2010MNRAS.406.1944W

We invert directly the redshift-luminosity distribution of observed long Swift gamma-ray bursts (GRBs) to obtain their rate and luminosity function. Our best-fitting rate is described by a broken power law that rises like for 0 < z < 3 and decreases like for z > 3. The local rate is ρ₀≃ 1.3^+0.6_–0.7(Gpc^–3/yr). The luminosity function is well described by a broken power law with a break at L* ≃ 10^52.5±0.2 (erg/s) and with indices α = 0.2^+0.2_–0.1 and β = 1.4^+0.3_–0.6. The recently detected GRB090423, with z ~ 8, fits nicely into the model's prediction, verifying that we are allowed to extend our results to high redshifts. While the GRB rate may follow the star formation rate (SFR) for z < 3, the high-redshift slope is shallower than the steep decline in the SFR for 4 < z. However, we cannot rule out a GRB rate that follows one of the recent SFR models.