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

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