# Born-Infeld-$f(R)$ gravity with de Sitter solutions

## TL;DR

This paper explores a modified gravity model combining Born-Infeld and $f(R)$ theories in the Palatini formulation, analyzing its solutions and showing it admits de Sitter space as a vacuum solution.

## Contribution

It introduces a novel Born-Infeld-$f(R)$ gravity model with explicit $f(R)$ functions and demonstrates the existence of de Sitter solutions within this framework.

## Key findings

- Both models reduce to the same form under conformal transformation.
- The model admits de Sitter vacuum solutions.
- Explicit analysis for $f(R)$ with positive and negative powers.

## Abstract

In this study, we consider the Born--Infeld-$f(R)$ gravity in which the $f(R)$ term enters directly into the square root in the Palatini formulation. We shortly analyzed this model for an explicit $f(R)$ function which includes positive and negative powers of the curvature scalar. We also show that both the ordinary Born--Infeld-$f(R)$ and this modification reduce to the same gravitational action form under the conformal approach. Then we consider the existence of a maximally symmetric vacuum solution for the gravitational field equations and find the de Sitter solution for this modified model.