We selected a complete sub-sample of 58 Swift bright long GRBs. The sample was selected considering bursts with favorable observing conditions for ground-based follow-up observations and with the 1-second peak flux above a flux threshold of 2.6 photons cm−2 s−1 in the 15-150 keV energy band. This sample has a redshift completeness level higher than 90%. Complete samples are at the base of any population study and we used this sample to investigate the properties of long GRBs. In particular, we derived their evolution with cosmic times, focusing on the GRB luminosity function, the prompt emission spectral-energy correlations and the nature of dark bursts. If we assume that long GRBs trace the cosmic star formation, then we can reject the no-evolution scenario in which the GRB luminosity function is constant in redshift. We also confirm the existence of strong Epeak − Eiso and Epeak − Liso correlations for the bursts of this complete sample and of a genuine dark population, with - 30% of dark-burst events expected for the whole class of long GRBs. These dark-bursts events seems to generate in much denser metal-rich environments where dust must be present with respect to normal bright events.
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