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)δ, 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 < ε < 0.6 and δ < 0.6, where ε is the metallicity threshold for the production of LGRBs. The best consistency is obtained with a parameter set (ε,  δ) = (∼ 0.4,  ∼ 0.4), and BAT might trigger a few LGRBs at z≃ 14. With increasing detections of GRBs at z > 4 (∼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.

Apparent redshift dependence of the jet opening angles (θ j ) of gamma-ray bursts (GRBs) is observed from current GRB sample. We investigate whether this dependence can be explained with instrumental selection effects and observational biases by a bootstrapping method. Assuming that (1) the GRB rate follows the star formation history and the cosmic metallicity history and (2) the intrinsic distributions of the jet-corrected luminosity (L γ ) and θ j are a Gaussian or a power-law function, we generate a mock Swift/BAT sample by considering various instrumental selection effects, including the flux threshold and the trigger probability of BAT, the probabilities of a GRB jet pointing to the instrument solid angle and the probability of redshift measurement. Our results well reproduce the observed θ j − z dependence. We find that in case of L γ ∝ θ 2 j good consistency between the mock and observed samples can be obtained, indicating that both L γ and θ j are degenerate for a flux-limited sample. The parameter set (L γ , θ j ) = (4.9 × 10 49 erg s −1 , 0.054rad) gives the best consistency for the current Swift GRB sample. Considering the beaming effect, the derived intrinsic local GRB rate accordingly is 2.85 × 10 2 Gpc −3 yr −1 , inferring that ∼ 0.59% of Type Ib/c SNe may be accompanied by a GRB.