The extragalactic neutrino background radiations from blazars and cosmic rays

Blazar emission of gamma rays and cosmic ray production of gamma rays in gas-rich clusters have been proposed recently as alternative sources of the high energy extragalactic diffuse gamma ray background radiation. We show that these sources also produce very different high energy extragalactic diffuse neutrino background radiations. An extragalactic neutrino background radiation may be detected by the new generation of large neutrino telescopes under construction and may be used to trace the origin of the extragalactic gamma radiation.