Can high energy neutrino annihilation on relic neutrinos generate the observed highest energy cosmic-rays?

Annihilation of high energy, $\sim 10^{21}$eV, neutrinos on big bang relic neutrinos of $\sim 1$eV mass, clustered in the Galactic halo or in a nearby galaxy cluster halo, has been suggested to generate, through hadronic Z decay, high energy nucleons and photons which may account for the detected flux of >10^{20}eV cosmic-rays. We show that the flux of high energy nucleons and photons produced by this process is dominated by annihilation on the uniform, non-clustered, neutrino background, and that the energy generation rate of 10^{21}eV neutrinos required to account for the detected flux of >10^{20}eV particles is >10^{48} erg/Mpc^3 yr. This energy generation rate, comparable to the total luminosity of the universe, is 4 orders of magnitude larger than the rate of production of high energy nucleons required to account for the flux of >10^{19}eV cosmic-rays. Thus, in order for neutrino annihilation to contribute significantly to the detected flux of >10^{20}eV cosmic-rays, the existence of a new class of high-energy neutrino sources, likely unrelated to the sources of >10^{19}eV cosmic-rays, must be invoked.