Extra dimensions and Strong Neutrino-Nucleon interactions above $10^{19}$ eV : Breaking the GZK Barrier

Cosmic ray events above $10^{20}$ eV are on the verge of confronting fundamental particle physics. The neutrino is the only candidate primary among established particles capable of crossing 100 Mpc intergalactic distances unimpeded. The magnitude of $\nu N$ cross sections indicated by events, plus consistency with the Standard Model at low-energy, point to new physics of massive spin-2 exchange. In models based on extra dimensions, we find that the $\nu N$ cross section rises to typical hadronic values of between 1 and 100 mb at energies above $10^{20}$ eV. Our calculations take into account constraints of unitarity. We conclude that air-showers observed with energies above $10^{19}$ eV are consistent with neutrino primaries and extra-dimension models. An {\it upper bound} of 1-10 TeV on the mass scale at which graviton exchange becomes strong in current Kaluza-Klein models follows.