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

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.