La regulación de las excepciones a la regla de exclusión, legislación o

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 [984]: ‘the missing-satellite problem’ [659, 681, 1133, 251], the ‘cusp-core problem’ [757, 1095, 1268] and sizes of mini-voids [1160]. These problems may be more or less solved by several different phenomena [e.g. 420], however one which could explain all of the above is warm dark matter (WDM) [193, 332, 219]. 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.

2.6.1

Warm dark matter particle candidates

Numerous WDM particle models can be constructed, but there are two that occur most com- monly 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 183, 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 ofthermalized 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. 211, 297].

Other possible WDM candidates exist, for example a non-thermal neutralino [593] or a non-thermal gravitino [116] etc.

2.6.2

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 [193]

T(k)≡

s

PWDM(k)

PCDM(k)

=1 + (αk)2µ−5/µ, (2.6.1)

with suitable parameter µ = 1.12 [1208] and with the scale break parameter, α, in the case of thermal relic DM α= 0.049mWDM keV −1.11_Ω WDM 0.25 0.11 _h 0.7 1.22 h−1Mpc. (2.6.2) 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 particlemWDM(e.g.,

gravitino), and the mass of the simplest sterile neutrino mνs, such that the two models have an

identical impact on cosmology [1208] mνs= 4.43 m_WDM keV 4/3ω_WDM 0.1225 −1/3 keV, (2.6.3)

whereω= 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.

2.6.3

Current constraints on the WDM particle from large-scale struc-

ture

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-αforest, which

can indirectly measure the fluctuations in the dark matter density on scales between ∼100 kpc and∼10 Mpc gives the limits ofmWDM>4 keV or equivalentlymνs>28 keV at 95% confidence

level [1206, 1208, 1068]. 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 limitmνs <1.8 keV at the 95%

confidence limit [221]. 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. 220, and references therein]. The weak lensing power spectrum from Euclid will be able to constrain the dark matter particle mass to aboutmWDM>2 keV [830].

2.6.4

Nonlinear structure in WDM

In order to extrapolate the matter power spectrum to later times one must take into account the nonlinear evolution of the matter density field.

Several fitting functions have been found to calculate the nonlinear power on the small scales of the present-day matter power spectrum in the scenario where all dark matter is warm. The most basic approach is simply to modify the linear matter power spectrum from Equation 2.6.1, which is based on the output of Bolzmann codes like _camb or _class [743, 190]. One can then either i) run simulations [194, 219, 1268, 1222, 335, 1209, 1056, 161, 68, 1073], ii) use the halo model [1107, 1056, 437] or iii) a fit analogous to Equation 2.6.1, where the ΛCDM nonlinear power spectrum is modified by a transfer function [1209] to calculate the present-day power on the small scales: Tnl(k)≡ s Pnl WDM(k) Pnl CDM(k) = 1 + (α k)µl−s/(2µ) , (2.6.4) where α(mWDM, z) = 0.0476 keV mWDM 1.85 1 +z 2 1.3 , (2.6.5)

andµ= 3,l= 0.6,s= 0.4 are the fitting parameters.

Such fits can be used to calculate further constraints on WDM from the weak lensing power spectrum or galaxy clustering [830, 829]

It should be noted that in order to use the present day clustering of structure as a probe for WDM it is crucial to take into account baryonic physics as well as neutrino effect, which are described in the following section.