Astronomy with energy dependent flavour ratios of extragalactic neutrinos

High energy astrophysical neutrinos interacting with ultralight dark matter (DM) can undergo flavour oscillations that induce an energy dependence in the flavour ratios. Such a dependence on the neutrino energy will reflect in the track to shower ratio in neutrino telescopes like IceCube or KM3NeT. This opens up a possibility to study DM density profiles of astrophysical objects like AGN, GRB etc., which are the suspected sources of such neutrinos.