Abstract
We show that starburst galaxies efficiently convert cosmic rays into pions, which in turn decay into high energy neutrinos and photons. The cumulative background of GeV neutrinos is Eν2Φν ≈ 10−7 GeV cm−2 s−1 sr−1, and its extrapolation to higher neutrino energies depends on the energy spectrum of the injected cosmic rays, with Eν2Φν ∝ Eν- 0.15±0.1 up to Eν ∼ 0.3 PeV and possibly higher neutrino energies. This flux, which constitutes a lower limit to the high energy extra-Galactic neutrino flux, may be detectable with forthcoming kilometre-scale neutrino telescopes.