A constraint on the distance scale to cosmological gamma-ray bursts

If gamma-ray bursts are cosmological in origin, the sources are expected to trace the large-scale structure of luminous matter in the universe. I use a new likelihood method that compares the counts-in-cells distribution of gamma-ray bursts in the BATSE 3B catalog with that expected from the known large-scale structure of the universe, in order to place a constraint on the distance scale to cosmological bursts. I find, at the 95% confidence level, that the comoving distance to the ''edge'' of the burst distribution is greater than 630 h(-1) Mpc (z > 0.25), and that the nearest burst is farther than 40 h(-1) Mpc. The median distance to the nearest burst is 170 h(-1) Mpc, implying that the total energy released in gamma-rays during a burst event is of order 3 x 10(51) h(-2) ergs. None of the bursts that have been observed by BATSE are in nearby galaxies, nor is a signature from the Coma Cluster or the ''Great Wall'' likely to be seen in the data at present.