On the non-minimal gravitational coupling to matter

The connection between f(R) theories of gravity and scalar-tensor models with a 'physical' metric coupled to the scalar field is well known. In this work, we pursue the equivalence between a suitable scalar theory and a model that generalizes the f(R) scenario, encompassing both a non-minimal scalar curvature term and a non-minimum coupling of the scalar curvature and matter. This equivalence allows for the calculation of the PPN parameters beta and gamma and, eventually, a solution to the debate concerning the weak-field limit of f(R) theories.