Generalized Energy-Momentum-Squared Gravity in the Palatini Formalism

TL;DR

This paper investigates a generalized energy-momentum squared gravity theory within the Palatini formalism, deriving field equations, analyzing weak field and cosmological behaviors, and identifying conditions for bouncing cosmological solutions.

Contribution

It introduces the most general form of Palatini EMSG, derives the equations of motion, and finds new bouncing solutions with specific conditions on parameters.

Findings

Derived the field equations for generalized Palatini EMSG.

Explored the weak field limit and obtained a generalized Poisson equation.

Identified conditions under which bouncing cosmological solutions occur.

Abstract

We study the generalized version of energy-momentum squared gravity (EMSG) in the Palatini formalism. This theory allows the existence of a scalar constructed with energy-momentum tensor as $T_{\alpha\beta}T^{\alpha\beta}$ in the generic action of the theory. We study the most general form of this theory in the Palatini framework and present the underlying field equations. The equations of motion of a massive test particle have been derived. The weak field limit of the theory is explored and the generalized version of the Poisson equation is obtained. Moreover, we explore the cosmological behavior of the theory with emphasis on bouncing solutions. Some new bouncing solutions for the specific Palatini EMSG model given by the Lagrangian density $\mathcal{L}=R+\beta R^2+\eta T_{\mu\nu}T^{\mu\nu}$ are introduced. We show that only the case $\eta>0$ can lead to viable cosmic bounce.