  Star-forming galaxies have been predicted to contribute considerably to the diffuse gamma-ray background as they are guaranteed reservoirs of cosmic rays. Assuming that the hadronic interactions responsible for high-energy gamma rays also produce high-energy neutrinos and that O(100) PeV cosmic rays can be produced and confined in starburst galaxies, we here discuss the possibility that star-forming galaxies are also the main sources of the high-energy neutrinos observed by the IceCube experiment. First, we compute the diffuse gamma-ray background from star-forming galaxies, adopting the latest Herschel PEP/HerMES luminosity function and relying on the correlation between the gamma-ray and infrared luminosities reported by Fermi observations. Then we derive the expected intensity of the diffuse high-energy neutrinos from star-forming galaxies including normal and starburst galaxies. Our results indicate that starbursts, including those with active galactic nuclei and galaxy mergers, could be the main sources of the high-energy neutrinos observed by the IceCube experiment. We find that assuming a cosmic-ray spectral index of 2.1-2.2 for all starburst-like galaxies, our predictions can be consistent with both the Fermi and IceCube data, but larger indices readily fail to explain the observed diffuse neutrino flux. Taking the starburst high-energy spectral index as free parameter, and extrapolating from GeV to PeV energies, we find that the spectra harder than E^(-2.15) are likely to be excluded by the IceCube data, which can be more constraining than the Fermi data for this population. 
Star-forming galaxies as the origin of diffuse high-energy backgrounds:   Gamma-ray and neutrino connections, and implications for starburst history