Neutrino oscillations are a widely observed and well established phenomenon. It is also well known that deviations with respect to flavor conversion probabilities in vacuum arise due to neutrino interactions with matter. In this work, we analyze the impact of new interactions between neutrinos and the dark matter present in the Milky Way on the neutrino oscillation pattern. The dark matter-neutrino interaction is modeled by using an effective coupling proportional to the Fermi constant $G_F$ with no further restrictions on its flavor structure. For the galactic dark matter profile we consider an homogeneous distribution as well as several density profiles, estimating in all cases the size of the interaction required to get an observable effect at different neutrino energies. Our discussion is mainly focused in the PeV neutrino energy range, to be explored in observatories like IceCube and KM3NeT. The obtained results may be interpreted in terms of a light $mathcal{O}$(sub-eV--keV) or WIMP-like dark matter particle or as a new interaction with a mediator of $mathcal{O}$(sub-eV--keV) mass.
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