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 BransDicke 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. The problem of dark energy is the problem of Ω: Ω = ρM/8πGH 2 < 1. Since ΩM can be regarded as the ratio of the right-hand-side of the Einstein equation (matter) to the lefthand-side of the Einstein equation (curvature=gravity), in order to make Ω = 1 one requires either (i) introduction of new form of matter(energy): dark energy or (ii) modification of gravity at large. Recent attempts to modify gravity by introducing R term [1,2] fall in the latter possibility: 1 S = 1 2κ ∫