## Warm dark matter

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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$\lambda _{FS}$ via
where $a(t)$ is a scale factor, $t_0$ is the time today (see the age of the Universe) and $v(t)$ is the velocity of DM particles. The velocity is given by the following expression
where $c$ is the speed of light and time of non-relativistic transition$t_{nr}$ is defined as the time when
where $m$ 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.