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, mx. Since structures form hierarchically, the presence of collapsed objects at high-redshifts can set strong lower limits on mx. We place robust constraints on mx using recent results from the {\it Swift} database of high-redshift gamma-ray bursts (GRBs). We parameterize the redshift evolution of the ratio between the cosmic GRB rate and star formation rate (SFR) as ∝(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 mx≳1.6-1.8 keV at 95% C.L., when marginalized over a flat prior in α. We further estimate that 5 years of a SVOM-like mission would tighten these constraints to mx≳2.3 keV. Our results show that GRBs are a powerful probe of high-redshift structures, providing robust and competitive constraints on mx.