Is the Redshift Clustering of Long-Duration Gamma-Ray Bursts Significant?

The 26 long-duration gamma-ray bursts (GRBs) with known redshifts form adistinct cosmological set, selected differently than other cosmological probessuch as quasars and galaxies. Since the progenitors are now believed to beconnected with active star-formation and since burst emission penetrates dust,one hope is that with a uniformly-selected sample, the large-scale redshiftdistribution of GRBs can help constrain the star-formation history of theUniverse. However, we show that strong observational biases in ground-basedredshift discovery hamper a clean determination of the large-scale GRB rate andhence the connection of GRBs to the star formation history. We then focus onthe properties of the small-scale (clustering) distribution of GRB redshifts.When corrected for heliocentric motion relative to the local Hubble flow, theobserved redshifts appear to show a propensity for clustering: 8 of 26 GRBsoccurred within a recession velocity difference of 1000 km/s of another GRB.That is, 4 pairs of GRBs occurred within 30 h_65^-1 Myr in cosmic time, despitebeing causally separated on the sky. We investigate the significance of thisclustering. Comparison of the numbers of close redshift pairs expected from thesimulation with that observed shows no significant small-scale clusteringexcess in the present sample; however, the four close pairs occur only in abouttwenty percent of the simulated datasets (the precise significance of theclustering is dependent upon the modeled biases). We conclude with someimpetuses and suggestions for future precise GRB redshift measurements.