Gamma-ray bursts and the cosmic star formation rate

We have tested several models of gamma-ray burst (GRB) luminosity and redsh ift distribution functions for compatibility with the BATSE 4B number versu s peak flux relation. Our results disagree with recent claims that current GRB observations can be used to constrain strongly the cosmic star formatio n history. Instead, we find that relaxing the assumption that GRBs are stan dard candles renders a very broad range of models that are consistent with the BATSE number-flux relation. We explicitly construct two sample distribu tions, one tracing the star formation history and one with a constant comov ing density. We show that both distributions are compatible with the observ ed fluxes and redshifts of the bursts GRB 970508, GRB 971214, and GRB 98070 3, and we discuss the measurements required to distinguish the two models.