Nearly Starobinsky inflation from modified gravity
  We study inflation induced by (power-low) scalar curvature corrections to
General Relativity. The class of inflationary scalar potentials
$V(\sigma)\sim\exp[n\,\sigma]$, $n$ general parameter, is investigated in the
Einsein frame and the corresponding actions in the Jordan frame are derived. We
found the conditions for which these potentials are able to reproduce viable
inflation according with the last cosmological data and lead to large scalar
curvature corrections which emerge only at a mass scale larger than the Planck
mass. Cosmological constant may appear or be set equal to zero in the Jordan
frame action without changing the behaviour of the model during inflation.
Moreover, polynomial corrections to General Relativity are analyzed in detail.
When de Sitter space-time emerges as an exact solution of the models, it is
necessary to use perturbative equations in the Jordan framework to study their
dynamics during the inflation. In this case, we demonstrate that the Ricci
scalar decreases after a correct amount of inflation, making the models
consistent with the observable evolution of the universe.
