The dark matter particle has NOT been found. Despite the quantity of models, I wonder if dark matter could be some (exotic) type of (interacting) gravitons. Is that possible?
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At a very basic level, it won't work. If gravity has a mass $m$, it has an effective range $\frac{\hbar}{mc}$, similar to the weak interaction. This effective range must be at least the scale of the largest galaxy clusters that we observe since they are gravitationally interacting. However, the effective range is (up to a factor of $2\pi$) also the Compton wavelength of the dark matter and so we cannot confine gravitons at scales smaller than this. This might barely be viable if all galaxies were the same size and we had no other measurements of dark matter (it would be the fuzzy dark matter case) but because we observe the need for dark matter on a variety of astrophysical scales (from hundreds of pc for the smallest dwarfs to Gpc for the largest galaxy clusters) it just won't work: the smallest dwarf galaxies require a graviton mass large enough that we would simply not observe gravity at the scale of the largest objects.
There are more formal reasons you would not think this would work in quantum field theory at all though. A massless spin-2 boson in 4 spacetime dimensions has 2 helicity states, $j=\pm 2$. A massive one has $5$, $j=2,1,0,-1,-2$. This alone tells you that they are quite different; you cannot simply add a mass to gravity in quantum field theory without also adding additional degrees of freedom. If your theory has a high-energy limit where the fields are approximately massless, you should instead describe the theory in terms of a massless spin-2 boson and $3$ additional degrees of freedom. If your theory does not have a massless limit, we would think of it as an effective theory where the cutoff is comparable to the mass scale in question (for example due to an infinite tower of higher mass states), and you would then seek to UV complete it, and we would expect many more states which are quite light compared to even neutrinos. Additionally, there are fairly strong arguments that any quantum field theory with a weakly interacting massless spin $2$ boson is not fundamental (in the sense that it must be an effective theory with cutoff that scales as the mass); see e.g. 1708.05716 (but note that there is a possible, if rather unusual, exception pointed out there).
While people do study so-called massive gravity, it is either in the context of classical field theory (which obviously cannot be a complete description), or a fairly pathological quantum field theory which seems to probably only be valid in the linearized regime and in any case does not explain dark matter.
Logan M
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It is still beyond the range of our current detectors to verify whether or not the graviton could have a non-zero mass.
The honest answer is that no one actually knows yet. But should the graviton prove to have a mass, it might answer many cosmological questions simultaneously.
