$\gamma$ Parameter and Solar System constraint in Chameleon Brans Dick Theory

TL;DR

This paper examines the post-Newtonian parameter in the Chameleon-Brans-Dicke theory, demonstrating it can satisfy solar system constraints and produce a large Brans-Dicke parameter consistent with previous bounds.

Contribution

It introduces a general form of the post-Newtonian parameter and effective gravitational constant in the Chameleon-Brans-Dicke framework, showing compatibility with solar system tests.

Findings

Chameleon-Brans-Dicke model satisfies solar system constraints.

The model yields an $\omega$ parameter of order 10^4.

Compatibility with previous experimental bounds.

Abstract

The post Newtonian parameter is considered in the Chameleon-Brans-Dicke frame. In the first step, the general form of this parameter and also effective gravitational constant is obtained. An arbitrary function for $f(\Phi)$, which indicates the coupling between matter and scalar field, is introduced to investigate validity of solar system constraint. It is shown that Chameleon-Brans-Dicke model can satisfy the solar system constraint and gives us an $\omega$ parameter of order $10^4$, which is in comparable to the constraint which has been indicated in {\cite{17-a}}.