Source evolution function of cosmological gamma-ray bursts

We test several possible source evolution functions of gamma-ray bursts (GRBs) by using the 〈V/V _max〉 statistic. Based on the star-formation-rate (SFR)-related source evolution function and the standard candle assumption, we consider an exponential function and compare it with two other source evolutionary scenarios, a constant number density (no evolution) and a broken power-law function evolution. Although the observed GRBs are well accounted for by using the standard model with a constant number density, we show that when the widths are sufficiently broad (Δz > 2.0), the assumed Gaussian-like functions can also fit the observed 〈V/V _max〉 within a 3σ significance level. We conclude that sharply peaked source evolution functions are ruled out.