  IceCube observed high-energy neutrino flux in the energy region from TeV to
PeV. The decay of a massive long-lived particle in the early universe can be
the origin of the IceCube neutrino events, which we call an "early decay
scenario." In this paper, we construct a particle physics model that contains
such a massive long-lived particle based on the Peccei-Quinn model. We
calculate the present neutrino flux, taking account of realistic initial energy
distributions of particles produced by the decay of the massive long-lived
particle. We show that the early decay scenario naturally fits into the
Peccei-Quinn model, and that the neutrino flux observed by IceCube can be
explained in such a framework. We also see that, based on that model, a
consistent cosmological history that explains the abundance of the massive
long-lived particle is realized.
