  Several cosmologically distant astrophysical sources may produce high-energy
cosmic neutrinos (E \geq 10^6 GeV) of all flavors above the atmospheric
neutrino background. We study the effects of vacuum neutrino mixing in three
flavor framework on this cosmic neutrino flux. We also consider the effects of
possible mixing between the three active neutrinos and the (fourth) sterile
neutrino with or without Big-Bang nucleosynthesis constraints and estimate the
resulting final high-energy cosmic neutrino flux ratios on earth compatible
with currently existing different neutrino oscillation hints in a model
independent way. Further, we discuss the case where the intrinsic cosmic
neutrino flux does not have the standard ratio.
