STANDARD COSMOLOGY AND THE BATSE NUMBER VERSUS PEAK FLUX DISTRIBUTION

Adopting a simple cosmological model for gamma-ray bursts (GRBs), following Mao & Paczynski, we generate number versus peak flux distributions for a range of values of Omega(0), (ratio of the density of the Universe to the critical density) and z(max) (the redshift at which the faintest GRB in the present sample is located), and compare these distributions to one from BATSE GRBs in the 2B catalogue. The observed BATSE distribution is consistent with the faintest GRBs in our sample originating from a redshift of z(max) similar to 0.8-3.0 (90 per cent), with the most likely values in the range of 1.0-2.2, and is largely insensitive to Omega(0) for models with no evolution. To constrain the model parameter Omega(0) to the range 0.1-1.0 using only log N-log F-peak distributions, more than 4000 GRBs, with a most likely value of similar to 9000 GRBs, above the 1024 ms averaged peak flux of 0.3 photon cm(-2) s(-1) would be needed. This requires a live integration time of > 6 yr with BATSE. Detectors sensitive to much lower limits (i.e., standard candle bursts out to z(max) = 10, similar to x 70-400 in sensitivity) require similar to 200 GRBs, with <0.03 yr 4 pi steradian coverage. We place limits on the amount of frequency density and, separately, peak luminosity evolution in the sample of GRBs. We find that frequency density evolution models can place the faintest GRBs at z(max) similar to 10-200, without conflicting with the observations of relative time dilation of similar to 2 reported by Norris et al. and Wijers & Paczyriski (see, however, Band), although this would require vastly different comoving burst rates in GRBs of different spectra.