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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 around $m_H=126 ~\rm{GeV}$.

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:

  1. a very light vector boson, so-called "dark photon" (0607094),
  2. 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 latter case, it is possible to have a very light CP-odd particle (pseudoscalar) in addition to the Higgs boson observed at the LHC. Usually the latter is identified with the lightest CP-even boson of these models (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 like the CMB measurements is not completely ruled out.

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The proposal in that article is that the Higgs boson is ~70GeV and stable. Since the article was written, it has been discovered that the Higgs boson is ~126GeV and decays. The hypothesis has been disproven.

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Thank you for the comment . How about the Gauge Higgs Unification ? Is it proved ? –  user44629 Apr 25 at 23:38

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