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We compute the luminosity function (LF) and the formation rate of long gammaray bursts (GRBs) in three different scenarios: i) GRBs follow the cosmic starformation and their LF is constant in time; ii) GRBs follow the cosmic starformation but the LF varies with redshift; iii) GRBs form preferentially inlow-metallicity environments. We then test model predictions against the Swift3-year data, showing that scenario i) is robustly ruled out. Moreover, we showthat the number of bright GRBs detected by Swift suggests that GRBs should haveexperienced some sort of luminosity evolution with redshift, being moreluminous in the past. Finally we propose to use the observations of theafterglow spectrum of GRBs at z>5.5 to constrain the reionization history andwe applied our method to the case of GRB 050904.

The Luminosity Function of Long Gamma-Ray Bursts and their rate at z>6