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 Swif/BAT trigger and redshift detection probabilities based on current Swift/BAT sample and CGRO/BATSE 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 (SFR), 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 parameterized 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)=(~0.4, ~0.4), and BAT might trigger a few LGRBs at z~14. With increasing detections of GRBs at z>4 (~15% of GRBs in current Swift LGRB sample based on our simulations), a window for very early Universe is opening by Swift and up-coming SVOM missions.
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