Constraining massless dilaton theory at Solar system scales with the planetary ephemeris INPOP

We expose the phenomenology of the massless dilaton theory in the Solar system for a nonuniversal quadratic coupling between the scalar field which represents the dilaton and the matter. Modified post-Newtonian equations of motion of an N-body system and the light time travel are derived from the action of the theory. We use the physical properties of the main planets of the Solar system to reduce the number of parameters to be tested to three in the linear coupling case. In the linear case, we have a universal coupling constant α0 and two coupling constants αT and αG related, respectively, to the telluric bodies and to the gaseous bodies. We then use the planetary ephemeris, INPOP19a, in order to constrain these constants. We succeeded to constrain the linear coupling scenario, and the constraints read α0=(1.01±23.7)×10-5, αT=(0.00±24.5)×10-6, αG=(-1.46±12.0)×10-5, at the 99.5% C.L.