Gravitational scalar field coupled directly to the Maxwell field and its   effect to solar-system experiments
  The effect of the massless gravitational scalar field assumed to couple directly to the Maxwell field to the solar-system experiments is estimated. We start with discussing the theoretical significances of this coupling. Rather disappointingly, however, we find that the scalar-field parameters never affect the observation in the limit of the geometric optics, indicating a marked difference from the well-known contribution through the spacetime metric. 
Yasunori Fujii and Misao Sasaki