STATISTICS OF COSMOLOGICAL GAMMA-RAY BURSTS - SOURCE EVOLUTION, COSMOLOGICAL GEOMETRY, AND RELATIVISTIC BEAMING

We calculate effects of source evolution, cosmological geometry, and l uminosity distribution on statistics of gamma-ray bursts in the cosmol ogical scenario. Nonstandard cosmological models affect the burst stat istics in such a way that effects of source evolution or luminosity di stribution may not be easily distinguishable from those of the cosmolo gical geometry. The probability of gravitational lensing of gamma-ray bursts depends sensitively on source evolution, which suggests that de tection of lensed bursts could not only confirm the cosmological origi n itself but also give some constraints on source evolution. If gamma rays are emitted from sources in relativistic bulk motion such as coll imated.jets, observed gamma rays are strongly beamed. The apparent obs erved luminosity of the burst is a function of an angle between the ob server's line of sight and the direction of bulk motion. We consider e ffects of apparent luminosity distributions (due to beaming) on the bu rst statistics. The predicted distributions of durations and the flux- duration relation differ greatly from those of the simplest cosmologic al model without beaming. Source evolution, luminosity distribution, a nd cosmological geometry are virtually indistinguishable from one anot her within the simplest statistical measures. More detailed statistica l measures such as the distribution of durations or the peak-flux-dura tion relation may provide further information.