  Theories with a non-minimal coupling between the space-time curvature and
matter fields introduce an extra force due to the non-conservation of the
matter energy momentum. In the present work the theoretical consistency of such
couplings is studied using a scalar field Lagrangian to model the matter
content. The conditions that the coupling does not introduce ghosts, classical
instabilities or superluminal propagation of perturbations are derived. These
consistency conditions are then employed to rule out or severely restrict the
forms of the non-minimal coupling functions considered in the previous
literature. For example, a power-law coupling is viable only for sublinear
positive power of the curvature scalar.

General Relativity and Quantum Cosmology;Cosmology and Nongalactic Astrophysics;High Energy Physics - Theory