  The discovery by the IceCube experiment of a high-energy astrophysical
neutrino flux with energies of the order of PeV, has opened new scenarios in
astroparticles physics. A possibility to explain this phenomenon is to consider
the minimal models of Dark Matter (DM) decay, the 4-dimensional operator $\sim
y_{\alpha \chi}\overline{{L_{L_{\alpha}}}}\, H\, \chi$, which is also able to
generate the correct abundance of DM in the Universe.
  Assuming that the cosmological background evolves according to the standard
cosmological model, it follows that the rate of DM decay $\Gamma_\chi \sim
|y_{\alpha \chi}|^2$ needed to get the correct DM relic abundance
($\Gamma_\chi\sim 10^{-58}$) differs by many orders of magnitude with respect
that one needed to explain the IceCube data ($\Gamma_\chi\sim 10^{-25}$),
making the four-dimensional operator unsuitable. In this paper we show that
assuming that the early Universe evolution is governed by a modified cosmology,
the discrepancy between the two the DM decay rates can be reconciled, and both
the IceCube neutrino rate and relic density can be explained in a minimal
model.
