COMPATIBILITY OF THE BATSE GAMMA-RAY BURST DATA WITH GENERAL FRIEDMANN COSMOLOGICAL MODELS

The intensity distribution of gamma-ray bursts observed by BATSE is used, in conjunction with an integral moment analysis, to investigate the compatibility of various nonevolving burst luminosity functions phi(L) and burst spectral indices alpha in Friedmann cosmological models containing a general value of the cosmological constant Lambda. We find that models with a zero cosmological constant and a burst spectral index of alpha = 2 are consistent with the observational data only if the maximum redshift observed by BATSE is less than z(max) = 1.25 (2.1 at the +3 sigma confidence level). Higher limiting redshifts in the standard Lambda = 0 model are possible only if alpha is decreased from the observed value of similar to 2 to smaller values, less than or similar to 1. One may obtain higher limiting redshifts for values of alpha > 2 only in the context of a cosmological model that has a value of the deceleration parameter q(0), in the range -1.4 to -3, corresponding to big bang models with a positive cosmological constant. The closer the actual value of the maximum observed redshift is to these limiting z(max) values, the narrower must be the width of the function phi(L) which describes the luminosity distribution of the bursts. Models which require bursts to possess a wide range of intrinsic luminosities must therefore have actual limiting redshifts significantly less than the theoretical z(max) derived here, yet still be in the range where the model can be considered ''cosmological.'' This constraint, combined with earlier work by Horack, Emslie, and Meegan (1994b) on Euclidean source distributions, mandates a positive value for the cosmological constant in any nonevolving scenario which requires gamma-ray bursts to possess a wide range of intrinsic luminosities.