Tests of new physics with astrophysical neutrinos

Neutrino telescopes have started to prove their value as instruments for precision particle physics. High-energy astrophysical neutrinos, recently discovered by IceCube, provide an opportunity to look for new physics at previously unexplored energies -- from tens of TeV to a few PeV, far beyond the reach of laboratory experiments. Because of cosmological-scale baselines -- Mpc to Gpc -- tiny new physics effects, otherwise unobservable, could accumulate up to observable levels. Effects include, for instance, neutrino decay, violation of fundamental symmetries, and exotic neutrino-neutrino interactions. I will show that the flavor composition and spectrum of neutrinos may reveal the presence of new physics and its type. Present-day data -- tens of astrophysical neutrino events -- are already sensitive to some of them. More statistics, improvements in detection techniques, and future detector upgrades will improve the sensitivity.