Hyperbolic Inflation

We propose a natural scenario for the cosmological inflation with the non-minimal coupling term invoking compact hyperbolic extra dimensions. Thanks to the unique mathematical properties of compact hyperbolic space, the large volume of extra dimensions, which provides a natural understanding of the proper size of couplings, does not necessarily accompany with the low Kaluza-Klein scale so that the model allows a single field inflation with a scale around $10^{13}$ GeV. The model fulfills all the observed data and predicts a sizable gravitational perturbation, r~0.003.