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

TL;DR

This paper presents a scalar-tensor reformulation of $f(R)$ gravity theories using conformal transformations, revealing non-conservation of matter stress tensor and anomalous particle accelerations.

Contribution

It introduces a scalar-tensor representation of $f(R)$ theories with a non-zero kinetic term, highlighting matter interaction effects not previously detailed.

Findings

Matter stress tensor is not conserved in the model.

Test particles experience anomalous acceleration.

Scalar field interacts with matter, affecting dynamics.

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.