216 Dark Matter
interactions, in which case they froze out early when their interaction rate became
smaller than the expansion rate, or they never even attained thermal equilibrium. Can-
didates in this category are theaxionand its SUSY partneraxino. The axion is a light
pseudoscalar boson with a 2훾coupling like the휋^0 , so it could convert to a real photon
by exchanging a virtual photon with a proton. Its mass is expected to be of the order
of 1μeV to 10meV. It was invented to prevent CP violation in QCD, and it is related to
a slightly broken baryon number symmetry in a five-dimensional space-time. Another
CDM candidate could be axion clusters with masses of the order of 10−^8 푀⊙.
The WIMPs would traverse terrestrial particle detectors with a typical virial velocity
of the order of 200kms−^1 , and perhaps leave measurable recoil energies in their elastic
scattering with protons. The proof that the recoil detected was due to a particle in the
galactic halo would be the annual modulation of the signal. Because of the motion of
the Earth around the Sun, the signal should have a maximum in June and a minimum
in December. Several experiments to detect such signals are currently running with
controversial or no results which only permit setting upper limits to the WIMP flux.
All WIMPs have in common that they are hitherto unobserved particles which only
are predicted by some theories. A signal worth looking for would be monoenergetic
photons from their annihilation
Xdm+Xdm→ 2 훾. (9.15)No such convincing signals have been observed. All reviews to date only list upper
limits.
The supersymmetric WIMP scenario is very uneconomical since it duplicates the
standard model with its large number of particles when actually only one new particle
would be needed for DM. In this sense also the mirror model is uneconomical.
DM Distribution. The ideal fluid approximation which is true for the collisionless
DM on large scales breaks down when they decouple from the plasma and start to
stream freely out of overdense regions and into underdense regions, thereby erasing
all small inhomogeneities (Landau damping). This defines the characteristic length
and mass scales for freely streaming particles of mass푚dm,
휆fs≃ 40(
30 eV
푚dm)
Mpc, (9.16)푀fs≃ 3 × 1015(
30 eV
푚dm) 2
푀⊙. (9.17)
Perturbations in CDM start growing from the time of matter–radiation equality,
while baryonic fluctuations are inhibited until recombination because of the tight
coupling with photons (or alternatively one can say because of the large baryonic
Jeans mass prior to recombination). After recombination, the baryons fall into the
CDM potential wells. A few expansion times later, the baryon perturbations catch up
with the DM, and both then grow together until훿>1, when perturbations become
Jeans unstable (cf. Chapter 10), collapse and virialize. The amplitude of radiation,
however, is unaffected by this growth, so the CMB anisotropies remain at the level