  We propose a model where sterile neutrinos are introduced to make light
neutrinos to be pseudo-Dirac particles. It is shown how tiny mass splitting
necessary for realizing pseudo-Dirac neutrinos can be achieved. Within the
model, we show how leptogenesis can be successfully generated. Motivated by the
recent observation of very high energy neutrino events at IceCube, we study a
possibility to observe the effects of the pseudo-Dirac property of neutrinos by
performing astronomical-scale baseline experiments to uncover the oscillation
effects of very tiny mass splitting. Using the result of global fit to neutrino
data for the input of neutrino mixing angles and CP phase at $1\sigma$ C.L. and
fixing neutrino energy and mass splittings, we study how the oscillation
effects induced by pseudo-Dirac neutrinos may affect the track-to-shower ratio
obtained from IceCube data. We also discuss future prospect to observe the
effects of the pseudo-Dirac property of neutrinos at high energy neutrino
experiments.
