Nonstandard neutrino properties and the high-energy cosmic neutrino flux

Recently, it has been shown that cosmic neutrino flux at the GRB/AGN source, $F_{\nu_e}^0 : F_{\nu_{\mu}}^0 : F_{\nu_{\tau}}^0 \simeq 1 :2 :0 $, inevitably oscillates (in the three neutrino framework) to 1 : 1: 1, irrespective of the mixing angle relevant to the solar data. It has also been pointed out that the intrinsic flux of the cosmic high-energy neutrinos may not have the standard ratio, in which case the cosmic neutrino flux in the far distance should be dependent of the mixing angle. For neutrinos with nonzero electromagnetic properties, we show in the latter case that matter effects on oscillations of high-energy cosmic neutrinos can substantially modify the vacuum oscillation probability, if the mass-squared difference is $\lsim 10^{-10}$ eV^2.