A Constraint on the Distance Scale to Cosmological Gamma--Ray Bursts

If gamma-ray bursts have a cosmological 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 $3 \times 10^{51}~h^{-2}$ erg. 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.