Numerous WDM particle models can be constructed, but there are two that occur most commonly in literature, because they are most plausible from particle physics theory as well as from cosmological observations:

- Sterile neutrinos may be constructed to extend the standard model of particle physics. The standard model active (left-handed) neutrinos can then receive the observed small masses through, e.g., a see-saw mechanism. This implies that right-handed sterile neutrinos must be rather heavy, but the lightest of them naturally has a mass in the keV region, which makes it a suitable WDM candidate. The simplest model of sterile neutrinos as WDM candidate assumes that these particles were produced at the same time as active neutrinos, but they never thermalized and were thus produced with a much reduced abundance due to their weak coupling [see 136, and references therein].
- The gravitino appears as the supersymmetric partner of the graviton in supergravity models. If it has a mass in the keV range, it will be a suitable WDM candidate. It belongs to a more general class of thermalized WDM candidates. It is assumed that this class of particles achieved a full thermal equilibrium, but at an earlier stage, when the number of degrees of freedom was much higher and hence their relative temperature with respect to the CMB is much reduced. Note that in order for the gravitino to be a good dark matter particle in general, it must be very stable, which in most models corresponds to it being the LSP [e.g. 151, 221].

Other possible WDM candidates exist, for example a non-thermal neutralino [438] or a non-thermal gravitino [82] etc.

The modification of the shape of the linear-theory power spectrum of CDM due to WDM can be calculated by multiplication by a transfer function [143]

with suitable parameter [929] and with the scale break parameter, in the case of thermal relic DM This is a fit to the solution of the full Boltzman equations.There is a one-to-one relation between the mass of the thermalized WDM particle (e.g., gravitino), and the mass of the simplest sterile neutrino , such that the two models have an identical impact on cosmology [929]

where . The difference comes from the fact that in the gravitino case the particle is fully thermalized, the number of effective degrees of freedom being determined by mass and energy density of dark matter, while in the simplest sterile neutrino case the number of degrees of freedom is fixed, while abundance is determined by mass and energy density of dark matter.In order to extrapolate the matter power spectrum to later times one must take into account the nonlinear evolution of the matter density field. This is not straightforward in the WDM case [630] and most likely needs to be explored through further simulations [974].

Measurements in the particle-physics energy domain can only reach masses uninteresting in the WDM context, since direct detectors look mainly for a WIMP, whose mass should be in the GeV – TeV range. However, as described above, cosmological observations are able to place constraints on light dark matter particles. Observation of the flux power spectrum of the Lyman- forest, which can indirectly measure the fluctuations in the dark matter density on scales between and gives the limits of or equivalently at 95% confidence level [927, 929, 812]. For the simplest sterile neutrino model, these lower limits are at odds with the upper limits derived from X-ray observations, which come from the lack of observed diffuse X-ray background from sterile neutrino annihilation and set the limit at the 95% confidence limit [161]. However, these results do not rule the simplest sterile neutrino models out. There exist theoretical means of evading small-scale power constraints [see e.g. 160, and references therein]. The weak lensing power spectrum from Euclid will be able to constrain the dark matter particle mass to about [630].

Living Rev. Relativity 16, (2013), 6
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