Applying our recently developed propagation code we review extragalactic neutrino fluxes above 10(14) eV in various scenarios and how they are constrained by current data. We specifically identify scenarios in which the cosmogenic neutrino flux above similar or equal to10(18) eV, produced by pion production of ultrahigh energy cosmic rays outside their sources, is considerably higher than the Waxman-Bahcall bound. This is easy to achieve for sources with hard injection spectra and luminosities that were higher in the past. Such fluxes would significantly increase the chances to detect ultrahigh energy neutrinos with experiments currently under construction or in the proposal stage.
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