1/R gravity and Scalar-Tensor Gravity

Abstract

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 are important recently.