The detection of the diffuse supernova neutrino background (DSNB) will preciously contribute to gauge the properties of the core-collapse supernova population. We estimate the DSNB event rate in the next-generation neutrino detectors, Hyper-Kamiokande enriched with Gadolinium, JUNO, and DUNE. The determination of the supernova unknowns through the DSNB will be heavily driven by Hyper-Kamiokande, given its higher expected event rate, and complemented by DUNE that will help in reducing the parameters uncertainties. Meanwhile, JUNO will be sensitive to the DSNB signal over the largest energy range. A joint statistical analysis of the expected rates in 20 years of data taking from the above detectors suggests that we will be sensitive to the local supernova rate at most at a 20−33% level. A non-zero fraction of supernovae forming black holes will be confirmed at a 90% CL, if the true value of that fraction is ≳20%. On the other hand, the DSNB events show extremely poor statistical sensitivity to the nuclear equation of state and mass accretion rate of the progenitors forming black holes.

The sources of cosmic rays with energies above 55 EeV are still mysterious. A guaranteed associated flux of ultra high energy neutrinos known as the cosmogenic neutrino flux will be measured by next generation radio facilities, such as the proposed Giant Radio Array for Neutrino Detection (GRAND). By using the orthogonal information provided by the cosmogenic neutrino flux, we here determine the prospects of GRAND to constrain the source redshift evolution and the chemical composition of the cosmic ray sources. If the redshift evolution is known, independently on GRAND's energy resolution, GRAND with 200,000 antennas will constrain the proton/iron fraction to the ∼ 5 − 10% level after one year of data taking; on the other hand, if hints on the average source composition are given, GRAND will measure the redshift evolution of the sources to a ∼ 10% uncertainty. However, the foreseen configuration of GRAND alone will not be able to break the degeneracy between redshift evolution of the sources and their composition. Our findings underline the discriminating potential of next generation radio array detectors and motivate further efforts in this direction.1 The Ultra High Energy Cosmic Ray (UHECR) typically refers to cosmic rays with energies 1 EeV. We use the term EECR adopted by the community to mean those with energies 55 EeV which have a short horizon.