Energy-Momentum Squared Gravity: A Brief Overview

TL;DR

This paper reviews Energy-Momentum Squared Gravity (EMSG), a modified gravity theory with quadratic energy-momentum terms, exploring its cosmological implications, deviations from General Relativity, and potential to address early universe issues.

Contribution

It provides a comprehensive overview of EMSG, emphasizing its unique features, thermodynamic interpretation, and implications for cosmology and dense astrophysical objects.

Findings

EMSG can potentially resolve the initial singularity problem.

Deviations from GR are significant in high-density regions.

Thermodynamic formalism interprets matter creation in EMSG.

Abstract

In this work, we present a review of Energy-Momentum Squared Gravity (EMSG) -- more specifically, $f(R,T_{\mu\nu}T^{\mu\nu})$ gravity, where $R$ represents the Ricci scalar and $T_{\mu\nu}$ denotes the energy-momentum tensor. The inclusion of quadratic contributions from the energy-momentum components has intriguing cosmological implications, particularly during the Universe's early epochs. These effects dominate under high-energy conditions, enabling EMSG to potentially address unresolved issues in General Relativity (GR), such as the initial singularity and aspects of big-bang nucleosynthesis in certain models. The theory's explicit non-minimal coupling between matter and geometry leads to the non-conservation of the energy-momentum tensor, which prompts the investigation of cosmological scenarios through the framework of irreversible thermodynamics of open systems. By employing this formalism, we interpret the energy-balance equations within EMSG from a thermodynamic perspective, viewing them as descriptions of irreversible matter creation processes. Since EMSG converges to GR in a vacuum and differences emerge only in the presence of an energy-momentum distribution, these distinctions become significant in high-curvature regions. Therefore, deviations from GR are expected to be pronounced in the dense cores of compact objects. This review delves into these facets of EMSG, highlighting its potential to shed light on some of the fundamental questions in modern cosmology and gravitational theory.