On the Clustering of GRBs on the Sky

The two-point correlation of the 4th (current) BATSE catalog (2494 objects) is calculated. It is shown to be consistent with zero at nearly all angular scales of interest. Assuming that GRBs trace the large scale structure in the universe we calculate the angular correlation function for the standard CDM (sCDM) model. It is shown to be $\le 10^{-4}$ at $\theta \simeq 5^\circ$ if the BATSE catalog is assumed to be a volume-limited sample up to $z \simeq 1$. Combined with the error analysis on the BATSE catalog this suggests that nearly $10^5$ GRBs will be needed to make a positive detection of the two-point angular correlation function at this angular scale.