We discuss the correlation between the dark matter content of elliptical galaxies and their ellipticities. We then explore a mechanism for which the correlation would emerge naturally. Such mechanism leads to identifying the dark matter particles to gravitons. A similar mechanism is known in Quantum Chromodynamics (QCD) and is essential to our understanding of the mass and structure of baryonic matter.

Alexandre Deur, "A correlation between the amount of dark matter in elliptical galaxies and their shape" (28 Jul 2014).

Every now and then there is a paper that suggests that the phenomena described as dark matter is really implied by General Relativity, or a trivial variant of General Relativity, and that the discrepancy between theory and observation that astronomers observe is because they inappropriately conclude that in systems like galaxies and galactic clusters that Newtonian gravity is a reasonably accurate approximation of General Relativity.

This is one of the stronger arguments that I have seen for that position.

Most of those papers argue basically that what a Newtonian gravitational approximation (mediated through a stylized approximation of a galaxy's structure or a numerical many body simulation much like those of lattice QCD) is missing is the gravitational effects of the coherent angular momentum of the many bodies in a galaxy as they rotate around a central black hole. On balance, I've found that the argument that this contribution is tiny is stronger than the argument that this is the main source of dark matter phenomena.

Put another way, they focus on the additional degrees of freedom (i.e. additional amount of information necessary to describe) the behavior of General Relativity (which requires a spin-2 tensor field graviton), rather than the spin-0 scalar field gravitons of Newtonian gravity.

This paper focuses on a different distinction between Newtonian gravitons and General Relativistic ones. Newtonian gravitons, like real world photons, don't interact with each other. They couple only to mass and electric charge, respectively. In contrast, in General Relativity, gravity is a function of both mass and energy. Thus, gravity can influence particles that have zero rest mass (i.e. photons and gluons), and in principle, gravity may even influence other gravitons. In this respect gravitons are more like gluons, which interact both with quarks and with each other, and less like photons.

Focusing on this self-interaction of gravitons suggests an effect of approximately the right order of magnitude to account for differences in the amount of "dark matter" effects seen in ellipical galaxies of different sizes. A previous paper from 2009 argues that the effect is on the right order of magnitude to account for the rotation curves of galaxies and the Tully-Fisher relation, and may also explain, or at least help to explain, dark matter phenomena in galaxy clusters.

I haven't had the time to rigorously review the accuracy of the analysis, but the approach does look like a fruitful one to explore that is understudied. Deur basically claims to have derived a versions of MOND (Milgrom's modified gravity theory) from first principles using a toy model approximation of GR that preserves the essentials of General Relativity in a symmetric and homogeneous case, while proving much more accurate for galactic clusters and that can explain the Bullet Cluster.

An interesting analysis of what would distinguish MOND from MOND-like theories is found in another 2009 paper by another author.

If he's right, he deserves the Nobel prize for physics. If this approach really works, of course, it would also eliminate the phenomenological need for any beyond the Standard Model particles other than the graviton, which is by far the best empirically supported hypothetical particle. Given our failure to discovery any other dark matter candidates, this increasingly looks like a feature rather than a bug.

Deur's approach was also discussed recently at the Physics Forums.