  We study matter effects on oscillations of high-energy neutrinos in the
Universe. Substantial effect can be produced by scattering of the neutrinos
from cosmological sources ($z\gta 1$) on the relic neutrino background,
provided that the latter has large CP-asymmetry: $\eta\equiv
(n_\nu-n_{\bar{\nu}})/n_\gamma\gta 1$, where $n_\nu$, $n_{\bar{\nu}}$ and
$n_\gamma$ are the concentrations of neutrinos, antineutrinos and photons. We
consider in details the dynamics of conversion in the expanding neutrino
background. Applications are given to the diffuse fluxes of neutrinos from
GRBs, AGN, and the decay of super-heavy relics. We find that the vacuum
oscillation probability can be modified by $\sim (10-20)%$ and in extreme cases
allowed by present bounds on $\eta$ the effect can reach $\sim 100%$.
Signatures of matter effects would consist (i) for both active-active and
active-sterile conversion, in a deviation of the numbers of events produced in
a detector by neutrinos of different flavours,
$N_{\alpha}~(\alpha=e,\mu,\tau)$, and of their ratios from the values given by
vacuum oscillations; such deviations can reach $\sim 5-15%$, (ii) for
active-sterile conversion, in a characteristic energy dependence of the ratios
$N_{e}/N_{\mu},N_{e}/N_{\tau},N_{\mu}/N_{\tau}$. Searches for these matter
effects will probe large CP and lepton asymmetries in the universe.
