Dark Matter-Enhanced Probe of Relic Neutrino Clustering

We propose heavy decaying dark matter (DM) as a new probe of the cosmic neutrino background (CνB). Heavy DM, with mass 10⁹ GeV, decaying into neutrinos can be a new source of ultra-high-energy (UHE) neutrinos. Including this contribution along with the measured astrophysical and predicted cosmogenic neutrino fluxes, we study the scattering of UHE neutrinos with the CνB via standard weak interactions mediated by the Z-boson. We solve the complete neutrino transport equation, taking into account both absorption and reinjection effects, to calculate the expected spectrum of UHE neutrino flux at future neutrino telescopes, such as IceCube-Gen2 Radio. We argue that such observations can be used to probe the CνB properties, and in particular, local CνB clustering. We find that, depending on the absolute neutrino mass and the DM mass and lifetime, a local CνB overdensity 10⁶ can be probed at IceCube-Gen2 Radio within 10 years of data taking.