Spectral and Spatial Distortions of PeV Neutrinos from Scattering with
  Dark Matter
  We study the effects on the spectrum and distribution of high-energy
neutrinos due to scattering with dark matter both outside and within our
galaxy, focusing on the neutrinos observed by the IceCube experiment with
energies up to several PeV. If these neutrinos originate from extra-galactic
astrophysical sources, then scattering in transit with dark matter particles
will delay their arrival to Earth. This results in a cut-off in their spectrum
at an energy set by the scattering cross section, allowing us to place an upper
limit on cross sections $\sigma$ which increase with energy E at the level of
$\sigma$ < 10^{-17} x (m / GeV) x (E / PeV)^2 cm^2, for dark matter particles
of mass m. Once these neutrinos enter our galaxy, the large dark matter
densities result in further scattering, especially towards the Galactic Centre.
Intriguingly, we find that for $\sigma$ ~ 10^{-22} x (m / GeV) x (E / PeV)^2
cm^2, the distribution of the neutrinos on the sky has a small cluster of
events towards the centre of the galaxy, potentially explaining the ~2 sigma
excess seen by IceCube in this region without needing a galactic source.
