice of the $f(R)$ gravity we made, and also we study in detail the inflationary dynamics of the resulting theory. As we demonstrate, the spectral index is identical to the one corresponding to the ordinary $R^2$ gravity, while the scalar-to-tensor ratio is found to be smaller than the $R^2$ inflation one consequently, compatibility with both the Planck 2015 and BICEP2/Keck-Array data is achieved.