Effects of neutrino mixing on high-energy cosmic neutrino flux

Several cosmologically distant astrophysical sources may produce high-energy cosmic neutrinos $(E>~{10}^6$ GeV) of all flavors above the atmospheric neutrino background. We study the effects of vacuum neutrino mixing in the 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.