Interpretation of $f(\mathsf{R},\mathsf{T})$ gravity in terms of a conserved effective fluid

Abstract

In the present work we introduce a novel approach to study $f(\mathsf{R},\mathsf{T})$ gravity theory from a different perspective. Here, $\mathsf{T}$ denotes the trace of energy-momentum tensor ({\sf EMT}) of matter fluids. The usual method (as discussed in the literature) is to choose an $h(\mathsf{T})$ function and then solve for the resulted Friedman equations. Nevertheless, our aim here is, without loss of generality, to reformulate a particular class of $f(\mathsf{R},\mathsf{T})$ gravity models in which the Einstein-Hilbert action is promoted by an arbitrary function of the trace of {\sf EMT}. The strategy is the redefinition of the equation of motion in terms of the components of an effective fluid. We show that in this case the {\sf EMT} is automatically conserved. As we shall see, adopting such a point of view (at least) in $f(\mathsf{R},\mathsf{T})$ gravity is accompanied by two significant points. On one hand, $h(\mathsf{T})$ function is chosen based upon a physical concept and on the other, we clearly understand the overall or effective behavior of matter in terms of a conserved effective fluid. To illustrate the idea, we study some models in which different physical properties for the effective fluid is attributed to each model. Particularly, we discuss models with constant effective density, constant effective pressure and constant effective equation of state ({\sf EoS}) parameter. Moreover, two models with a relation between the effective density and the effective pressure will be considered. An elegant result is that in $f(\mathsf{R},\mathsf{T})$ gravity, there is a possibility that a perfect fluid could effectively behave as a modified Chaplygin gas with four free parameters.

21 pages, 3 figures

References in corpus (10)

• The Confrontation between General Relativity and Experiment
• f(R,T) gravity
• Hubble parameter measurement constraints on the redshift of the deceleration-acceleration transition, dynamical dark energy, and space curvature
• Generalized curvature-matter couplings in modified gravity
• Thermodynamic interpretation of the generalized gravity models with geometry - matter coupling
• Dark Matter From f(R,T) Gravity
• Emergent Universe with Exotic Matter
• Consequences of energy conservation violation: Late time solutions of $\Lambda (T)CDM$ subclass of $f(R,T)$ gravity using dynamical system approach
• Late-time cosmological evolution of a general class of f(R, T) gravity with minimal curvature-matter coupling
• Bouncing solutions from generalized EoS

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