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

If \g--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 \g--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 \g--rays during a burst event is of order $3\times 10^{51}~h^{-2}$ 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.