Unraveling the Dirac neutrino with cosmological and terrestrial detectors

We propose a method for testing the Dirac neutrino hypothesis by combining data from terrestrial neutrino experiments, such as tritium beta decay, with data from cosmological observations, such as the cosmic microwave background and large scale structure surveys. If the neutrinos are Dirac particles, and if the active neutrinos' sterile partners were once thermalized in the early universe, then this new cosmological relic would simultaneously contribute to the effective number of relativistic species, $N_\text{eff}$, and also lead to a mismatch between the cosmologically-measured effective neutrino mass sum $\Sigma m_\nu$ and the terrestrially-measured active neutrino mass sum $\Sigma_i m_i$. We point out that specifically correlated deviations in $N_\text{eff} \gtrsim 3$ and $\Sigma m_\nu \gtrsim \Sigma_i m_i$ above their standard predictions could be the harbinger revealing the Dirac nature of neutrinos. We provide several benchmark examples, including Dirac leptogenesis, that predict a thermal relic population of the sterile partners, and we discuss the relevant observational prospects with current and near-future experiments. This work provides a novel approach to probe an important possibility of the origin of neutrino mass.