Modified gravity with a nonminimal gravitational coupling to matter

We consider modified theories of gravity with a direct coupling between matter and geometry, denoted by an arbitrary function in terms of the Ricci scalar. Because of such a coupling, the matter stress tensor is no longer conserved and there is an energy transfer between the two components. By solving the conservation equation, we argue that the matter system should gain energy in this interaction, as demanded by the second law of thermodynamics. In a cosmological setting, we show that although this kind of interaction may account for cosmic acceleration, this latter together with the direction of the energy transfer constrain the coupling function.