Gamma-ray Bursts and the Early Star-formation History
  We review the uncertainties in high-z star-formation rate (SFR) measures and the constraints that one obtains from high-z gamma-ray burst (GRB) rates on them. We show that at the present time, the GRB rates per unit star-formation at z>3 are higher than at lower redshift. We also compare metallicity predictions made using a hierarchical model of cosmic chemical evolution based on two recently proposed SFRs, one based on the observed galaxy luminosity function at high redshift and one based on the GRB rate and find that within the considerable scatter in metal abundance measures, they both are consistent with the data. Analyzing the ensemble of different measurements together, we conclude that despite metallicity biases, GRBs may be a less biased probe of star-formation at z>3 than at z<2. There is likely to be a common origin to the high GRB rate per unit star-formation and the high observed Lyman-continuum production rate in high redshift galaxies and that this may be due to a relative overabundance of stars with mass $>$25Msun which are likely GRB progenitors. We also find that to reconcile these measurements with the Thomson scattering cross section of cosmic microwave background (CMB) photons measured by Planck, the escape fraction of Lyman-continuum photons from galaxies must be low, about 15 percent or less and that the clumping factor of the IGM is likely to be small, about 3. Finally, we demonstrate that GRBs are unique probes of metallicity evolution in low-mass galaxy samples and that GRB hosts likely lost a significant fraction of metals to the intergalactic medium (IGM) due to feedback processes such as stellar winds and supernovae. 
R. Chary, P. Petitjean, B. Robertson, M. Trenti, E. Vangioni
astro-ph.GA