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)?
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.