Direct Smooth Reconstruction of Inflationary Models in f(R) gravity

Starting from parametrization of scalar perturbations generated during inflation in terms of $e$--fold $N$ and using an approach recently developed by Starobinsky, dubbed "direct smooth reconstruction", we show that, in the slow--roll approximation, it is possible to reconstruct the inflation potential in the Einstein frame and its corresponding Lagrangian $f(R)$ model