Diluting Gravity with Compact Hyperboloids

I give a brief informal introduction to the idea and tests of large extra dimensions, focusing on the case in which the space-time manifold has a direct product structure. I then describe some attractive implementations in which the internal space comprises a compact hyperbolic manifold. This construction yields an exponential hierarchy between the usual Planck scale and the true fundamental scale of physics by tuning only $\mathcal{O}(1)$ coefficients, since the linear size of the internal space remains small. In addition, this allows an early universe cosmology with normal evolution up to substantial temperatures, and completely evades astrophysical constraints.