Dynamical Stability of Six-Dimensional Warped Brane-Worlds

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 1013 GeV on the 4-brane, making it a natural setting for inflation from the ultraviolet brane.