1/R gravity and scalar-tensor gravity

We point out that extended gravity theories, the Lagrangian of which is an arbitrary function of scalar curvature R, are equivalent to a class of the scalar-tensor theories of gravity. The corresponding gravity theory is ω=0 Brans–Dicke gravity with a potential for the Brans–Dicke scalar field, which is not compatible with solar system experiments if the field is very light: the case when such modifications become important recently.