Energy-Momentum Squared Gravity

TL;DR

This paper introduces a covariant extension of Einstein's gravity with a $T_{\alpha\beta}T^{\alpha\beta}$ term, leading to a non-singular bouncing universe and exact solutions for charged black holes, with implications for early universe cosmology.

Contribution

It develops a new gravity theory incorporating energy-momentum squared terms, providing exact black hole solutions and resolving the initial singularity through a cosmological bounce.

Findings

Existence of a maximum energy density and minimum scale factor.

The universe undergoes a bounce, avoiding the Big Bang singularity.

The theory supports a sequence of cosmological eras with a significant role for the cosmological constant.

Abstract

A new covariant generalization of Einstein's general relativity is developed which allows the existence of a term proportional to $T_{\alpha\beta}T^{\alpha\beta}$ in the action functional of the theory ($T_{\alpha\beta}$ is the energy-momentum tensor). Consequently the relevant field equations are different from general relativity only in the presence of matter sources. In the case of a charged black hole, we find exact solutions for the field equations. Applying this theory to a homogeneous and isotropic space-time, we find that there is a maximum energy density $\rho_{\text{max}}$, and correspondingly a minimum length $a_{\text{min}}$, at early universe. This means that there is a bounce at early times and this theory avoids the existence of an early time singularity. Moreover we show that this theory possesses a true sequence of cosmological eras. Also, we argue that although in the context of the standard cosmological model the cosmological constant $\Lambda$ does not play any important role in the early times and becomes important only after the matter dominated era, in this theory the "repulsive" nature of the cosmological constant plays a crucial role at early times for resolving the singularity.