Fundamental physics with the diffuse supernova background neutrinos

The Universe is awash with tens-of-MeV neutrinos of all species coming from all past core-collapse supernovae. These have never been observed, but this state of affairs will change in the near future. In the less than ten years, the Super-Kamiokande experiment, loaded with gadolinium, is expected to collect dozens of events induced by the scattering of neutrinos from the diffuse supernova neutrino background (DSNB). Next-generation projects, including Hyper-Kamiokande and Theia, are expected to collect data samples with hundreds of DSNB events after a decade of running. Here, we study quantitatively how well the DSNB, including its energy spectrum, will be measured by different current or upcoming large neutrino detectors. We analyze the simulated data in order to estimate how well measurements of the DSNB can be used to inform research topics in cosmology -- including measurements of the Hubble parameter -- astrophysics -- including the star-formation-rate -- and particle physics -- including the neutrino lifetime and the possibility that neutrinos are pseudo-Dirac fermions.