Solar System constraints to nonminimally coupled gravity

We extend the analysis of Chiba et al. [Phys. Rev. D 75, 124014 (2007)] of Solar System constraints on f(R) gravity to a class of nonminimally coupled (NMC) theories of gravity. These generalize f(R) theories by replacing the action functional of general relativity with a more general form involving two functions f1(R) and f2(R) of the Ricci scalar curvature R. While the function f1(R) is a nonlinear term in the action, analogous to f(R) gravity, the function f2(R) yields a NMC between the matter Lagrangian density Lm and the scalar curvature. The developed method allows for obtaining constraints on the admissible classes of functions f1(R) and f2(R), by requiring that predictions of NMC gravity are compatible with Solar System tests of gravity. Then we consider a NMC model which accounts for the observed accelerated expansion of the Universe and we show that such a model cannot be constrained by the present method.