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 mx 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 α(1 + z)^α, 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 ≳ 1.6-1.8 keV at 95 per cent CL, when marginalized over a flat prior in α. We further estimate that 5 years of aSino-French space-based multiband astronomical variable objects monitor like mission would tightenthese constraints to m_x ≳ 2.3 keV. Our results show that GRBs are a powerful probe of high-redshift structures, providing robust and competitive constraints on m_x.