Sub-GeV dark matter and relic neutrinos at high energies

Dark matter (DM) below a GeV is motivated by some cosmological histories and possibly by anomalies in data. Leading detectors cannot easily test it, due to its small kinetic energy. In this talk I will discuss the high-energy DM fluxes that necessarily reach us on Earth, and the novel DM detection techniques that they open today, with existing experiments. In particular I will present searches, at large neutrino detectors (like Super- and Hyper-Kamiokande, JUNO and DUNE), for DM i) upscattered by cosmic rays and ii) produced in atmospheric showers. These will result in the strongest existing limits on a wide class of sub-GeV DM models. I will finally discuss how analogous ideas allow to obtain novel knowledge about the relic neutrino background, using data from ultra-high-energy CR telescopes.