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I'm afraid this question could sound a little too vague. I don't even know if dark matter (DM) can be genuinely described by quantum field theory, or if quantum field theory should be somehow "modified" in order to include dark matter.

Assuming that ordinary QFT describes DM, what can be said (or what is known) about the number of degrees of freedom dark matter should have?

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personally, I'm fond of conformal gravity, which gets rid of the need for DM by replacing the Einstein field equations –  Christoph Oct 8 '12 at 19:28
    
doesn't that reference only account for the rotation curves of (certain) galaxies? shouldn't anything else be overcome? –  c.p. Oct 8 '12 at 20:41
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up vote 4 down vote accepted

It is trivial to design a dark matter candidate that is compatible with quantum field theory: massive sterile neutrinos are a moderately popular possibility already.

But that doesn't prove anything, because it is just a dark matter candidate. Indeed the question is rather speculative until we know something about what the dark matter is rather than just things about what it isn't.

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thanks, how many degrees of freedom then? –  c.p. Oct 8 '12 at 20:42
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Two per flavor if they are Majorana, or four if Dirac. The data do not as yet indicate how many sterile flavors there might be, but in some models there is more phase space available for two or three than for one. –  dmckee Oct 8 '12 at 21:09
    
Thanks @dmckee. What does one understand by "more phase space" available? I mean, between the things one knows about what dark matter isn't, which one gives preference to three or two generations over one? (Sorry, should I pose a separate question about it? [it might not be worthy]) –  c.p. Oct 15 '12 at 23:16
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@JorgeCampos The combination of the many neutrino oscillation experiments puts some limits on the combination of $\theta_{nm}$'s and $\Delta m^2_{nm}$'s that are consistent with the data. It turns out that there are few viable combination where there is only one sterile flavor, and rather more if there are more than one. There have been a number of preprints on the matter in recent years. I'll see if I can find you a reference. –  dmckee Oct 15 '12 at 23:24
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Try prd.aps.org/abstract/PRD/v70/i7/e073004 (pay link) and perhaps the rather extensive white paper arXiv:1204.5379. –  dmckee Oct 15 '12 at 23:53
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Dark matter candidates can quite naturally be described for example by supersymmetric quantum field theories. The MSSM (Minimal Supersymmetric Standard Model) is the simplest but not necessarily the most realistic version of these types of effective theories to describe nature, taking the so far obtained LHC results into account. Since R-parity is assumed to be conserved in the MSSM, the lightest supersymmetric particle (LSP) of its spectrum, for example a neutralino, is stable and could therfore serve as a dark matter candidate. The MSSM doubles the numbers of particles of the standard model and it contains a total number of five not eaten higgs particles (the graviton and the gravitino should not be included in the picture of the spectrum since gravity is not included in the MSSM).

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