Connecting the Gamma Ray Burst Rate and the Cosmic Star Formation
  History: Implications for Reionization and Galaxy Evolution
  (Abridged) The contemporary discoveries of galaxies and gamma ray bursts
(GRBs) at high redshift have supplied the first direct information on star
formation when the universe was only a few hundred million years old. The
probable origin of long duration GRBs in the deaths of massive stars would link
the universal GRB rate to the redshift-dependent star formation rate density,
although exactly how is currently unknown. As the most distant GRBs and
star-forming galaxies probe the reionization epoch, the potential rewards of
understanding the redshift-dependent ratio Psi(z) of the GRB rate to star
formation rate are significant and include addressing fundamental questions
such as incompleteness in rest-frame UV surveys for determining the star
formation rate at high redshift and time variations in the stellar initial mass
function. Using an extensive sample of 112 GRBs above a fixed luminosity limit
drawn from the Second Swift Burst Alert Telescope catalog, we compare the
cumulative redshift distribution N(< z) of GRBs with the star formation density
rho_sfr(z) measured from UV-selected galaxies over 0 < z < 4. Strong evolution
(e.g., Psi(z) \propto (1+z)^{1.5}) is disfavored, while more modest evolution
(e.g., Psi(z) \propto (1+z)^{0.5}) is consistent with the data. If such trends
continue beyond z ~ 4, we find the discovery rate of distant GRBs implies a
star formation rate density much higher than that inferred from UV-selected
galaxies. We show that such a star formation history would over-predict the
observed stellar mass density at z > 4 measured from rest-frame optical
surveys. The resolution of this important disagreement is currently unclear,
and the GRB production rate at early times is likely more complex than a simple
function of star formation rate and progenitor metallicity.
