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.

arXiv comment20 pages, 6 figures, Accepted for publication in PRD

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• Gravitationally induced matter creation in scalar-tensor $f(R,T_{\mu \nu }{T}^{\mu \nu })$ gravity
• Cosmological models in scale-independent energy-momentum squared gravity
• Energy-Momentum Squared Gravity: A Brief Overview
• Relativistic structure of charged quark stars in energy-momentum squared gravity
• Shadow behavior of an EMSG charged black hole
• Dynamical analysis of logarithmic energy-momentum squared gravity
• Evolution of Spherical Overdensities in Energy-Momentum-Squared Gravity
• Weak field and slow motion limits in energy-momentum powered gravity
• Relativistic binary systems in scale-independent energy-momentum squared gravity
• Big Bang Nucleosynthesis constraints on the Energy-Momentum Squared Gravity: The ${\mathbb{T}}^2$ model
• Baryon asymmetry from higher-order matter contributions in gravity
• Gödel-type universes in energy-momentum-squared gravity
• Cosmological perturbations in the energy-momentum squared gravity theory: constraints from gravitational wave standard sirens and redshift space distortions
• Light bending and gravitational lensing in energy-momentum-squared gravity