PPN Parameter $\gamma$ and Solar System Constraints of Massive Brans-Dicke Theories

TL;DR

This paper derives solar system constraints on the Brans-Dicke parameter for any scalar field mass, showing how these constraints vary with the field's mass, especially for moderate values.

Contribution

It provides a unified analysis of solar system constraints on Brans-Dicke theories considering arbitrary scalar field masses, bridging previous assumptions.

Findings

Constraints relax for scalar masses above 20 times the inverse astronomical unit.

For D parameter, constraints depend on the scalar field mass.

The analysis covers a continuous range of scalar field masses.

Abstract

Previous solar system constraints of the Brans-Dicke (BD) parameter $\omega$ have either ignored the effects of the scalar field potential (mass terms) or assumed a highly massive scalar field. Here, we interpolate between the above two assumptions and derive the solar system constraints on the BD parameter $\omega$ for {\it any} field mass. We show that for $\omega=O(1)$ the solar system constraints relax for a field mass $m \gsim 20 \times m_{AU}= 20\times 10^{-27}GeV$.