Modified Jordan-Brans-Dicke theory with scalar current and the
  Eddington-Robertson gamma-parameter
  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 gamma that is significantly
different from the general relativistic value of unity. This contradicts
precision solar system measurements that tightly constrain gamma 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
gamma-parameter. In particular, a specific choice of the scalar current yields
gamma=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 modified gravity theory (MOG).
