Constraining Dark Matter candidates from structure formation

We show that collisional damping of adiabatic primordial fluctuations yields constraints on the possible range of mass and interaction rates of Dark Matter particles. Our analysis relies on a general classification of Dark Matter candidates, that we establish independently of any specific particle theory or model. From a relation between the collisional damping scale and the Dark Matter interaction rate, we find that Dark Matter candidates must have cross-sections at decoupling smaller than $10^{-33} \frac{m_{dm}}{1 MeV} cm^2$ with photons and $10^{-37} \frac{m_{dm}}{1 MeV} cm^2$ with neutrinos, to explain the observed primordial structures of $10^9$ Solar mass. These damping constraints are particularly relevant for Warm Dark Matter candidates. They also leave open less known regions of parameter space corresponding to particles having rather high interaction rates with other species than neutrinos and photons.