Exponential Inflation with $F(R)$ Gravity

Understand

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.