Cosmological implications of Born-Infeld-$f(R)$ gravity

TL;DR

This paper explores a modified Born-Infeld gravity theory with an added $f(R)$ term, analyzing its cosmological implications and how different auxiliary metric structures influence cosmic acceleration and singularities.

Contribution

It introduces a novel combination of Born-Infeld and $f(R)$ gravity, analyzing its effects on cosmic acceleration and singularity formation in a simplified conformal framework.

Findings

Modified auxiliary metric functions can lead to Big Rip singularities.

Certain structures induce Little Rip dark energy models.

The theory provides insights into cosmic acceleration without matter.

Abstract

A modified Born-Infeld gravitation theory with a $f\left(R\right)$ function being added to the determinant action is analyzed from a cosmological viewpoint. The corresponding accelerating dynamics are studied in a simplified conformal approach without matter. Three different structures for the auxiliary metric function are analyzed, with the aim to establish a deeper understanding of the role of this function in cosmology. After performing the analysis, it is seen that, by modifying the auxiliary metric function, a Big Rip singularity or either a Little Rip dark energy model may arise.