TY - JOUR AU - Beltran Jimenez, J. AU - Heisenberg, L. AU - Olmo, G. J. AU - Rubiera-Garcia, D. PY - 2018 DA - 2018// TI - Born-Infeld inspired modifications of gravity T2 - Phys. Rep. JO - Physics Reports SP - 1 EP - 129 VL - 727 PB - Elsevier Science Bv KW - Born-Infeld gravity KW - Astrophysics KW - Black holes KW - Cosmology KW - Early universe KW - Compact objects KW - Singularities AB - 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. SN - 0370-1573 UR - http://arxiv.org/abs/1704.03351 UR - https://doi.org/10.1016/j.physrep.2017.11.001 DO - 10.1016/j.physrep.2017.11.001 LA - English N1 - WOS:000425482900001 ID - BeltranJimenez_etal2018 ER -