A Born-Infeld-like f(R) gravity

TL;DR

This paper explores a modified f(R) gravity theory with a maximum curvature, revealing nonsingular cosmological solutions that include a bounce and transition to de Sitter and radiation-dominated phases.

Contribution

It introduces a Born-Infeld-like f(R) gravity model with a maximum curvature, analyzing its phase space and cosmological solutions.

Findings

The theory admits vacuum solutions of GR.

It features nonsingular bouncing cosmologies.

The universe transitions to de Sitter and radiation phases.

Abstract

Several features of an $f(R)$ theory in which there is a maximum value for the curvature are analyzed. The theory admits the vaccuum solutions of GR, and also the radiation evolution for the scale factor of the standard cosmological model. Working in the Jordan frame, a complete analysis of the phase space is performed, and its results supported with examples obtainted by numerical integration. In particular, we showed that theory has nonsingular cosmological solutions which after the bounce enter a phase of de Sitter expansion and subsequently relax to a GR-like radiation-dominated evolution.