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

TL;DR

This paper calculates Post-Newtonian parameters for Brans-Dicke gravity in multiple dimensions, revealing how experimental constraints impact the theory's parameters and linking extra dimensions to scalar fields like the dilaton.

Contribution

It extends Post-Newtonian parameter calculations to higher dimensions in Brans-Dicke gravity and analyzes the physical viability of the theory under experimental constraints.

Findings

Gamma depends on omega and becomes negative in the Jordan frame, indicating non-physicality.

Extra dimensions can be interpreted as a massless scalar dilaton.

Gamma behavior in the Einstein frame aligns with string theory predictions.

Abstract

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 gamma, which measures the amount of spacetime curvature per unit mass, becomes a function of omega, the coefficient of the scalar kinetic term in the Brans-Dicke Lagrangian. Experiment has placed strong constraints on gamma which require that omega become 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 gamma as constrained by experiment replicates that which is predicted by string theory.