  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.
