High-energy neutrino conversion and the lepton asymmetry in the universe

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 $\sim (10\div 20)%$ and in extreme cases allowed by present bounds on $\eta$ the effect can reach $\sim 100%$. Signatures of matter effects would consist in: (i) 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 $\sim 5\div 15%$, (ii) 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.