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.