Dynamical Stability of Six-Dimensional Warped Brane-Worlds

TL;DR

This paper explores a six-dimensional warped brane-world model with two extra dimensions, analyzing its stability, radion properties, and implications for hierarchy problem and inflation, offering a novel extension of the Randall-Sundrum framework.

Contribution

It introduces a two-warped extra dimension model without negative tension branes, analyzing its stability and radion phenomenology, extending Randall-Sundrum mechanisms.

Findings

Radion can be stable or tachyonic depending on brane stress-energy.

Stable radion mass is in the milli-eV range, coupling gravitationally.

Model predicts a high energy scale suitable for inflation.

Abstract

We study a generalization of the Randall-Sundrum mechanism for generating the weak/Planck hierarchy, which uses two rather than one warped extra dimension, and which requires no negative tension branes. A 4-brane with one exponentially large compact dimension plays the role of the Planck brane. We investigate the dynamical stability with respect to graviton, graviphoton and radion modes. The radion is shown to have a tachyonic instability for certain models of the 4-brane stress-energy, while it is stable in others, and massless in a special case. If stable, its mass is in the milli-eV range, for parameters of the model which solve the hierarchy problem. The radion is shown to couple to matter with gravitational strength, so that it is potentially detectable by submillimeter-range gravity experiments. The radion mass can be increased using a bulk scalar field in the manner of Goldberger and Wise, but only to order MeV, due to the effect of the large extra dimension. The model predicts a natural scale of 10^{13} GeV on the 4-brane, making it a natural setting for inflation from the ultraviolet brane.