  Active galactic nuclei and gamma ray bursts at cosmological distances are
sources of high-energy electron and muon neutrinos and provide a unique test
bench for neutrino instability. The typical lifetime-to-mass ratio one can
reach there is $\tau/m\sim 500 Mpc/cE_{\nu}\sim 500$ s/eV. We study the rapid
decay channel $\nu_i\to\nu_j+\phi$, where $\phi$ is a massless or very light
scalar (possibly a Goldstone boson), and point out that one can test the
coupling strength of $g_{ij}\nu_i\nu_j$ down to $g_{ij}\lsim 10^{-8} eV/m$ by
measuring the relative fluxes of $\nu_{e}$, $\nu_{\mu}$ and $\nu_{\tau}$. This
is orders of magnitude more stringent bound than what one can obtain in other
phenomena, e.g. in neutrinoless double beta decay with scalar emission.
