Matter may matter

Abstract

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.