  We review the computation of and associated uncertainties in the current
understanding of the relic neutrino background due to core-collapse supernovae,
black hole formation and neutron-star merger events. We consider the current
status of uncertainties due to the nuclear equation of state (EoS), the
progenitor masses, the source supernova neutrino spectrum, the cosmological
star formation rate, the stellar initial mass function, neutrino oscillations,
and neutrino self-interactions. We summarize the current viability of future
neutrino detectors to distinguish the nuclear EoS and the temperature of
supernova neutrinos via the detected relic supernova neutrino spectrum.
