  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.
