The redshift distribution of Swift gamma-ray bursts:: evidence for evolution

We predict the redshift distribution of long gamma-ray bursts (GRBs) with Monte Carlo simulations. Our improved analysis constrains free parameters with three kinds of observation: (i) the log N - log P diagram of Burst and Transient Source Experiment (BATSE) bursts; (ii) the peak energy distribution of bright BATSE bursts and (iii) the High Energy Transient Explorer (HETE2) fraction of X-ray rich GRBs and X-ray flashes. The statistical analysis of the Monte Carlo simulation results allows us to carefully study the impact of the uncertainties in the GRB intrinsic properties on the redshift distribution. The comparison with Swift data then leads to the following conclusions. The Amati relation should be intrinsic, if observationally confirmed by Swift. The progenitor and/or the GRB properties have to evolve to reproduce the high mean redshift of Swift bursts. Our results favour an evolution of the efficiency of GRB production by massive stars, that would be nearly six to seven times higher at z similar to 7 than at z similar to 2. We finally predict around 10 GRBs detected by Swift at redshift z > 6 for a 3-yr mission. These may be sufficient to open a new observational window over the high redshift Universe.