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

We calculate effects of source evolution, cosmological geometry, and luminosity distribution on statistics of gamma-ray bursts in the cosmological scenario. Nonstandard cosmological models affect the burst statistics in such a way that effects of source evolution or luminosity distribution may not be easily distinguishable from those of the cosmological geometry. The probability of gravitational lensing of gamma-ray bursts depends sensitively on source evolution, which suggests that detection of lensed bursts could not only confirm the cosmological origin itself but also give some constraints on source evolution. If gamma rays are emitted from sources in relativistic bulk motion such as collimated.jets, observed gamma rays are strongly beamed. The apparent observed luminosity of the burst is a function of an angle between the observer's line of sight and the direction of bulk motion. We consider effects of apparent luminosity distributions (due to beaming) on the burst statistics. The predicted distributions of durations and the flux-duration relation differ greatly from those of the simplest cosmological model without beaming. Source evolution, luminosity distribution, and cosmological geometry are virtually indistinguishable from one another within the simplest statistical measures. More detailed statistical measures such as the distribution of durations or the peak-flux-duration relation may provide further information.