If cold dark matter consists of particles , these must be non-interacting and non-relativistic by definition .
In most cold dark matter models however , dark matter particles inherit a non-vanishing velocity dispersion from interactions in the early universe , a velocity that redshifts with cosmic expansion but certainly remains non-zero .
In this article , we place model-independent constraints on the dark matter temperature to mass ratio , whose square root determines the dark matter velocity dispersion .
We only assume that dark matter particles decoupled kinetically while non-relativistic , when galactic scales had not entered the horizon yet , and that their momentum distribution has been Maxwellian since that time .
Under these assumptions , using cosmic microwave background and matter power spectrum observations , we place upper limits on the temperature to mass ratio of cold dark matter today ( away from collapsed structures ) .
These limits imply that the present cold dark matter velocity dispersion has to be smaller than 54 m/s .
Cold dark matter has to be quite cold , indeed .