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 previous work \cite{ad} 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 $e^{2βy_2} \cong 10^{32}$ and thus produced gross disagreement with experiment. In this work we include a scalar stabilizing field $ϕ$ and solve the coupled Einstein and scalar equations to leading order for the case where $ϕ_{0}^2/M_{5}^3$ is small and the vacuum field $ϕ_{0}(y)$ is a decreasing function of $y$. $f^T$ then grows a mass factor $e^{-μr}$ where however, $μ$ is suppressed from its natural value, $\mathcal{O}(M_{Pl})$, by an exponential factor $e^{-(1+λ_b)βy_2}$, $λ_b > 0$. Thus agreement with 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.