The redshift distribution of gamma-ray bursts revisited
  In this letter, we calculate the redshift distribution of gamma-ray bursts assuming that they trace (i) the globally averaged star formation rate or (ii) the average metallicity in the Universe. While at redshifts 5 and below, both the star formation rate and metallicity are observationally determined modulo some uncertainties, at higher redshifts there are few constraints. We extrapolate the star formation rate and metallicity to higher redshifts and explore models that are broadly consistent with bounds on the optical depth from WMAP results. In addition, we also include parametric descriptions of the luminosity function, and the typical spectrum for GRBs. With these essential ingredients included in the modeling, we find that a substantial fraction 75% of GRBs are expected to originate at redshifts below 4, in variance with some previous estimates. Conversely, if we assume as expected for the collapsar model that gamma-ray bursts favour a low metallicity environment and therefore, relate the GRB rate to a simple model of the average metallicity as a function of redshift, we find that a higher fraction of bursts, about 40% originate from redshifts greater than 4. We conclude with the implications of SWIFT GRB detections. 
Priyamvada Natarajan, Badr Albanna, Jens Hjorth, Enrico Ramirez-Ruiz,   Nial Tanvir and Ralph Wijers