Solar System tests of a scalar-tensor gravity with a general potential: Insensitivity of light deflection and Cassini tracking

In the work of Hohmann et al. [Phys. Rev. D 88, 084054 (2013)], the authors worked out the parametrized post-Newtonian (PPN) parameters $\gamma$ and $\beta$ of a scalar-tensor theory with an arbitrary coupling function and a generic potential, and they found that these two PPN parameters depend on the radial distance $r$ from the Sun, $\gamma (r)$ and $\beta (r)$. Based on the assumption that measurements on the PPN parameters can be characterized by the shortest distance to the Sun, the authors obtained their best constraints on the model parameters of the scalar-tenor theory by light deflection observation and the Cassini tracking experiment. However, as the authors stated, this approach might not be rigorous. In the present work, we physically model astronomical observations and physical experiments by calculating the null and timelike geodesics in the scalar-tensor theory. We show that, contrary to the results in the previous work, the light deflection and the Cassini tracking cannot distinguish the scalar-tensor theory from general relativity. We also investigate the additional advances in perihelia caused by the largest correction of the scalar field on the Newtonian potential. Since this correction has a Yukawa-like form, we obtain very much improved lower bounds on the model parameters by using current upper limits on the Yukawa parameters.