The Impact of Star Formation and Gamma-Ray Burst Rates at High Redshift   on Cosmic Chemical Evolution and Reionization
  Recent observations in the total luminosity density have led to significant progress in establishing the star formation rate (SFR) at high redshift. Concurrently observed gamma-ray burst rates have also been used to extract the SFR at high redshift. The SFR in turn can be used to make a host of predictions concerning the ionization history of the Universe, the chemical abundances, and supernova rates. We compare the predictions made using a hierarchical model of cosmic chemical evolution based on three recently proposed SFRs: two based on extracting the SFR from the observed gamma-ray burst rate at high redshift, and one based on the observed galaxy luminosity function at high redshift. Using the WMAP/Planck data on the optical depth and epoch of reionization, we find that only the SFR inferred from gamma-ray burst data at high redshift suffices to allow a single mode (in the initial mass function) of star formation which extends from z = 0 to redshifts > 10. For the case of the more conservative SFR based on the observed galaxy luminosity function, the reionization history of the Universe requires a bimodal IMF which includes at least a coeval high (or intermediate) mass mode of star formation at high redshift (z> 10). Therefore, we also consider here a more general bimodal case which includes an early-forming high mass mode as a fourth model to test the chemical history of the Universe. We compute the abundances of several trace elements, as well as the expected supernova rates, the stellar mass density and the specific SFR, sSFR, as a function of redshift   for each of the four models considered. We conclude that observational constraints on the global metallicity and optical depth at high redshift favor unseen faint but active star forming galaxies as pointed out in many recent studies. 
E. Vangioni, K.A. Olive, T. Prestegard, J. Silk, P. Petitjean, and V.   Mandic
astro-ph.GA astro-ph.CO