Comments on Scalar-Tensor Representation of $f(R)$ Theories

Abstract

We propose a scalar-tensor representation of $f(R)$ theories with use of conformal transformations. In this representation, the model takes the form of the Brans-Dicke model with a potential function and a non-zero kinetic term for the scalar field. We show that due to interaction of the scalar field with matter systems, the corresponding matter stress tensor is not conserved and test particles experience an anomalous acceleration.