IceCube neutrinos, decaying dark matter, and the Hubble constant
Cosmological parameters deduced from the Planck measurements of anisotropies in the cosmic microwave background are at some tension with direct astronomical measurements of various parameters at low redshifts. Very recently, it has been conjectured that this discrepancy can be reconciled if a certain fraction of dark matter is unstable and decays between recombination and the present epoch. Herein we show that if the superheavy relics have a branching into neutrinos B (X \to \nu \bar \nu) \sim 3 \times 10^{-9}, then this scenario can also accommodate the recently discovered extraterrestrial flux of neutrinos, relaxing the tension between IceCube results and Fermi LAT data. The model is fully predictive and can be confronted with future IceCube data. We demonstrate that in 10 years of observation IceCube will be able to distinguish the mono-energetic signal from X decay at the 3\sigma level. In a few years of data taking with the upgraded IceCube-Gen2 enough statistics will be gathered to elucidate the dark matter--neutrino connection at the 5\sigma level.