Cosmogenic neutrinos and signals of TeV gravity in air showers and neutrino telescopes

The existence of extra dimensions allows the possibility that the fundamental scale of gravity is at the TeV. If that is the case, gravity could dominate the interactions of ultra-high energy cosmic rays. In particular, the production of microscopic black holes by cosmogenic neutrinos has been estimated in a number of papers. We consider here gravity-mediated interactions at larger distances, where they can be calculated in the eikonal approximation. We show that for the expected flux of cosmogenic neutrinos these elastic processes give a stronger signal than black hole production in neutrino telescopes. Taking the bounds on the higher dimensional Planck mass M_D (D=4+n) from current air shower experiments, for n=2 (6) elastic collisions could produce up to 118 (34) events per year at IceCube. On the other hand, the absence of any signal would imply a bound of M_D>~5 TeV.