Spitzer observations of gamma-ray burst host galaxies:: A unique window into high-redshift chemical evolution and star formation

We present deep 3.6 mu m observations of three z similar to 5 GRB host galaxies with the Spitzer Space Telescope. The host of GRB 060510B, at z 4.942, is detected with a flux density of 0.23 +/- 0.04 mu Jy, corresponding to a rest-frame V-band luminosity of 1.3 x 10(10) L-circle dot, or approximate to 0.15 L-*,L-V,L-z=3. We do not detect the hosts of GRBs 060223A and 060522 and constrain their rest-frame V-band luminosity to <0.1 L-*,L-V,L-z=3. Our observations reveal that z similar to 5 GRB host galaxies are a factor of similar to 3 less luminous than the median luminosity of spectroscopically confirmed z similar to 5 galaxies in the Great Observatories Origins Deep Survey and the Hubble Ultra Deep Field. The strong connection between GRBs and massive star formation implies that not all star-forming galaxies at these redshifts are currently being accounted for in deep surveys and GRBs provide a unique way to measure the contribution to the star formation rate density from galaxies at the faint end of the galaxy luminosity function. By correlating the comoving star formation rate density with comoving GRB rates at lower redshifts, we estimate a lower limit to the star formation rate density of 0.12 +/- 0.09 and 0.09 +/- 0.05 M-circle dot yr(-1) Mpc(-3) at z similar to 4.5 and z similar to 6, respectively. This is in excellent agreement with extinction-corrected estimates from Lyman break galaxy samples. Finally, our observations provide initial evidence that the metallicity of star-forming galaxies evolves more slowly than the stellar mass density between z similar to 5 and z similar to 0, probably indicative of the loss of a significant fraction of metals to the intergalactic medium, especially in low-mass galaxies.