Observations of long gamma-ray bursts ( LGRBs ) offer a unique opportunity for probing the cosmic star formation history , although whether or not LGRB rates are biased tracers of star formation rate history is highly debated .
Based on an extensive sample of LGRBs compiled by Robertson & Ellis ( 41 ) , we analyze various models of star formation rate and the possible effect of the evolution of cosmic metallicity under the assumption that LGRBs tend to occur in low-metallicity galaxies .
The models of star formation rate tested in this work include empirical fits from observational data as well as a self-consistent model calculated in the framework of the hierarchical structure formation .
Comparing with the observational data , we find a relatively higher metallicity cut of Z \gtrsim 0.6 Z _ { \odot } for the empirical fits and no metallicity cut for the self-consistent model .
These results imply that there is no strong metallicity preference for the host galaxy of LGRBs , in contrast to previous work which suggest a cut of Z \sim 0.1 - 0.3 Z _ { \odot } , and that the inferred dependencies of LGRBs on their host galaxy properties are strongly related to the specific models of star formation rate .
Furthermore , a significant fraction of LGRBs occur in small dark matter halos down to 3 \times 10 ^ { 8 } \mathrm { M _ { \odot } } can provide an alternative explanation for the discrepancy between the star formation rate history and LGRB rate history .