Energy-Momentum Squared Gravity

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.

References in corpus (5)

• f(R,T) gravity
• Quantum Nature of the Big Bang: Improved dynamics
• Are f(R) dark energy models cosmologically viable ?
• Generalized energy conditions in Extended Theories of Gravity
• Stability of a non-minimally conformally coupled scalar field in F(T) cosmology

Cited by in corpus (29)

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• Bouncing cosmologies with dark matter and dark energy
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• Generalized Energy-Momentum-Squared Gravity in the Palatini Formalism
• Low redshift constraints on energy-momentum-powered gravity models
• Jeans analysis in energy-momentum-squared gravity
• Temporally Varying Universal Gravitational "Constant" and Speed of Light in Energy Momentum Squared Gravity
• Emergent Universe from Energy-Momentum Squared Gravity
• Noether Symmetry Approach in Energy-Momentum Squared Gravity
• Lessons from black hole quasinormal modes in modified gravity
• Thermodynamics and Perturbative Analysis of Some Newly Developed $\mathcal{F}(R,L_m,T)$ Theories Under the Scenario of Conserved Energy-momentum Tensor
• Non-exotic traversable wormholes in $f\left(R,T_{ab}{T}^{ab}\right)$ gravity
• Constraining Energy-Momentum-Squared Gravity by binary pulsar observations
• Cosmological models in scale-independent energy-momentum squared gravity
• Cosmological implications of Rastall-$f(R)$ theory
• Compact Objects admitting Finch-Skea Symmetry in $f(\mathcal{R},T^2)$ Gravity
• Relativistic structure of charged quark stars in energy-momentum squared gravity
• The phase space analysis of modified gravity (MOG)
• Non-Singular Bouncing Model in Energy Momentum Squared Gravity
• Impact of Charge on Gravastars in $f(\mathfrak{R},{\mathcal{T}}^2)$ Gravity
• Complexity Factor for Static Cylindrical System in Energy-momentum Squared Gravity
• Non-minimal Energy-momentum squared gravity
• Observational constraints on nonlinear matter extensions of general relativity: Separable trace power models
• Gravitational Collapse in Energy-momentum squared gravity: Nature of singularities
• Gödel-type universes in energy-momentum-squared gravity
• Matter perturbations in Einstein dark energy model
• Light bending and gravitational lensing in energy-momentum-squared gravity
• From Special Relativity to embedded generators in Cartan subalgebras of rank-4 spin algebras