  The flavor composition of astrophysical neutrinos observed at neutrino
telescopes is related to the initial composition at their sources via
oscillation-averaged flavor transitions. If the time evolution of the neutrino
flavor states is unitary, the probability of neutrinos changing flavor is
solely determined by the unitary mixing matrix that relates the neutrino flavor
and propagation eigenstates. In this paper we derive general bounds on the
flavor composition of TeV-PeV astrophysical neutrinos based on unitarity
constraints. These bounds are useful for studying the flavor composition of
high-energy neutrinos, where energy-dependent nonstandard flavor mixing can
dominate over the standard mixing observed in accelerator, reactor, and
atmospheric neutrino oscillations.
