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 $e^{2\beta y_2}\cong 10^{32}$ and thus produced gross disagreement with experiment. In this work we include a scalar stabilizing field $\varphi$ and solve the coupled Einstein and scalar equations to leading order for the case where ${\varphi }_0^2/M_5^3$ is small and the vacuum field ${\varphi }_0(y)$ 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.

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References in corpus (2)

• Higher order corrections to the Newtonian potential in the Randall-Sundrum model
• Gravitational Forces in the Brane World

Cited by in corpus (3)

• Transition between nuclear and quark-gluon descriptions of hadrons and light nuclei
• Graviton localization and Newton's law for brane models with a non-minimally coupled bulk scalar field
• Non-minimal Coupling Branes