WIMP Exclusions And Other Constraints On Dark Matter Properties

For clarity, I don't think that dark matter particles exist. I think that dark matter phenomena is due to a gravitational effect or a fifth force. But ruling out dark matter particle candidates strengthens that case.

WIMPs (weakly interacting massive particles), which are predicted by supersymmetry, for example, which should be possible to detect in sensitive dark dark matter detection experiments, are strongly disfavored as dark matter candidates given the latest data.

Additional data, not considered in this chart, strongly disfavor GeV and heavier dark matter candidates based upon galaxy dynamics, separate and apart from the direct dark matter detection observations shown below.

This is a blow not just to the WIMP dark matter particle candidate (that has quietly ceased to be the subject of many publications about dark matter), but also to supersymmetry, which has a WIMP candidate as one of its core predictions, and to many versions of string theory, for which supersymmetry is a low energy approximation. Non-detection of any sign of supersymmetric particles at the Large Hadron Collider (LHC) further disfavors supersymmetric WIMPs and supersymmetry.

The original WIMP prediction assumed an interaction cross-section comparable to that of a neutrino which would have arisen from the Standard Model  weak force, and a mass on the order of 100 GeV which would have been optimal for resolving the "hierarchy problem" at the electro-weak scale, which was the initial motivation for supersymmetry.

An interaction of 10-1000 GeV mass dark matter particles with ordinary matter, if such a particle exists, has to be at least 10,000,000 times weaker than the interactions between neutrinos and ordinary matter. If it has a mass of about 40 GeV the interaction has to be about 100,000,000 times weaker. This excludes not just weak force mediated interactions but also Higgs field mediated interactions. 

An interaction weaker than a weak force interaction is experimentally excluded down to about 2 GeV of WIMP mass.

The bottom line is that if dark matter particles exist and have a mass in  the 10-1000 GeV mass range, they have absolutely no non-gravitational interactions with ordinary matter. This is a dark matter particle property that faces another observational constraint. There is a tight correlation between inferred dark matter particle distributions in inferred dark matter halos with ordinary matter distributions. This correlation is much stronger than should be possible from gravitational interactions alone.

So, WIMPs are pretty definitively not the correct explanation for dark matter phenomena. 

Many new dark matter particle papers argue that WIMPs are "well-motivated" dark matter candidates based upon citations to older papers. But this is no longer the case.

The interaction cross section as a function of WIMP mass. The original expectation of 10^-39cm² is at top. Gray areas are regions that were experimentally excluded by 2008 (before the blue-green prediction) and by 2022, which is the most recent update as of this writing. The most sensitive limit is 10^-47 cm², eight orders of magnitude below the original prediction.

Via Triton Station. 

At masses much below 10 GeV, and certainly at masses below 1 MeV, direct dark matter detection experiments of that kind that are the basis for the chart below lose most of their observational power because the background noise from neutrinos overwhelms any possible signal from dark matter interactions with the detector. 

The chart below showing this background and the caption are also via Triton Station.

WIMP experimental limits (via Hamdan 2021) with the expected neutrino background in orange. Once this sensitivity is reached, any WIMP signal becomes obscured by the neutrino background.

To subtract this background to try to improve the signal would require a better understanding of the neutrino background than we have at this time and would even then degrade the precision of the measurement. 

Fermionic Dark Matter Can't Be Less Massive Than A Neutrino

Stacy McGaugh also makes a notable observation in a comment which rules out a very different part of the dark matter parameters space:

neutrinos are fermions and subject to a close-packing limit imposed by the Pauli Exclusion Principle. A less well-known problem for neutrinos as dark matter is that there are some regions where the dark matter density is too high to be explained by fermions of neutrino mass. They can’t be packed in tightly enough.

Thus, we can pretty much categorically rule out all fermionic dark matter candidates which are less massive than neutrinos (realistically, having less than meV mass). So, light dark matter candidates must be bosons.

Dark Matter Must Be Wave-Like And Thus Light

Another large generic exclusion of dark matter parameter space is that there is observational evidence that dark matter particles, if they exist, must be "wave-like" which suggests that it must have a particle mass of not more than about 10 keV. The same line of research favors a dark matter particle mass of much, much less than the neutrino mass, which we know, from McGaugh's comment, must also be a boson (realistically spin-0, spin-1, or spin-2). 

The requirement that dark matter be wave-like also rules out, for example, all hadronic dark matter candidates and primordial black holes, in addition to providing another means to exclude WIMPs down to the MeV mass or so, even if they are sterile (i.e. having no non-gravitational interactions). 

The requirement that dark matter be wave-like also generically rules out "thermal freeze out" dark matter candidates, other than warm dark matter with a dark matter particle mass on the order of 1-10 keV, which would have too high of a mean velocity at the necessarily low dark matter particle masses.