# $f(R)$ constant-roll inflation

## TL;DR

This paper extends constant-roll inflation models to $f(R)$ gravity, deriving exact solutions and identifying parameter regions consistent with current observational constraints on primordial perturbations.

## Contribution

It generalizes constant-roll inflation to $f(R)$ gravity, providing exact expressions and analyzing observationally viable parameter spaces.

## Key findings

- Derived exact expressions for scalaron potential and inflation dynamics in $f(R)$ gravity.
- Identified parameter regions compatible with latest observational constraints.
- Extended constant-roll inflation models beyond General Relativity.

## Abstract

The previously introduced class of two-parametric phenomenological inflationary models in General Relativity in which the slow-roll assumption is replaced by the more general, constant-roll condition is generalized to the case of $f(R)$ gravity. A simple constant-roll condition is defined in the original Jordan frame, and exact expressions for a scalaron potential in the Einstein frame, for a function $f(R)$ (in the parametric form) and for inflationary dynamics are obtained. The region of the model parameters permitted by the latest observational constraints on the scalar spectral index and the tensor-to-scalar ratio of primordial metric perturbations generated during inflation is determined.