FRW models in the conformal frame of f(R) gravity

We study the late time evolution of Friedmann-Robertson-Walker (FRW) models with a perfect fluid matter source and a scalar field arising in the conformal frame of f(R) theories nonminimally coupled to matter. We prove using the approach of dynamical systems, that equilibria corresponding to non-negative local minima for V are asymptotically stable. We show that if γ, the parameter of the equation of state is larger than one, then there is a transfer of energy from the fluid to the scalar field and the latter eventually dominates. The results are valid for a large class of nonnegative potentials without any particular assumptions about the behavior of the potential at infinity.