Constraints on warm dark matter models from high-redshift long gamma-ray bursts

Structures in warm dark matter (WDM) models are exponentially suppressed below a certain scale, characterized by the dark matter particle mass, m(x). Since structures form hierarchically, the presence of collapsed objects at high redshifts can set strong lower limits on m(x). We place robust constraints on m(x) using recent results from the Swift data base of high-redshift gamma-ray bursts (GRBs). We parametrize the redshift evolution of the ratio between the cosmic GRB rate and star formation rate (SFR) as proportional to(1 + z)(alpha), thereby allowing astrophysical uncertainties to partially mimic the cosmological suppression of structures in WDM models. Using a maximum-likelihood estimator on two different z > 4 GRB subsamples (including two bursts at z > 8), we constrain m(x) greater than or similar to 1.6-1.8 keV at 95 per cent CL, when marginalized over a flat prior in alpha. We further estimate that 5 years of a Sino-French space-based multi-band astronomical variable objects monitor like mission would tighten these constraints to m(x) greater than or similar to 2.3 keV. Our results show that GRBs are a powerful probe of high-redshift structures, providing robust and competitive constraints on m(x).