Star-forming and starburst galaxies are considered as one of the viable candidate sources of the high-energy cosmic neutrino background detected in IceCube .
We revisit contributions of supernova remnants ( SNRs ) and hypernova remnants ( HNRs ) in such galaxies to the diffuse high-energy neutrino and gamma-ray backgrounds , in light of the latest Fermi data above 50 GeV .
We also take into account possible time dependent effects of the cosmic-ray ( CR ) acceleration during the SNR evolution .
CRs accelerated by the SNR shocks can produce high-energy neutrinos up to \sim 100 TeV energies , but CRs from HNRs can extend the spectrum up to PeV energies .
We show that , only if HNRs are dominant over SNRs , the diffuse neutrino background above 100 TeV can be explained without contradicting the gamma-ray data .
However , the neutrino data around 30 TeV remain unexplained , which might suggest a different population of gamma-ray dark CR sources .
We also consider possible contributions of Pop-III HNRs up to z \lesssim 10 , and show that they are not constrained by the gamma-ray data , and thus could contribute to the diffuse high-energy backgrounds if their explosion energy reaches { \mathcal { E } } _ { POP - III } \sim { a~ { } few } \times 10 ^ { 53 } erg .
More conservatively , our results suggest that the explosion energy of POP-III HNRs is { \mathcal { E } } _ { POP - III } \lesssim 7 \times { 10 } ^ { 53 } erg .