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Dark matter does not interact with electromagnetic radiation. Neutrinos also don't interact via electromagnetism, which would make neutrinos a good candidate for dark matter. However because of the extremely low mass of the known three types of neutrinos they can only supply a tiny fraction of the dark matter in the universe (see the section of the Wikipedia page comparing baryonic and non-baryonic matter).

But I have heard there have been speculations in the past, that there could be a fourth type of neutrino, which should be much more heavy that the other three types of neutrinos. Wouldn't such a heavy 4th generation neutrino be the perfect, natural candidate for dark matter?

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Weak physics rates (I think the $Z^0$ lifetime is generally quoted as giving the strongest single constraint) give pretty strong reason to doubt the existence of the fourth generation of 'normal' neutrinos with a mass lower than $\approx 45\,\mathrm{GeV}$, but so-called "sterile neutrinos" (which don't couple directly to the weak interaction, but do mix with the better know flavors) have been on the radar as candidates for some time.

I haven't checked with a recent review article, but my general feeling is that improved measurements of the mixing parameters have been constraining the possible space for such a mixing term, though it will be essentially impossible to remove all doubt. However the smaller the mixing the harder it is to arrange a large enough mass of such neutrinos in the early universe to explain the observed structure.

These are not WIMPs and would not be detected by the current and planned generation of direct observation experiments.

Only a day latter I learn of this recent paper jointly published by Daya Bay and MINOS putting new limits on the mass and mixing angles for oscillation to sterile neutrinos in a minimal 4 flavor model. That said, a few years ago there was a round of interest in 5 flavor models which seems for a time to be more likely (they are, of course, also harder to constrain).

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Surprisingly the other neutrino candidate could be an Axion, a very light version (10−6 to 1 eV/c2). If it is true that Axions were massively produced in the very early universe, the could be a very good candidate for some of the dark matter.

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    $\begingroup$ Huh? This is written as if an axion was a type of neutrino, but they're different things. $\endgroup$
    – user4552
    Apr 8, 2018 at 17:34

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