Generalized Energy-Momentum-Squared Gravity in the Palatini Formalism

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.

20 pages, 6 figures, Accepted for publication in PRD

References in corpus (11)

• f(R,T) gravity
• Palatini Approach to Modified Gravity: f(R) Theories and Beyond
• Energy-Momentum Squared Gravity
• Bouncing Cosmologies in Palatini $f(R)$ Gravity
• A formal framework for a nonlocal generalization of Einstein's theory of gravitation
• Geodesic deviation, Raychaudhuri equation, and tidal forces in modified gravity with an arbitrary curvature-matter coupling
• A tensor instability in the Eddington inspired Born-Infeld Theory of Gravity
• Geodesic Deviation Equation in $f(T)$ gravity
• Low redshift constraints on energy-momentum-powered gravity models
• Jeans analysis in energy-momentum-squared gravity
• Geodesic Congruences in the Palatini f(R) Theory