MODIFIED JORDAN–BRANS–DICKE THEORY WITH SCALAR CURRENT AND THE EDDINGTON–ROBERTSON γ-PARAMETER

Abstract

The Jordan–Brans–Dicke theory of gravitation, which promotes the gravitational constant to a dynamical scalar field, predicts a value for the Eddington–Robertson post-Newtonian parameter γ that is significantly different from the general relativistic value of unity. This contradicts precision solar system measurements that tightly constrain γ around 1. We consider a modification of the theory, in which the scalar field is sourced explicitly by matter. We find that this leads to a modified expression for the γ-parameter. In particular, a specific choice of the scalar current yields γ = 1, just as in general relativity, while the weak equivalence principle is also satisfied. This result has important implications for theories that mimic Jordan–Brans–Dicke theory in the post-Newtonian limit in the solar system, including our scalar–tensor–vector gravity (STVG) modified gravity theory (MOG).