Cosmological effects on the observed flux and fluence distributions of gamma-ray bursts

Abstract Several claims have been put forward that an essential fraction of long-duration BATSE gamma-ray bursts should lie at redshifts larger than 5. This point-of-view follows from the natural assumption that fainter objects should, on average, lie at larger redshifts. However, redshifts larger than 5 are rare for bursts observed by Swift. The purpose of this article is to show that the most distant bursts in general need not be the faintest ones. We derive the cosmological relationships between the observed and emitted quantities, and arrive at a prediction that is tested on the ensembles of BATSE, Swift and Fermi bursts. This analysis is independent on the assumed cosmology, on the observational biases, as well as on any gamma-ray burst model. We arrive to the conclusion that apparently fainter bursts need not, in general, lie at large redshifts. Such a behaviour is possible, when the luminosities (or emitted energies) in a sample of bursts increase more than the dimming of the observed values with redshift. In such a case dP(z)/dz > 0 can hold, where P(z) is either the peak-flux or the fluence. This also means that the hundreds of faint, long-duration BATSE bursts need not lie at high redshifts, and that the observed redshift distribution of long Swift bursts might actually represent the actual distribution.