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I know many collaborations are attempting to detect the interaction of WIMPs with nucleons or with themselves, with the recent result from Ice Cube (http://physics.aps.org/synopsis-for/10.1103/PhysRevLett.110.131302) showing no evidence for WIMP self-interaction. I am wondering if WIMPs might actually have zero non-gravitational interaction with SM particles and zero self-interaction. Is such a thing possible or likely? If so, what sorts of theories predict such WIMP candidates, and could they be detected indirectly by other means (e.g., cosmological ratio of WIMP mass-energy to ordinary matter mass-energy, or something like that)?

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Well ... do the WIMPS have to be created somehow in the Big Bang? If they do, that requires that they interact with something. –  Peter Shor Apr 1 '13 at 20:20
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WIMP means Weakly Interacting Massive Particle and the "Weakly" means the weak nuclear force in particular (rather than just "not a strong interaction"). So, by definition, yes, they do. Of course @PeterShor identifies good reasons why they have to be expected to interact somehow. That does not guarantee that the dark matter is WIMPs, they are simply the leading candidate at this time. –  dmckee Apr 1 '13 at 20:35
    
Just to play the devil's advocate for @PeterShor's answer, couldn't they somehow be produced by scattering gravitons in some non-trivial manner? Assuming gravity is all these particles couple to. I suppose that might mean cooking up a totally exotic way for particles to couple to gravity :-? –  Siva Apr 2 '13 at 2:51
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@Siva: I don't think that scenario works because the dark matter has to be created during inflation, when I assume that the temperature was too small for gravitons to do something non-trivial when scattering. –  Peter Shor Jun 1 '13 at 11:48

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The sterile neutrino is an example of a WIMP that interacts only through the gravitational force.

Some people had suggested that the WMAP measurements of the CMB indicated sterile neutrinos, or something similar, were needed to explain the results. However the recent Planck results have contradicted this and sterile neutrinos are no longer required.

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Don't sterile neutrinos have Yukawa couplings to the Higgs and SM neutrinos (in order to generate SM neutrino mass)? –  Michael Brown Apr 2 '13 at 9:02
    
Do we know that sterile neutrinos only interact through the gravitational force? If they exist, couldn't they also interact via a yet-to-be-discovered force? –  Peter Shor Jun 1 '13 at 11:49

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