Star Formation History up to z = 7.4: Implications for Gamma-Ray Bursts and the Cosmic Metallicity Evolution

The current Swift sample of gamma-ray bursts (GRBs) with measured redshifts allows to test the assumption that GRBs trace the star formation in the Universe. Some authors have claimed that the rate of GRBs increases with cosmic redshift faster than the star formation rate, whose cause is not known yet. In this paper, I investigate the possibility for interpreting the observed discrepancy between the GRB rate history and the star formation rate history by the cosmic metallicity evolution, motivated by the observation that the cosmic metallicity evolves with redshift and GRBs prefer to occur in low metallicity galaxies. First, I derive a star formation history up to redshift z=7.4 from an updated sample of star formation rate densities obtained by adding the new UV measurements of Bouwens et al. and the new UV and infrared measurements of Reddy et al. to the existing sample compiled by Hopkins & Beacom. Then, adopting a simple model for the relation between the GRB production and the cosmic metallicity history as proposed by Langer & Norman, I show that the observed redshift distribution of the Swift GRBs can be reproduced with a fairly good accuracy. Although the results are limited by the small size of the GRB sample and the poorly understood selection biases in detection and localization of GRBs and in redshift determination, they suggest that GRBs trace both the star formation and the metallicity evolution. If the star formation history can be accurately measured with other approaches, which is presumably achievable in the near future, it will be possible to determine the cosmic metallicity evolution with the study on the redshift distribution of GRBs.