Gravitational Forces in the Randall-Sundrum Model with a Scalar Stabilizing Field

TL;DR

This paper investigates how a scalar stabilizing field in a five-dimensional Randall-Sundrum model affects gravitational forces between branes, showing that it can suppress unwanted enhancements and align predictions with experimental data.

Contribution

The study introduces a scalar stabilizing field into the Randall-Sundrum model and analyzes its impact on gravitational force calculations, providing conditions for compatibility with experiments.

Findings

Scalar field suppresses the mass factor $ o e^{- ext{constant} imes y_2}$

Agreement with experiment depends on the balance of exponential factors

Current data constrains the model's parameter space

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 $e^{2\beta y_2} \cong 10^{32}$ and thus produced gross disagreement with experiment. In this work we include a scalar stabilizing field $\phi$ and solve the coupled Einstein and scalar equations to leading order for the case where $\phi_{0}^2/M_{5}^3$ is small and the vacuum field $\phi_{0}(y)$ is a decreasing function of $y$. $f^T$ then grows a mass factor $e^{-\mu r}$ where however, $\mu$ is suppressed from its natural value, $\mathcal{O}(M_{Pl})$, by an exponential factor $e^{-(1+\lambda_b)\beta y_2}$, $\lambda_b > 0$. 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.