Eddington's theory of gravity and its progeny

Abstract

We resurrect Eddington's proposal for the gravitational action in the presence of a cosmological constant and extend it to include matter fields. We show that the Newton-Poisson equation is modified in the presence of sources and that charged black holes show great similarities with those arising in Born-Infeld electrodynamics coupled to gravity. When we consider homogeneous and isotropic space-times we find that there is a minimum length (and maximum density) at early times, clearly pointing to an alternative theory of the Big Bang. We thus argue that the modern formulation of Eddington's theory, Born-Infeld gravity, presents us with a novel, non-singular description of the Universe.