Gravitational forces in the Randall-Sundrum model with a scalar stabilizing field

Abstract

We consider the problem of gravitational forces between point particles on the branes in a five-dimensional (5D) Randall-Sundrum model with two branes (at ${y}_{1}$ and ${y}_{2}$) and ${S}^{1}/{Z}_{2}$ symmetry of the fifth dimension. The matter on the branes is viewed as a perturbation on the vacuum metric and treated to linear order. In a previous work [R. Arnowitt and J. Dent, Phys. Rev. D 71, 124024 (2005).] it was seen that the trace of the transverse part of the 4D metric on the TeV brane, ${f}^{T}({y}_{2})$, contributed a Newtonian potential enhanced by ${e}^{2\ensuremath{\beta}{y}_{2}}\ensuremath{\cong}{10}^{32}$ and thus produced gross disagreement with the experiment. In this work we include a scalar stabilizing field $\ensuremath{\phi}$ and solve the coupled Einstein and scalar equations to leading order for the case where ${\ensuremath{\phi}}_{0}^{2}/{M}_{5}^{3}$ is small and the vacuum field ${\ensuremath{\phi}}_{0}(y)$ is a decreasing function of $y$. ${f}^{T}$ then grows a mass factor ${e}^{\ensuremath{-}\ensuremath{\mu}r}$ where, however, $\ensuremath{\mu}$ is suppressed from its natural value, $\mathcal{O}({M}_{Pl})$, by an exponential factor ${e}^{\ensuremath{-}(1+{\ensuremath{\lambda}}_{b})\ensuremath{\beta}{y}_{2}}$, ${\ensuremath{\lambda}}_{b}g0$. Thus agreement with the experiment depends on the interplay between the enhancing and decaying exponentials. Current data eliminates a significant part of the parameter space, and the Randall-Sundrum model will be sensitive to any improvements on the tests of the Newtonian force law at smaller distances. An example of coupling of the $\ensuremath{\phi}$ field to the Higgs field is examined and found to generally produce very small effects.