$1020eV$ cosmic ray and particle physics with IceCube

We show that a kilometer-scale neutrino observatory, though optimized for detecting neutrinos of TeV to PeV energy, can reveal the science associated with the enigmatic super-EeV radiation in the Universe. Speculations regarding its origin include heavy relics from the early Universe, particle interactions associated with the Greisen cutoff, and topological defects which are remnant cosmic structures associated with phase transitions in grand unified gauge theories. We show that it is a misconception that new instruments optimized to EeV energy can exclusively do this important science. Because kilometer-scale neutrino telescopes such as IceCube can reject the atmospheric neutrino background by identifying the very high energy of the signal events, they have sensitivity over the full solid angle, including the horizon where most of the signal is concentrated. This is critical because upgoing neutrino-induced muons, considered in previous calculations, are absorbed by the Earth. Previous calculations have underestimated the event rates of IceCube for EeV signals by over one order of magnitude.