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, $m_{\rm x}$. Since structures form hierarchically, the presence of collapsed objects at high-redshifts can set strong lower limits on $m_{\rm x}$. We place robust constraints on $m_{\rm x}$ 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 $\propto (1+z)^\alpha$, 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 $m_{\rm x} \gtrsim 1.6$-1.8 keV at 95% C.L., when marginalized over a flat prior in $\alpha$. We further estimate that 5 years of a SVOM-like mission would tighten these constraints to $m_{\rm x} \gtrsim 2.3$ keV. Our results show that GRBs are a powerful probe of high-redshift structures, providing robust and competitive constraints on $m_{\rm x}$.