Based on their
clustering properties all
dark matter models are subdivided onto
cold (CDM),
warm (WDM), and
hot (HDM).
DM particles are considered
warm is they either decoupled from primordial plasma while still being relativistic or never were in thermal equilibrium and were created relativistic. The former case is sometime referred to as thermal relics. In both cases the particles became non-relativistic still in the
radiation-dominated epoch.
To quantify the clustering properties of
DM one defines a comoving
free streaming horizon via
where
is a scale factor,
is the time
today (see
the age of the Universe) and
is the velocity of DM particles. The velocity is given by the following expression
where
is the speed of light and
time of non-relativistic transition is defined as the time when
where
is the mass of the DM particle.
It is customary to consider particle as
warm is its free-streaming horizon is about Mpc or below:
Such scales are not probed by the
CMB experiments or by
large scale structure surveys. Therefore,
WDM fits the CMB and LSS data as well as CDM models.