Strong constraints on the cosmic star formation history (SFH) have recently been established using ultraviolet and far-infrared measurements, refining the results of numerous measurements over the past decade. The data show a compellingly consistent picture of the SFH out to redshift z ≈ 6, with especially tight constraints for z approx < 1. We fit these data with simple analytical forms and derive conservative uncertainties. Since the z approx < 1 SFH data are quite precise, we investigate the sequence of assumptions and corrections that together affect the SFH normalization to test their accuracy, both in this redshift range and beyond. As lower limits on this normalization, we consider the evolution in stellar and metal mass densities, and supernova rate density, finding it unlikely that the SFH normalization is much lower than indicated by our direct fit. As a corresponding upper limit on the SFH normalization, we consider the Super-Kamiokande limit on the electron antineutrino (蚠e) flux from past core-collapse supernovae, which applies primarily to z approx < 1. We find consistency with the SFH only if the neutrino temperatures from supernova events are relatively modest. Constraints on the assumed initial mass function (IMF) also become apparent. The traditional Salpeter IMF, assumed for convenience by many authors, is known to be a poor representation at low stellar masses (approx < 1 solar mass), and we show that recently favored IMFs are also constrained. In particular, somewhat shallow, or top-heavy, IMFs may be preferred, although they cannot be too top-heavy. To resolve the outstanding issues, improved data are called for on the supernova rate density evolution, the ranges of stellar masses leading to core-collapse and type Ⅰa supernovae, and the antineutrino and neutrino backgrounds from core-collapse supernovae.
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