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The high‐redshift star formation rate (SFR) is difficult to measure directly even by modern approaches. Long‐duration gamma‐ray bursts (GRBs) can be detected to the edge of the visible universe because of their high luminosities. The collapsar model of long GRBs indicates that they may trace the star formation history. So, long GRBs may be a useful tool of measuring the high‐redshift SFR. Observations show that long GRBs prefer to form in a low‐metallicity environment. We study the high‐redshift SFR up to   z ∼ 8.3  considering the  Swift  GRBs tracing the star formation history and the cosmic metallicity evolution in different background cosmological models including Λ cold dark matter (ΛCDM), quintessence, quintessence with a time‐varying equation of state and brane‐world model. We use latest  Swift  GRBs including two highest‐ z  GRBs, GRB 080913 at   z = 6.7  and GRB 090423 at   z = 8.3 . We find that the SFR at   z  &gt; 4  shows a steep decay with a slope of ∼−5.0 in ΛCDM. In the other three models, the high‐redshift SFR is slightly different from ΛCDM model and also shows a steep decay.

High‐redshift star formation rate up to z ∼ 8.3 derived from gamma‐ray bursts and influence of background cosmology