The consistency of standard cosmology and the BATSE number versus brightness relation

The integrated number-peak-flux relation measured by the Burst and Transient Source Experiment (BATSE) on board the Compton Gamma Ray Observatory is compared with several standard cosmological distributions for gamma-ray bursts (GRBs). Friedmann-Robertson-Walker models were used along with the assumption that the bursts are standard candles and have no number or luminosity evolution. For a given Omega spectral shape, we used a free parameter, essentially the comoving number density of bursts, to generate a best fit between the cosmology and the measured relation. Our results are shown for a subsample of the first 260 GRBs recorded by BATSE. We find acceptable fits between simple cosmological models and the brightness distribution data, as determined by the Kolmogorov-Smirnov one-distribution statistical test. One cannot distinguish a single best cosmological model from the goodness of the fits. The best fit implies that BATSE GRBs are complete out to a redshift of about unity. However, significantly higher and lower redshifts, by as much as a factor of 2, are possible for other marginally acceptable fits.