# Born-Infeld inspired modifications of gravity

## TL;DR

This paper reviews Born-Infeld inspired modifications of gravity, highlighting their ability to regularize singularities and their potential applications in cosmology and black hole physics, without requiring quantum gravity effects.

## Contribution

It provides a comprehensive overview of the motivations, formulations, results, and open problems of Born-Infeld inspired gravity theories, emphasizing their regularization capabilities.

## Key findings

- Regularize gravitational singularities effectively
- Enable non-singular cosmological models
- Show observational viability of these theories

## Abstract

General Relativity has shown an outstanding observational success in the scales where it has been directly tested. However, modifications have been intensively explored in the regimes where it seems either incomplete or signals its own limit of validity. In particular, the breakdown of unitarity near the Planck scale strongly suggests that General Relativity needs to be modified at high energies and quantum gravity effects are expected to be important. This is related to the existence of spacetime singularities when the solutions of General Relativity are extrapolated to regimes where curvatures are large. In this sense, Born-Infeld inspired modifications of gravity have shown an extraordinary ability to regularise the gravitational dynamics, leading to non-singular cosmologies and regular black hole spacetimes in a very robust manner and without resorting to quantum gravity effects. This has boosted the interest in these theories in applications to stellar structure, compact objects, inflationary scenarios, cosmological singularities, and black hole and wormhole physics, among others. We review the motivations, various formulations, and main results achieved within these theories, including their observational viability, and provide an overview of current open problems and future research opportunities.