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) congruent-to 1 x 10(5) for TeV neutrinos and z(tr) congruent-to 3 x 10(6) for 10 MeV neutrinos. One might expect the production of detectable neutrino flux at z less-than-or-similar-to 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 almost-equal-to 0. For the thermal relics which annihilate through the gauge bosons of SU(3)x SU(2) x U(1) group, the neutrino flux can be marginally detectable at 0.1 < E(nu) < 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 E(nu) = 1/2M(G), 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) less-than-or-similar-to 100 GeV) can make up the dark matter in the universe.