Dark matter in modified cosmologies

The IceCube experiment discovered a high-energy astrophysical neutrino flux with energies of the order of PeV. To explain this phenomenon one may consider the minimal 4-dimensional operator $\sim y_{\alpha \chi }\overline{L_{L\alpha }}H\chi .$. An interesting possibility is to also explain the relic abundance of DM in the Universe. Assuming that the cosmological background evolves according to the standard cosmological model, this model fails since the rate of DM decay ${\Gamma }_{\chi }\sim {|y_{\alpha \chi }|}^2$ needed to get the correct DM relic abundance differs by many orders of magnitude with respect that one needed to explain the IceCube data. We show that such a discrepancy can be solved if the Universe evolution is governed by a modified cosmology. (paper)