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 (C$\nu$B). 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 $\nu^{}_e + ~^3{\rm H} \to ~^3{\rm He} + e^-$ against the corresponding tritium beta decay. We stress that this kind of direct laboratory detection of the C$\nu$B and its sterile component might not be hopeless in the long term.
Comment: Minor changes. Accepted for publication in Phys. Lett. B