FRW cosmology in F(R, T) gravity

In this paper, we consider a theory of gravity with a metric-dependent torsion namely the F(R, T) gravity, where R is the curvature scalar and T is the torsion scalar. We study the geometric root of such theory. In particular we give the derivation of the model from the geometrical point of view. Then we present the more general form of F(R, T) gravity with two arbitrary functions and give some of its particular cases. In particular, the usual F(R) and F(T) gravity theories are particular cases of the F(R, T) gravity. In the cosmological context, we find that our new gravitational theory can describe the accelerated expansion of the Universe.