Solar System Constraints on Scalar Tensor Theories with Non-Standard Action

We compute the Post-Newtonian parameter (PPN),$γ$, for scalar-tensor gravity theory when the action functional for the scalar field is a non-standard one, namely the Dirac-Born-Infeld (DBI) type action, used in the literature for a tachyon field. We investigate two different cases (Linear and conformal couplings) when the scalar field is non-minimally coupled to gravity via the scalar curvature. We find that the PPN parameter $γ$, which measures the amount of space curvature per unit rest mass, becomes a function of the effective mass of the scalar field. Using this PPN parameter, we calculate the time delay $Δτ$ for the signal to travel the round trip distance bertween a ground based antenna and a reflector placed in a spacecraft which is produced due to the grvitational field of Sun. We use this $Δτ$ to compare our result with that obtained by the Cassini mission and derive the constraints on the model parameters.