  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 $\delta m^2 \alt 10^{-12}$ 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 $L/E$, 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.
