Eddington's theory of gravity and its progeny

TL;DR

This paper revisits Eddington's gravity theory, extends it to include matter, and demonstrates it predicts a non-singular early universe with a minimum length, offering an alternative to the Big Bang.

Contribution

It extends Eddington's gravitational action to matter fields and shows it leads to a non-singular cosmological model with a minimum length scale.

Findings

Modified Newton-Poisson equation with sources

Charged black holes resemble Born-Infeld electrodynamics

Existence of a minimum length and maximum density in early universe

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.