Generic slow-roll and non-gaussianity parameters in f(R) theories

In this paper we establish formulae for the inflationary slow-roll parameters epsilon, η and ζ as functions of the Ricci scalar R for f(R) theories of gravity. As examples, we present the analytic and numerical solutions of epsilon, η and ζ as functions of the number of e-folds N in two important instances: for the Starobinsky model and for a f(R) reconstruction of the α-Attractors. The highlight of our proposal is to rewrite the slow-roll parameters in terms of f(R), which allows to find directly ns, r, αs and fequilNL as functions of R itself. We obtain that both models indicate a small contribution to the non-Gaussianity parameters, which are in good agreement with current observational constraints.