PeV IceCube signals and Dark Matter relic abundance in modified cosmologies

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.