Eddington-inspired Born-Infeld gravity: astrophysical and cosmological constraints

TL;DR

This paper derives astrophysical and cosmological constraints on Eddington-inspired Born-Infeld gravity, showing that the theory's parameters are tightly limited by the existence and properties of compact objects like neutron stars.

Contribution

It provides the first detailed astrophysical constraints on the fundamental length and mass scales of Eddington-inspired Born-Infeld gravity, surpassing previous cosmological bounds.

Findings

The effective Jeans length is approximately equal to the fundamental length scale R_*.

The critical mass for collapse into a black hole is about M_*.

Maximum density inside stable compact stars is roughly the fundamental density ρ_*.

Abstract

In this letter we compute stringent astrophysical and cosmological constraints on a recently proposed Eddington-inspired Born-Infeld theory of gravity. We find, using a generalized version of the Zel'dovich approximation, that in this theory a pressureless cold dark matter fluid has a non-zero effective sound speed. We compute the corresponding effective Jeans length and show that it is approximately equal to the fundamental length of the theory $R_*=\kappa^{1/2} G^{-1/2}$, where $\kappa$ is the only additional parameter of theory with respect to general relativity and $G$ is the gravitational constant. This scale determines the minimum size of compact objects which are held together by gravity. We also estimate the critical mass above which pressureless compact objects are unstable to colapse into a black hole, showing that it is approximately equal to the fundamental mass $M_* = \kappa^{1/2} c^2 G^{-3/2}$, and we show that the maximum density attainable inside stable compact stars is roughly equal to the fundamental density $\rho_*=\kappa^{-1} c^2$, where $c$ is the speed of light in vacuum. We find that the mere existence of astrophysical objects of size $R$ which are held together by their own gravity leads to the constraint $\kappa < G R^2$. In the case of neutron stars this implies that $\kappa < 10^{-2} \, {\rm m^5 \, kg^{-1} \, s^{-2}}$, a limit which is stronger by about 10 orders of magnitude than big bang nucleosynthesis constraints and by more than 7 orders of magnitude than solar constraints.