Unveiling Dark Matter free-streaming at the smallest scales with high redshift Lyman-alpha forest

This study introduces novel constraints on the free-streaming of thermal relic warm dark matter (WDM) from Lyman-$\alpha$ forest flux power spectra. Our analysis utilises a high-resolution, high-redshift sample of quasar spectra observed using the HIRES and UVES spectrographs ($z=4.2-5.0$). We employ a Bayesian inference framework and a simulation-based likelihood that encompasses various parameters including the free-streaming of dark matter, cosmological parameters, the thermal history of the intergalactic medium, and inhomogeneous reionization, to establish lower limits on the mass of a thermal relic WDM particle of $5.7\;\mathrm{keV}$ (at 95\% C.L.). This result surpasses previous limits from the Lyman-$\alpha$ forest through reduction of the measured uncertainties due to a larger statistical sample and by measuring clustering to smaller scales ($k_{\rm max}=0.2\;\mathrm{km^{-1}\,s}$). The approximately two-fold improvement due to the expanded statistical sample suggests that the effectiveness of Lyman-$\alpha$ forest constraints on WDM models at high redshifts are limited by the availability of high-quality quasar spectra. Restricting the analysis to comparable scales and thermal history priors as in prior studies ($k_{\rm max}