Simulations on high-z long gamma-ray burst rate

Since the launch of Swift satellite, the detections of high-z (z > 4) long gamma-ray bursts (LGRBs) have been rapidly growing, even approaching the very early Universe (the record holder currently is z = 8.3). The observed high-z LGRB rate shows significant excess over that estimated from the star formation history. We investigate what may be responsible for this high productivity of GRBs at high-z through Monte Carlo simulations, with effective Swift/Burst Alert Telescope (BAT) trigger and redshift detection probabilities based on current Swift/BAT sample and Compton Gamma-ray Observatory/Burst and Transient Source Experiment LGRB sample. We compare our simulations to the Swift observations via log N - log P, peak luminosity (L) and redshift distributions. In the case that LGRB rate is purely proportional to the star formation rate, our simulations poorly reproduce the LGRB rate at z > 4, although the simulated log N - log P distribution is in good agreement with the observed one. Assuming that the excess of high-z GRB rate is due to the cosmic metallicity evolution or unknown LGRB rate increase parametrized as (1 + z)delta, we find that although the two scenarios alone can improve the consistency between our simulations and observations, incorporation of them gives much better consistency. We get 0.2 < epsilon < 0.6 and delta < 0.6, where epsilon is the metallicity threshold for the production of LGRBs. The best consistency is obtained with a parameter set (epsilon, delta) = (similar to 0.4, similar to 0.4), and BAT might trigger a few LGRBs at z similar or equal to 14. With increasing detections of GRBs at z > 4 (similar to 15 per cent of GRBs in current Swift LGRB sample based on our simulations), a window for very early Universe is opening by Swift and up-coming space-based multiband astronomical variable object monitor missions.