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

Abstract

In this paper 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 nonzero effective sound speed. We compute the corresponding effective Jeans length and show that it is approximately equal to the fundamental length of the theory ${R}_{*}={\ensuremath{\kappa}}^{1/2}{G}^{\ensuremath{-}1/2}$, where $\ensuremath{\kappa}$ 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 against collapse into a black hole, showing that it is approximately equal to the fundamental mass ${M}_{*}={\ensuremath{\kappa}}^{1/2}{c}^{2}{G}^{\ensuremath{-}3/2}$, and we show that the maximum density attainable inside stable compact stars is roughly equal to the fundamental density ${\ensuremath{\rho}}_{*}={\ensuremath{\kappa}}^{\ensuremath{-}1}{c}^{2}$, 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 $\ensuremath{\kappa}<G{R}^{2}$. In the case of neutron stars this implies that $\ensuremath{\kappa}<{10}^{\ensuremath{-}2}\text{ }\text{ }{\mathrm{m}}^{5}\text{ }{\mathrm{kg}}^{\ensuremath{-}1}\text{ }{\mathrm{s}}^{\ensuremath{-}2}$, 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.