Parameterized post-Newtonian coefficients for Brans-Dicke gravity with d + 1 dimensions

We present calculations of post-Newtonian parameters for Brans-Dicke tensor-scalar gravity in an arbitrary number of compact extra dimensions in both the Jordan and Einstein conformal frames. We find that the parameter γ, which measures the amount of spacetime curvature per unit mass, becomes a function of ω, the coefficient of the scalar kinetic term in the Brans-Dicke Lagrangian. Experiment has placed strong constraints on γ which require that ω becomes negative in the Jordan frame for any number of extra dimensions, highlighting that this formulation is not physical. We also confirm the well-known result that a compact extra dimension can be equivalently viewed as a massless scalar 'dilaton.' In the Einstein frame, we find that the behavior of γ as constrained by experiment replicates that which is predicted by string theory.