The Cumulative Bakground of High-Energy Neutrinos from Starburst Galaxies

We show that starburst galaxies convert efficiently cosmic-rays into pions, which in turn decay into high-energy neutrinos and photons. The cumulative background of GeV neutrinos is 10^{-7}GeV/cm^2/s/sr. Its extrapolation to higher neutrino energies depends on the energy spectrum of the injected cosmic-rays and is proportional to E^{-0.15+-0.1} up to E~0.3PeV and possibly higher neutrino energies. This flux, which constitutes a lower limit to the high energy extra-Galactic neutrino flux, is likely to be detectable by forthcoming km-scale neutrino telescopes.