2.7 Constraints on warm dark matter

N-body simulations of large-scale structures that assume a ΛCDM cosmology appear to over-predict the power on small scales when compared to observations [744]: ‘the missing-satellite problem’ [494, 511, 869, 188], the ‘cusp-core problem’ [568, 833, 974Jump To The Next Citation Point] and sizes of mini-voids [888]. These problems may be more or less solved by several different phenomena [e.g. 310], however one which could explain all of the above is warm dark matter (WDM) [143, 248, 159]. If the dark matter particle is very light, it can cause a suppression of the growth of structures on small scales via free-streaming of the dark matter particles whilst relativistic in the early universe.

2.7.1 Warm dark matter particle candidates

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:

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

2.7.2 Dark matter free-streaming

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]

∘ ---------- P (k) [ ] T (k) ≡ --WDM---- = 1 + (αk )2μ −5∕μ , (2.7.1 ) PCDM (k)
with suitable parameter μ = 1.12 [929Jump To The Next Citation Point] and with the scale break parameter, α in the case of thermal relic DM
( ) −1.11( )0.11 ( )1.22 α = 0.049 mWDM--- ΩWDM--- -h- h−1Mpc. (2.7.2 ) keV 0.25 0.7
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 mWDM (e.g., gravitino), and the mass of the simplest sterile neutrino m νs, such that the two models have an identical impact on cosmology [929Jump To The Next Citation Point]

(mWDM )4∕3( ωWDM ) −1∕3 m νs = 4.43 ------- ------- keV, (2.7.3 ) keV 0.1225
where ω = Ωh2. 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 [630Jump To The Next Citation Point] and most likely needs to be explored through further simulations [974].

2.7.3 Current constraints on the WDM particle from large-scale structure

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-α forest, which can indirectly measure the fluctuations in the dark matter density on scales between ∼ 100 kpc and ∼ 10 Mpc gives the limits of mWDM > 4 keV or equivalently m νs > 28 keV 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 m νs < 1.8 keV 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 mWDM > 2 keV [630Jump To The Next Citation Point].

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