The luminosity function and the rate of Swift's Gamma Ray Bursts

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 (1 + 2) 2.1+0.5 -0.6 for 0 3. The local rate is ρ 0 ≃ 1.3 +0.6 -0.7 (Gpc -3 yr -1 ). The luminosity function is well described by a broken power law with a break at L* ≃ 10 52.5±0.2 (erg s -1 ) and with indices α = 0.2 +0.2 -0.1 and β = 1.4 +0.3 -0.6 . The recently detected GRB 090423, 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.