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 τ/m∼ 500 Mpc/cE_ν∼ 500 s/eV. We study the rapid decay channel ν_i→ν_j+ϕ, where ϕ is a massless or very light scalar (possibly a Goldstone boson), and point out that one can test the coupling strength of g_ijν_iν_j down to g_ij 10^-8 eV/m by measuring the

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... tive fluxes of ν_e, ν_μ and ν_τ. 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.