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

## TL;DR

This paper derives formulas for inflationary slow-roll parameters in $f(R)$ gravity theories, enabling direct computation of key cosmological observables and showing consistency with current observational constraints.

## Contribution

It introduces a method to express slow-roll parameters directly in terms of $f(R)$, facilitating analysis of inflationary models and their non-Gaussianity predictions.

## Key findings

- Both models predict small non-Gaussianity contributions.
- Formulas allow direct calculation of $n_s$, $r$, and $ ext{f}_{ ext{NL}}^{ ext{equil}}$ from $f(R)$.
- Results agree with observational constraints.

## Abstract

In this paper we establish \textit{formulae} for the inflationary slow-roll parameters $\epsilon$, $\eta$ and $\zeta$ as functions of the Ricci scalar $R$ for $f(R)$ theories of gravity. As examples, we present the analytic and numerical solutions of $\epsilon$, $\eta$ and $\zeta$ 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 $\alpha$-Attractors. The highlight of our proposal is to rewrite the slow-roll parameters in terms of $f(R)$, which allows to find directly $n_{\rm s}$, $r$, $\alpha_{\rm s}$ and $f^{\text{equil}}_{\text{NL}}$ 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.