Compact hyperbolic extra dimensions: Branes, Kaluza-Klein modes, and cosmology

We reconsider theories with low gravitational (or string) scale M-* where Newton's constant is generated via new large-volume spatial dimensions, while standard model states are localized to a 3-brane. Utilizing compact hyperbolic manifolds we show that the spectrum of Kaluza-Klein modes is radically altered. This allows the early Universe to evolve normally up to substantial temperatures, and completely negates the astrophysical constraints on M-*. Furthermore, an exponential hierarchy between the usual Planck scale and the true fundamental scale of physics can emerge with only O(1) coefficients. The linear size of the internal space remains small. The proposal has striking testable signatures.