The $\gamma$ parameter in Brans-Dicke-like (light-)Scalar-Tensor theory with a universal scalar/matter coupling and a new decoupling scenario

TL;DR

This paper investigates the post-Newtonian parameter gamma in Brans-Dicke-like Scalar-Tensor theories with scalar/matter coupling, revealing conditions under which gamma equals one and its implications for solar system phenomenology.

Contribution

It provides a new analysis of gamma in scalar-tensor theories using a perfect fluid formalism and explores a decoupling scenario where gamma equals one.

Findings

Gamma can be positive, zero, or negative depending on the coupling function.

Theories with gamma=1 and beta=1 mimic general relativity in the solar system.

Scalar-tensor theories without coupling always predict gamma<1.

Abstract

The post-Newtonian parameter $\gamma$ resulting from a universal scalar/matter coupling is investigated in Brans-Dicke-like Scalar-Tensor theories where the scalar potential is assumed to be negligible. Conversely to previous studies, we use a perfect fluid formalism in order to get the explicit scalar-field equation. It is shown that the metric can be put in its standard post-Newtonian form. However, it is pointed out that $1-\gamma$ could be either positive, null or negative for finite value of $\omega_0$, depending on the coupling function; while Scalar-Tensor theories without coupling always predict $\gamma<1$ for finite value of $\omega_0$. Moreover, regardless the value of $\omega_0$, the subclass of theories satisfying $\gamma=1$ and $\beta=1$ surprisingly leads to almost the same phenomenology as general relativity in the solar system.