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.Comment: 4 pages, 1 figure. References added. Version to appear in PR

We consider the consequences for the relic neutrino abundance if extra neutrino interactions are allowed, e.g., the coupling of neutrinos to a light (compared to m(nu)) boson. For a wide range of couplings not excluded by other considerations, the relic neutrinos would annihilate to bosons at late times and thus make a negligible contribution to the matter density today. This mechanism evades the neutrino mass limits arising from large scale structure.

We assess a mechanism which can transform neutrino-antineutrino asymmetries between flavors in the early universe, and confirm that such transformation is unavoidable in the near bi-maximal framework emerging for the neutrino mixing matrix. We show that the process is a standard Mikheyev-SmirnovWolfenstein flavor transformation dictated by a synchronization of momentum states. We also show that flavor "equilibration" is a special feature of maximal mixing, and carefully examine new constraints placed on neutrino asymmetries. In particular, the big bang nucleosynthesis limit on electron neutrino degeneracy |ξ e |0.04 does not apply directly to all flavors, yet confirmation of the large-mixing-angle solution to the solar neutrino problem will eliminate the possibility of degenerate big bang nucleosynthesis.

We discuss the prospects for next generation neutrino telescopes, such as IceCube, to measure the flavor ratios of high-energy astrophysical neutrinos. The expected flavor ratios at the sources are φν e : φν µ : φν τ = 1 : 2 : 0, and neutrino oscillations quickly transform these to 1 : 1 : 1. The flavor ratios can be deduced from the relative rates of showers (νe charged-current, most ντ chargedcurrent, and all flavors neutral-current), muon tracks (νµ charged-current only), and tau lepton lollipops and double-bangs (ντ charged-current only). The peak sensitivities for these interactions are at different neutrino energies, but the flavor ratios can be reliably connected by a reasonable measurement of the spectrum shape. Measurement of the astrophysical neutrino flavor ratios tests the assumed production mechanism and also provides a very long baseline test of a number of exotic scenarios, including neutrino decay, CPT violation, and small-δm 2 oscillations to sterile neutrinos.PACS numbers: 95.85. Ry, 96.40.Tv, 13.35.Hb, 14.60.Pq

We consider dark matter annihilation into standard model particles and show that the least detectable final states, namely, neutrinos, define an upper bound on the total cross section. Calculating the cosmic diffuse neutrino signal, and comparing it to the measured terrestrial atmospheric neutrino background, we derive a strong and general bound. This can be evaded if the annihilation products are dominantly new and truly invisible particles. Our bound is much stronger than the unitarity bound at the most interesting masses, shows that dark matter halos cannot be significantly modified by annihilations, and can be improved by a factor of 10-100 with existing neutrino experiments.