The diffuse supernova neutrino flux, star formation rate and SN1987A

I calculate the diffuse flux of electron antineutrinos from all supernovae by imposing compatibility with the SN1987A neutrino data and with the existing constraints on the cosmological rate of core collapse supernovae. For the latter I use observational results on the cosmological star formation rate, taking into account the error on the ratio of the supernova rate and star formation rate. The flux above the SuperKamiokande (SK) energy cut of 19.3 MeV is found to be between 0.02 and 4.3 cm^{-2} s^{-1} (0.03 - 9.0 events/year at SK). Part of this interval is already excluded by the current SK upper limit on the flux of 1.2 cm^{-2} s^{-1}. Still, to place constraints on the cosmological supernova rate, water Cerenkov experiments with the same energy threshold should either improve the upper bound down to the level of 0.3 cm^{-2} s^{-1} (0.5 events/year at SK), or place a lower bound (i.e. evidence of the flux) at or above 0.2 cm^{-2} s^{-1} (0.4 events/year at SK). These are realistic goals for the next generation Megaton detectors.