On the non-minimal gravitational coupling to matter

TL;DR

This paper explores the equivalence between a generalized scalar-tensor theory with non-minimal matter coupling and $f(R)$ gravity, enabling analysis of weak-field limits and PPN parameters to address debates in $f(R)$ theories.

Contribution

It establishes an equivalence between a generalized scalar-tensor model with non-minimal coupling and $f(R)$ gravity, facilitating weak-field analysis.

Findings

Derived expressions for PPN parameters $eta$ and $\gamma$ in the generalized model.

Provided insights into the weak-field limit of $f(R)$ theories.

Addressed the debate on the weak-field behavior of $f(R)$ gravity.

Abstract

The connection between $f(R)$ theories of gravity and scalar-tensor models with a "physical" metric coupled to the scalar field is well known. In this work, we pursue the equivalence between a suitable scalar theory and a model that generalises the $f(R)$ scenario, encompassing both a non-trivial scalar curvature term and a non-minimum coupling of the scalar curvature and matter. This equivalence allows for the calculation of the PPN parameters $\beta$ and $\gamma$ and, eventually, a solution to the debate concerning the weak-field limit of $f(R)$ theories.