The cosmic star formation history (SFH) has been constrained by ultraviolet and far-infrared measurements, revealing a consistent picture up to redshift z ≈ 6, with tight constraints for z ≲ 1. Analytical fits to these data show that the SFH normalisation is unlikely to be much lower than indicated by direct fits. The SFH also predicts a delay time of ~3 Gyr for supernova type Ia. The Super-Kamiokande (SK) limit on the electron antineutrino flux from core-collapse supernovae provides an upper limit on the SFH normalisation, consistent with modest neutrino temperatures from SN events. The traditional Salpeter initial mass function (IMF) is not a good representation at low stellar masses, and recently favoured IMFs are also constrained. Shallow or top-heavy IMFs may be preferred, but they cannot be too top-heavy. Improved data on supernova rate density evolution, stellar mass ranges for core-collapse and type Ia supernovae, and antineutrino backgrounds are needed to resolve outstanding issues. The SFH data compilation, including UV and FIR measurements, is used to fit parametric forms, with the best fit for the SalA IMF and BG IMF. The SFH normalisation is constrained by the SK limit, with effective temperatures at the lower end of the predicted range. The SFH predictions for stellar and metal mass densities, and SN rate evolution, are consistent with the SK limit. The SFH also predicts a delay time of ~3 Gyr for supernova type Ia. The results show that the SFH normalisation is consistent with the SK limit, and that the SFH is sensitive to the assumed IMF. The SFH predictions for stellar and metal mass densities, and SN rate evolution, are consistent with the SK limit. The SFH also predicts a delay time of ~3 Gyr for supernova type Ia. The results show that the SFH normalisation is consistent with the SK limit, and that the SFH is sensitive to the assumed IMF.The cosmic star formation history (SFH) has been constrained by ultraviolet and far-infrared measurements, revealing a consistent picture up to redshift z ≈ 6, with tight constraints for z ≲ 1. Analytical fits to these data show that the SFH normalisation is unlikely to be much lower than indicated by direct fits. The SFH also predicts a delay time of ~3 Gyr for supernova type Ia. The Super-Kamiokande (SK) limit on the electron antineutrino flux from core-collapse supernovae provides an upper limit on the SFH normalisation, consistent with modest neutrino temperatures from SN events. The traditional Salpeter initial mass function (IMF) is not a good representation at low stellar masses, and recently favoured IMFs are also constrained. Shallow or top-heavy IMFs may be preferred, but they cannot be too top-heavy. Improved data on supernova rate density evolution, stellar mass ranges for core-collapse and type Ia supernovae, and antineutrino backgrounds are needed to resolve outstanding issues. The SFH data compilation, including UV and FIR measurements, is used to fit parametric forms, with the best fit for the SalA IMF and BG IMF. The SFH normalisation is constrained by the SK limit, with effective temperatures at the lower end of the predicted range. The SFH predictions for stellar and metal mass densities, and SN rate evolution, are consistent with the SK limit. The SFH also predicts a delay time of ~3 Gyr for supernova type Ia. The results show that the SFH normalisation is consistent with the SK limit, and that the SFH is sensitive to the assumed IMF. The SFH predictions for stellar and metal mass densities, and SN rate evolution, are consistent with the SK limit. The SFH also predicts a delay time of ~3 Gyr for supernova type Ia. The results show that the SFH normalisation is consistent with the SK limit, and that the SFH is sensitive to the assumed IMF.