Jumping from Metric f(R) to Scalar-Tensor Theories and the relations between their post-Newtonian Parameters

TL;DR

This paper explores the equivalence between $f(R)$ gravity and scalar-tensor theories, deriving post-Newtonian parameters to help constrain $f(R)$ models using observational data.

Contribution

It provides a new derivation of post-Newtonian parameters for $f(R)$ gravity based on scalar-tensor equivalence, correcting previous results.

Findings

Derived explicit expressions for $eta$ and $\gamma$ in terms of scalar field mass.

Showed how to use these parameters to constrain $f(R)$ theories with observations.

Revealed differences from earlier literature in post-Newtonian parameter calculations.

Abstract

We review the dynamical equivalence between $f(R)$ gravity in the metric formalism and scalar-tensor gravity, and use this equivalence to deduce the post-Newtonian parameters $\gamma$ and $\beta$ for a $f(R)$ theory, obtaining a result that is different with respect to that known in the literature. Then, we obtain explicit expressions of these paremeters in terms of the mass of the scalar field (or, differently speaking, the mass of the additional scalar degree of freedom associated to a $f(R)$ theory) which can be used to constrain $f(R)$ gravity by means of current observations.