Dynamical Stability of Six-Dimensional Warped Brane-Worlds

We study a generalization of the Randall-Sundrum mechanism for generating theweak/Planck hierarchy, which uses two rather than one warped extra dimension,and which requires no negative tension branes. A 4-brane with one exponentiallylarge compact dimension plays the role of the Planck brane. We investigate thedynamical stability with respect to graviton, graviphoton and radion modes. Theradion is shown to have a tachyonic instability for certain models of the4-brane stress-energy, while it is stable in others, and massless in a specialcase. If stable, its mass is in the milli-eV range, for parameters of the modelwhich solve the hierarchy problem. The radion is shown to couple to matter withgravitational strength, so that it is potentially detectable bysubmillimeter-range gravity experiments. The radion mass can be increased usinga bulk scalar field in the manner of Goldberger and Wise, but only to orderMeV, due to the effect of the large extra dimension. The model predicts anatural scale of 10^{13} GeV on the 4-brane, making it a natural setting forinflation from the ultraviolet brane.Comment: 28 pages, 7 figure