Oscillations of high-energy cosmic neutrinos in the copious MeV neutrino background

The core -collapse of massive stars and the merger of neutron star binaries are among the most promising candidate sites for the production of high-energy cosmic neutrinos. We demonstrate that the high-energy neutrinos produced in such extreme environments can experience efficient flavor conversions on scales much shorter than those expected in vacuum, due to their coherent forward scatterings with the bath of decohered low -energy neutrinos emitted from the central engine. These low -energy neutrinos, which exist as mass eigenstates, provide a very special and peculiar dominant background for the propagation of the high-energy ones. We point out that the high-energy neutrino flavor ratio is modified to a value independent of neutrinos energies, which is distinct from the conventional prediction with the matter effect. We also suggest that the signals can be used as a novel probe of new neutrino interactions beyond the Standard Model. This is yet another context where neutrino -neutrino interactions can play a crucial role in their flavor evolution.