Implications of ultra-high energy neutrino flux constraints for Lorentz-invariance violating cosmogenic neutrinos

We consider the implications of Lorentz-invariance violation (LIV) on cosmogenic neutrino observations, with particular focus on the constraints imposed on several well-developed models for ultra-high energy cosmogenic neutrino production by recent results from the Antarctic Impulsive Transient Antenna (ANITA) long-duration balloon payload, and Radio Ice Cherenkov Experiment (RICE) at the South Pole. Under a scenario proposed originally by Coleman and Glashow, each lepton family may attain maximum velocities that can exceed the speed of light, leading to energy-loss through several interaction channels during propagation. We show that future observations of cosmogenic neutrinos will provide by far the most stringent limit on LIV in the neutrino sector. We derive the implied level of LIV required to suppress observation of predicted fluxes from several mainstream cosmogenic neutrino models, and specifically those recently constrained by the ANITA and RICE experiments. We simulate via detailed Monte Carlo code the propagation of cosmogenic neutrino fluxes in the presence of LIV-induced energy losses. We show that this process produces several detectable effects in the resulting attenuated neutrino spectra, even at LIV-induced neutrino superluminality of (u_{\nu}-c)/c ~ 10^{-26}, about 13 orders of magnitude below current bounds.