How Cold is Cold Dark Matter?
  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.
