  We propose that supernova relic neutrino (SRN) observation can be used to set
constraints on the neutrino decay models. Because of the long distance scale
from cosmological supernovae to the Earth, SRN have possibility to provide much
stronger limit than the present one obtained from solar neutrino observation.
Since the currently available data are only the upper limit on the flux
integrated over $E_{\bar\nu_e}>19.3$ MeV, the decay models on which we can set
constraints is quite restricted; they must satisfy specific conditions such
that the daughter neutrinos are active species, the neutrino mass spectrum is
quasi-degenerate, and the neutrino mass hierarchy is normal. Our numerical
calculation clearly indicates that the neutrino decay model with
$(\tau_2/m,\tau_3/m)\alt (10^{10},10^{10})$ [s/eV], where $\tau_i$ represents
the lifetime of mass eigenstates $\bar\nu_i$, appears to give the SRN flux that
is larger than the current upper limit. However, since the theoretical SRN
prediction contains many uncertainties concerning a supernova rate in the
universe or simulation of supernova explosions, we cannot conclude that there
exists the excluded parameter region of the neutrino lifetime. In the near
future, further reduced upper limit is actually expected, and it will provide
more severe constraints on the neutrino decay models.
