Warm dark matter 203decays, it turns out that only a few candidates survive as viable solutions.
These schemes beyond pure CDM which presently enjoy most scientific
favour accompany CDM with a conspicous amount of ‘vacuum’ energy density, a
form of unclustered energy which could be due to the presence of a cosmological
constant. We will deal with this interesting class of DM models, calledCDM
models, in the final part of this report.
5.6 Warm dark matter
Another route which has been followed in the attempt to go beyond the pure
CDM proposal is the possibility of having some form of warm DM (WDM).
The implementation of this idea is quite attractive in SUSY models where the
breaking of SUSY is conveyed by gauge interactions instead of gravity (these
are the so-called gauge-mediated SUSY breaking (GMSB) models, for a review
see [32]). This scenario had already been critically considered in the old days
of the early constructions of SUSY models and was subject to renewed interest
with the proposal in [37–39], where some guidelines for the realization of low-
energy SUSY breaking are provided. In these schemes, the gravitino mass (m 3 / 2 )
loses its role of fixing the typical size of soft breaking terms and we expect it
to be much smaller than that in models with a hidden sector. Indeed, given the
well-known relation [34] betweenm 3 / 2 and the scale of SUSY breaking
√
F,i.e.
m 3 / 2 =O(F/M),whereMis the reduced Planck scale, we expectm 3 / 2 in the
keV range for a scale
√
FofO( 106 GeV) that has been proposed in models with
low-energy SUSY breaking in a visible sector.
In the following we briefly report some implications of SUSY models with a
light gravitino (in the keV range) in relation with the dark matter (DM) problem.
We anticipate that a gravitino of that mass behaves as a warm dark matter (WDM)
particle [24, 25, 27], that is, a particle whose free-streaming scale involves a mass
comparable to that of a galaxy,∼ 1011 −^12 M.
5.6.1 Thermal history of light gravitinos and WDM models
Suppose that the gravitinos were once in thermal equilibrium and were frozen out
at the temperatureTψμdduring the cosmic expansion. It can be shown that the
density parameterψμcontributed by relic thermal gravitinos is:
ψμh^20 = 1. 17(m 3 / 2
1keV)(g∗(Tψμd)
100)− 1
, (5.43)
whereg∗(Tψμd)represents the effective massless degrees of freedom at the
temperatureTψμd. Therefore, a gravitino in the previously mentioned keV range
provides a significant portion of the mass density of the present universe.