Dark Matter candidates have to interact very weakly with the particles of the Standard Model in order to have a relic density compatible with the one measured by the Plank satellite. The Higgs boson cannot be Dark Matter, because the decay rate for a process like $H\to f\bar{f}$ is very high for a mass $m_H=126 ~\rm{GeV}$.
However, there are still some very interesting possibilities concerning scalar particles. If we want to have the correct relic density without considering extremely heavy dark matter particles, then we have to suppose the existence of a mediator that makes the connections between the Standard Model and the "Dark Sector".
Two possibilities are:
- a very light vector boson, so-called "dark photon" (0607094),
- a light pseudoscalar boson (0712.0016).
In particular, in most extension of the SM there are several "Higgs bosons" and maybe one of these particles can be such a mediator. Two particular examples are the Minimal Supersymmetric Standard Model (MSSM) and the Next-to-Minimal Supersymmetric Standard Model (NMSSM). In the later, it is possible to have a very light CP-odd particle (pseudoscalar) in addition to the Higgs boson observed at the LHC, which is identified with the lightest CP-even boson (cf. 1301.1325).
In conclusion, we know very few about dark matter and its interaction, but the possibility of having a new Higgs boson that could explain the experimental results is not completely ruled out.
This post imported from StackExchange Physics at 2014-04-25 16:56 (UCT), posted by SE-user Melquíades