  We study cosmological scenarios in which high-energy neutrinos are emitted
from the decay of long-lived massive particles at the cosmic time later than a
redshift of 10^6. The high-energy neutrino events recently observed by the
IceCube experiment suggest a new source of high-energy cosmic-ray neutrinos;
decay of a heavy particle can be one of the possibilities. We calculate the
spectrum of the high-energy neutrinos emitted from the decay of long-lived
particles, taking account of the neutrino scattering processes with background
neutrinos. Then, we derive bounds on the scenario using the observation of
high-energy cosmic-ray neutrino flux. We also study constraints from the
spectral distortions of the cosmic microwave background and the big-bang
nucleosynthesis. In addition, we show that the PeV neutrinos observed by the
IceCube experiment can originate from the decay of a massive particle with its
mass as large as O(10^10 GeV).
