Solar System constraints on scalar tensor theories with nonstandard action

Abstract

We compute the parametrized post-Newtonian (PPN), $\ensuremath{\gamma}$, for scalar tensor gravity theory when the action functional for the scalar field is a nonstandard one, namely, the Dirac-Born-Infeld type action, used in the literature for a tachyon field. We investigate two different cases (linear and conformal couplings) when the scalar field is nonminimally coupled to gravity via the scalar curvature. We find that the PPN parameter $\ensuremath{\gamma}$, 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 $\ensuremath{\Delta}\ensuremath{\tau}$ for the signal to travel the round-trip distance between a ground-based antenna and a reflector placed in a spacecraft which is produced due to the gravitational field of the Sun. We use this $\ensuremath{\Delta}\ensuremath{\tau}$ to compare our result with that obtained by the Cassini mission and derive the constraints on the model parameters.