CONSTRAINTS ON THE REDSHIFT AND LUMINOSITY DISTRIBUTIONS OF GAMMA-RAYBURSTS IN AN EINSTEIN-DE-SITTER UNIVERSE

Two models of the gamma-ray burst population, one with a standard cand le luminosity and one with a power-law luminosity distribution, are ch i(2)-fitted to the union of two data sets: the differential number ver sus peak. flux distribution of BATSE's long-duration bursts and the ti me dilation and energy shifting versus peak flux information of pulse duration time dilation factors, interpulse duration time dilation fact ors, and peak energy shifting factors. The differential peak flux dist ribution is corrected for threshold effects at low peak fluxes and at short burst durations, and the pulse duration time dilation factors ar e also corrected for energy stretching and similar effects. Within an Einstein-de Sitter cosmology, we place strong bounds on the evolution of the bursts, and these bounds are incompatible with a homogeneous po pulation, assuming a power-law spectrum and no luminosity evolution. A dditionally, under the implied conditions of moderate evolution, the 9 0% width of the observed luminosity distribution is shown to be less t han or similar to 10(2), which is less constrained than others have de monstrated it to be assuming no evolution. Finally, redshift considera tions indicate that if the redshifts of BATSE's faintest bursts are to be compatible with that which is currently known for galaxies, a stan dard candle luminosity is unacceptable, and, in the case of the power- law luminosity distribution, a mean luminosity less than or similar to 10(57) photons s(-1) is favored.