  We study possible effects of non-local gravity corrections on the recent
discovery by the IceCube collaboration reporting high-energy neutrino flux
detected at energies of order PeV. Considering the 4-dimensional operator $\sim
y_{\alpha \chi}\bar{{L_{{\alpha}}}}\, H\, \chi$, it is possible to explain both
the IceCube neutrino rate and the abundance of Dark Matter, provided that
non-local corrections are present in the cosmological background. Furthermore,
the mechanism could constitute a natural way to address the $H_0$ tension
issue.
