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 $O\left(1\right)$ coefficients. The linear size of the internal space remains small. The proposal has striking testable signatures.