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

Structures in Warm Dark Matter (WDM) models are exponentially suppressed belowa certain scale, characterized by the dark matter particle mass, mx . Since structuresform hierarchically, the presence of collapsed objects at high-redshifts can set stronglower limits on mx . We place robust constraints on mx using recent results fromthe Swift database of high-redshift gamma-ray bursts (GRBs). We parameterize theredshift 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 thecosmological suppression of structures in WDM models. Using a maximum likelihoodestimator on two different z > 4 GRB subsamples (including two bursts at z > 8), weconstrain mx 1.6-1.8 keV at 95% CL, when marginalized over a flat prior in α. Wefurther estimate that 5 years of a SVOM-like mission would tighten these constraintsto mx 2.3 keV. Our results show that GRBs are a powerful probe of high-redshiftstructures, providing robust and competitive constraints on mx .