We use large-scale cosmological observations to place constraints on the dark-matter pressure, sound speed and viscosity, and infer a limit on the mass of warm-dark-matter particles. Measurements of the cosmic microwave background (CMB) anisotropies constrain the equation of state and sound speed of the dark matter at last scattering at the per mille level. Since the redshifting of collisionless particles universally implies that these quantities scale like $a^{-2}$ absent shell crossing, we infer that today $w_{rm (DM)}< 10^{-10.0}$, $c_{rm s,(DM)}^2 < 10^{-10.7}$ and $c_{rm vis, (DM)}^{2} < 10^{-10.3}$ at the $99%$ confidence level. This very general bound can be translated to model-dependent constraints on dark-matter models: for warm dark matter these constraints imply $m> 70$ eV, assuming it decoupled while relativistic around the same time as the neutrinos; for a cold relic, we show that $m>100$ eV. We separately constrain the properties of the DM fluid on linear scales at late times, and find upper bounds $c_{rm s, (DM)}^2<10^{-5.9}$, $c_{rm vis, (DM)}^{2} < 10^{-5.7}$, with no detection of non-dust properties for the DM.
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