Born-Infeld gravity and its functional extensions

TL;DR

This paper explores extensions of Born-Infeld gravity, providing formal solutions and showing that non-singular bouncing cosmologies are common in these theories.

Contribution

It introduces a family of functional extensions of Born-Infeld gravity and derives generic solutions, highlighting the robustness of bouncing cosmologies.

Findings

Non-singular bouncing universes are generic in these theories.

A formal solution for the connection is provided.

An Einstein-like form of the field equations is derived.

Abstract

We investigate the dynamics of a family of functional extensions of the (Eddington-inspired) Born-Infeld gravity theory, constructed with the inverse of the metric and the Ricci tensor. We provide a generic formal solution for the connection and an Einstein-like representation for the metric field equations of this family of theories. For particular cases we consider applications to the early-time cosmology and find that non-singular universes with a cosmic bounce are very generic and robust solutions.