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

## TL;DR

This paper introduces a new perspective on $f(R,T)$ gravity by reformulating it in terms of a conserved effective fluid, providing clearer physical interpretation and analyzing various models with constant or related effective properties.

## Contribution

The paper presents a novel approach to $f(R,T)$ gravity by expressing it through a conserved effective fluid, enhancing physical understanding and exploring specific models with unique effective properties.

## Key findings

- Effective fluid formulation leads to automatic conservation of EMT.
- Models with constant effective density, pressure, or EoS are analyzed.
- Perfect fluid can behave as a modified Chaplygin gas with four parameters.

## Abstract

In the present work we introduce a novel approach to study $f({\sf R},{\sf T})$ gravity theory from a different perspective. Here, ${\sf T}$ denotes the trace of energy-momentum tensor ({\sf EMT}) of matter fluids. The usual method (as discussed in the literature) is to choose an $h({\sf T})$ function and then solve for the resulted Friedman equations. Nevertheless, our aim here is, without loss of generality, to reformulate a particular class of $f({\sf R},{\sf T})$ 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 $f({\sf R},{\sf T})$ gravity is accompanied by two significant points. On one hand, $h({\sf T})$ 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 $f({\sf R},{\sf T})$ gravity, there is a possibility that a perfect fluid could effectively behave as a modified Chaplygin gas with four free parameters.