An Alternative f (R, T) Gravity Theory and the Dark Energy Problem

TL;DR

This paper explores a modified gravity theory based on an arbitrary function of Ricci scalar R and stress-energy tensor trace T, addressing the dark energy problem by ensuring energy-momentum conservation and analyzing cosmological implications.

Contribution

It determines part of the function f(R,T) by enforcing stress-energy conservation and studies the resulting cosmological and energy condition implications.

Findings

Part of the f(R,T) function is fixed by conservation laws.

Cosmological solutions are derived for homogeneous and isotropic models.

Energy conditions are analyzed in the context of this modified gravity.

Abstract

Recently, a generalized gravity theory was proposed by Harko etal where the Lagrangian density is an arbitrary function of the Ricci scalar R and the trace of the stress-energy tensor T, known as F(R,T) gravity. In their derivation of the field equations, they have not considered conservation of the stress-energy tensor. In the present work, we have shown that a part of the arbitrary function f(R,T) can be determined if we take into account of the conservation of stress-energy tensor, although the form of the field equations remain similar. For homogeneous and isotropic model of the universe the field equations are solved and corresponding cosmological aspects has been discussed. Finally, we have studied the energy conditions in this modified gravity theory both generally and a particular case of perfect fluid with constant equation of state.