Exponential Inflation with $F(R)$ Gravity

TL;DR

This paper explores an exponential inflation model within vacuum $F(R)$ gravity, deriving conditions for realization, calculating inflationary parameters, and confirming compatibility with recent observational data.

Contribution

It introduces a reconstruction method for $F(R)$ gravity that can realize exponential inflation and derives general formulas for slow-roll and observational indices without assuming smallness.

Findings

Model is compatible with Planck and BICEP2/Keck-Array data.

Provides general formulas for inflationary indices in $F(R)$ gravity.

Identifies parameter ranges where the model fits observational constraints.

Abstract

In this paper we shall consider an exponential inflationary model in the context of vacuum $F(R)$ gravity. By using well-known reconstruction techniques, we shall investigate which $F(R)$ gravity can realize the exponential inflation scenario at leading order in terms of the scalar curvature, and we shall calculate the slow-roll indices and the corresponding observational indices, in the context of slow-roll inflation. We also provide some general formulas of the slow-roll and the corresponding observational indices in terms of the $e$-foldings number. In addition, for the calculation of the slow-roll and of the observational indices, we shall consider quite general formulas for which the assumption that all the slow-roll indices are much smaller than unity, is not necessary to hold true. Finally, we investigate the phenomenological viability of the model by comparing it with the latest Planck and BICEP2/Keck-Array observational data. As we demonstrate, the model is compatible with the current observational data for a wide range of the free parameters of the model.