Neutrino astronomy and massive long-lived particles from the big bang

We consider the neutrino flux from the decay of long-lived big-bang particles. The red-shift z_tr at which the neutrino transparency of the universe sets in is calculated as a function of neutrino energy: z_tr 1 × 10⁵ for TeV neutrinos and z_tr 3 × 10⁶ for 10 MeV neutrinos. One might expect the production of detectable neutrino flux at z z_tr, but, as demonstrated in this paper, the various upper limits, most notably due to nucleosynthesis and diffuse X- and gamma-rays, preclude this possibility. Unless the particle decay is strongly dominated by the pure neutrino channel, observable neutrino flux can be produced only at the current epoch, corresponding to red-shift z ≈ 0. For the thermal relics which annihilate through the gauge bosons of SU(3)×SU(2)×U(1) group, the neutrino flux can be marginally detectable at 0.1 < E_v < 10 TeV. As an example of non-thermal relics we consider gravitinos. If gravitinos are the lightest supersymmetric particles (LSP) they can produce the detectable neutrino flux in the form of a neutrino line with energy , where M_G is the gravitino mass. The flux strongly depends on the mechanisms of R-parity violation. It is shown that heavy gravitinos (M_G 100 GeV) can make up the dark matter in the universe.