Modified Gravity with a Non-minimal Gravitational Coupling to Matter

Abstract

We consider modified theories of gravity with a direct coupling between matter and geometry, denoted by an arbitrary function in terms of the Ricci scalar. Due to such a coupling, the matter stress tensor is no longer conserved and there is an energy transfer between the two components. By solving the conservation equation, we argue that the matter system should gain energy in this interaction, as demanded by the second law of thermodynamics. In a cosmological setting, we show that although this kind of interaction may account for cosmic acceleration, this latter together with direction of the energy transfer constrain the coupling function.

13 Pages, Two figures, Accepted for publication in Physical Review D

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• Anisotropic strange star with Tolman-Kuchowicz metric under $f(R,T)$ gravity
• Recovering a MOND-like acceleration law in mimetic gravity
• Conservation laws in theories with universal gravity/matter coupling
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• Effects of quantum fluctuations of metric on the universe
• Neutron stars in $f(R,T)$ gravity with conserved energy-momentum tensor: Hydrostatic equilibrium and asteroseismology
• Cosmic strings in $f\left(R,L_m\right)$ gravity
• Non-minimal Gravitational Coupling of Phantom and Big Rip Singularity
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• Compact stellar models in modified gravity
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• Ether and Relativity
• Reexamining RHDE Models in FRW Universe with two IR cut-off with redshift parametrization
• White dwarf cooling in $f(R,T)$ gravity