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

New Insights into Uncertainties in the Relic Neutrino Background and Effects from the Nuclear Equation of State