  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.
