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We investigate the sensitivity of tritium $\beta$-decay experiments forkeV-scale sterile neutrinos. Relic sterile neutrinos in the keV mass range cancontribute both to the cold and warm dark matter content of the universe. Thiswork shows that a large-scale tritium beta-decay experiment, similar to theKATRIN experiment that is under construction, can reach a statisticalsensitivity of the active-sterile neutrino mixing of $\sin^2\theta \sim10^{-8}$. The effect of uncertainties in the known theoretical corrections tothe tritium $\beta$-decay spectrum were investigated, and found not to affectthe sensitivity significantly. It is demonstrated that controlling uncorrelatedsystematic effects will be one of the main challenges in such an experiment.

Sensitivity of Next-Generation Tritium Beta-Decay Experiments for keV-Scale Sterile Neutrinos