  Neutrinos produced in extragalactic sources may experience
flavor-oscillations and decoherence on their way to Earth due to their
interaction with dark matter (DM). As a result, they may be detected in
pointer-states other than the flavor states at the source. The oscillation
pattern and the structure of the pointer-states can give us information on the
characteristics of the DM and the kind of interaction that has taken place.
From this perspective, neutrinos can be viewed as DM-tracers. We study the
local evolution of neutrino flavor-eigenstates due to local effects produced by
the presence of DM. To explore the sensitivity of the model, we consider
different DM density profiles, masses and interactions. Starting from the
eigenstates of the neutrino-mass Hamiltonian, we construct the flavor-states
with the neutrino mixing-matrix in vacuum. We then include local interactions
with DM, acting along the neutrino path towards the Earth, and analyse the
resulting probabilities. In doing so, we adopt different DM density profiles,
e.g. a constant, a local isotropic and a Navarro-Frenk-White density
distribution. Finally, by following the time evolution of the flavor-states, we
identify pointer-states and interpret the results in terms of the adopted DM
model. Due to the interaction with DM, neutrinos experience the MSW effect, the
extent of which depends on the DM density profile. The interaction with DM
produces the enhancement or suppression of oscillations. Decoherence effects
may take place. We model the time evolution of extragalactic neutrino
flavor-states by letting them interact with DM. The features of the calculated
response seem to support the notion that these neutrinos can be taken as DM
tracers. From a theoretical point of view, the coexistence and/or competition
of decoherence and MSW effects is sustained by the results.
