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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 non universal 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 3 in the linear coupling case. In the linear case, we have an universal coupling constant $α_0$ and two coupling constants $α_T$ and $α_G$ 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 $α_0=(1.01\pm23.7)\times 10^{-5}$, $α_T=(0.00\pm24.5)\times 10^{-6}$, $α_G=(-1.46\pm12.0)\times 10^{-5}$, at the 99.5 \% C.L.