Decay of High-Energy Astrophysical Neutrinos
  Existing limits on the non-radiative decay of one neutrino to another plus a massless particle (e.g., a singlet Majoron) are very weak. The best limits on the lifetime to mass ratio come from solar neutrino observations, and are $\tau/m \agt 10^{-4}$ s/eV for the relevant mass eigenstate(s). For lifetimes even several orders of magnitude longer, high-energy neutrinos from distant astrophysical sources would decay. This would strongly alter the flavor ratios from the $\phi_{\nu_e}:\phi_{\nu_{\mu}}:\phi_{\nu_{\tau}} = 1:1:1$ expected from oscillations alone, and should be readily visible in the near future in detectors such as IceCube. 
John F. Beacom, Nicole F. Bell, Dan Hooper, Sandip Pakvasa, and Thomas   J. Weiler