Interpretation of f(R,T) gravity in terms of a conserved effective fluid

Abstract

In the present work, we introduce a novel approach to study [Formula: see text] gravity theory from a different perspective. Here, [Formula: see text] denotes the trace of energy–momentum tensor ( EMT ) of matter fluids. The usual method (as discussed in the literature) is to choose an [Formula: see text] function and then solve for the resulted Friedman equations. Nevertheless, our aim here is, without loss of generality, to reformulate a particular class of [Formula: see text] gravity models in which the Einstein–Hilbert action is promoted by an arbitrary function of the trace of 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 EMT is automatically conserved. As we shall see, adopting such a point of view (at least) in [Formula: see text] gravity is accompanied by two significant points. On one hand, [Formula: see text] 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 ( 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 [Formula: see text] gravity, there is a possibility that a perfect fluid could effectively behave as a modified Chaplygin gas with four free parameters.