Exponential Inflation with $F(R)$ Gravity
  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.
