Pseudo-Dirac Neutrinos, a Challenge for Neutrino Telescopes

Neutrinos may be pseudo-Dirac states, such that each generation is actually composed of two maximally-mixed Majorana neutrinos separated by a tiny mass difference. The usual active neutrino oscillation phenomenology would be unaltered if the pseudo-Dirac splittings are $\delta m^2\text{alt}{10}^{-12}$ eV${}^2$; in addition, neutrinoless double beta decay would be highly suppressed. However, it may be possible to distinguish pseudo-Dirac from Dirac neutrinos using high-energy astrophysical neutrinos. By measuring flavor ratios as a function of $L\mathrm{/}E$, mass-squared differences down to $\delta m^2\sim {10}^{-18}$ eV${}^2$ can be reached. We comment on the possibility of probing cosmological parameters with neutrinos.