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.
