The diffuse cosmic supernova neutrino background (DSNB) is observational target of the gadolinium-loaded Super-Kamiokande (SK) detector and the forthcoming JUNO and Hyper-Kamiokande detectors. Current predictions are hampered by our still incomplete understanding of the supernova (SN) explosion mechanism and of the neutron star (NS) equation of state and maximum mass. In our comprehensive study we revisit this problem on grounds of the landscapes of successful and failed SN explosions obtained by Sukhbold et al. and Ertl et al. with parametrized one-dimensional neutrino engines for large sets of single-star and helium-star progenitors, with the latter serving as proxy of binary evolution effects. Besides considering engines of different strengths, leading to different fractions of failed SNe with black-hole (BH) formation, we also vary the NS mass limit, the spectral shape of the neutrino emission, and include contributions from poorly understood alternative NS-formation channels such as accretion-induced or merger-induced collapse events. Since the neutrino signals of our large model sets are approximate, we calibrate the associated degrees of freedom by using state-of-the-art simulations of proto-neutron star cooling. Our predictions are higher than other recent ones because of a large fraction of failed SNe with long delay to BH formation. Our best-guess model predicts a DSNB electron-antineutrino-flux of 28.8^{+24.6}_{-10.9} cm^{-2}s^{-1} with 6.0^{+5.1}_{-2.1} cm^{-2}s^{-1} in the favorable measurement interval of [10,30] MeV, and 1.3^{+1.1}_{-0.4} cm^{-2}s^{-1} with electron-antineutrino energies > 17.3 MeV, which is roughly a factor of two below the current SK limit. The uncertainty range is dominated by the still insufficiently constrained cosmic rate of stellar core-collapse events.
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