  We propose a gravitational theory in which the effective Lagrangian of the
gravitational field is given by an arbitrary function of the Ricci scalar, the
trace of the matter energy-momentum tensor, and the contraction of the Ricci
tensor with the matter energy-momentum tensor. The matter energy-momentum
tensor is generally not conserved, thus leading to the appearance of an
extra-force, acting on massive particles in a gravitational field. The
stability conditions of the theory with respect to local perturbations are also
obtained. The cosmological implications of the theory are investigated,
representing an exponential solution. Hence a Ricci tensor - energy-momentum
tensor coupling may explain the recent acceleration of the Universe, without
resorting to the mysterious dark energy.
