Direct detection of the cosmic neutrino background including light sterile neutrinos

Current cosmological data drop an interesting hint about the existence of sub-eV sterile neutrinos, which should be a part of the cosmic neutrino background (CνB). We point out that such light sterile neutrinos may leave a distinct imprint on the electron energy spectrum in the capture of relic electron neutrinos by means of radioactive beta-decaying nuclei. We examine possible signals of sterile neutrinos relative to active neutrinos, characterized by their masses and sensitive to their number densities, in the reaction νe+H3→He3+e− against the corresponding tritium beta decay. We stress that this kind of direct laboratory detection of the CνB and its sterile component might not be hopeless in the long term.