Born–Infeld inspired modifications of gravity

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.

On gravitational waves in Born-Infeld inspired non-singular cosmologies

“…This theory and its extensions have been extensively studied in the literature due to their many applications in cosmology, black hole physics and astrophysics [9] (see [10] for a recent review on this class of theories). A prominent feature of this theory is that it indeed succeeds in avoiding cosmological and black hole singularities in traditional scenarios such as FLRW cosmologies [8,11] and spherically symmetric configurations with electromagnetic [12] and scalar fields [13].…”

Kinetic theory of Jean instability in Eddington-inspired Born–Infeld gravity

“…On th one hand these are motivated by their capability to explain the dynamics of self-gravitating systems and the accelerated expansion of the Universe without resorting to dark matter and/or dark energy [5][6][7][8][9][10][11][12][13][14]. On the other hand, they are also motivated by the fact that GR is not the quantum theory of gravity needed to describe the spacetime near the singularities, which, as is well known, seemingly cannot be avoided [15].…”

“…One of the most interesting features is that EiBI is equivalent to GR in the vacuum while it introduces modifications in dense matter environments, where GR is experimentally not well probed. EiBI is able to describe, with only a single extra parameter (κ), astrophysical objects such as the Sun [19] and the internal structure of compact objects [20][21][22][23][24][25][26], and the cosmological expansion of the Universe [22,[27][28][29][30][31] (for comprehensive reviews see [7,12] and the references therein).…”

The Mimetic Born-Infeld Gravity: The Primordial Cosmos and Spherically Symmetric Solutions

“…It should be stressed that for the original EiBI gravity as well as the mimetic Born-Infeld gravity, in which only the symmetric part of the Ricci tensor is considered in the action, there is a projective gauge symmetry and the torsion field in the affine connection can be removed by a gauge fixing procedure. A symmetric affine connection can be chosen after the corresponding gauge fixing and an initial torsionless assumption is in general not necessary [34]. Furthermore, the theory is expected to be free of ghosts since the theory is formulated within the Palatini approach in which the equations of motion contain derivatives (naturally) up to only second order.…”

“…See references [34,35] for a review of Born-Infeld theories of gravity and the mimetic gravity, respectively.…”