Einstein's or even Newton's gravity seems to predict much faster speeds near the center, close to Kepler's or Newton's model of the Solar System. This is the simplest manifestation of the fact that without some additions, Newton's or Einstein's predictions for the motion caused purely by the visible stars' gravity contradict the observed motion of galaxies.
There is a conceptually smooth solution to this discrepancy: postulate the existence of dark matter – matter that isn't seen in the telescopes because it doesn't interact with the electromagnetic field but that still affects the motion of the stars within galaxies. Every good theorist agrees that there is nothing wrong with a theory that has electrically neutral – and therefore "dark" – particle species. The refusal to add this "dark matter" may be labeled "MOND", Modified Newtonian Dynamics which assumes that the visible stars are responsible for all the motion which means that their "forces" must differ from the Newtonian ones in some way. MOND has celebrated some partial successes in predicting the speed patterns in a broad set of galaxies.
Even if we embrace dark matter, we don't know what it is made of. Axions and WIMPs remain the fundamental theoretical physicists' preferred choices (and maybe axions became a bit more likely in recent years when a big part of the WIMP parameter space was excluded) – but SIMPs and various other astrophysical objects named after superheroes have been proposed, MACHO, RAMBO, TERMINATOR, BRUCEWILLIS, GRETA, and others.
A particular eclectic program has gotten lots of the good press in the "mainstream" media in recent years and it's the superfluid dark matter – kickstarted by Berezhiani and Khoury in 2015. At galactic and shorter length scales, this type of dark matter is designed so that it reproduces the universal formulae – the Mass Discrepancy Acceleration Relation (MDAR) – by a trick analogous to how MOND explains MDAR. At longer than galactic length scales, the extra forces lose their importance and the superfluid dark matter reduces to that of the ordinary cold dark matter, CDM.
This is the summary you may already read in the abstract of a new, Princeton-TelAviv hep-ph paper
The Inconsistency of Superfluid Dark Matter with Milky Way Dynamicsby Mariangela Lisanti and three dudes (don't overlook which sex gets sidelined here). Princeton's Mariangela is a nontrivial achieved young researcher, the 2001 winner of the Intel's Got Talent contest, a real expert both in cosmology and collider physics, and a Soros Fellow but before you throw up, check the first names LOL. Also, I remember Lisanti as the ex-president of Women in Science at Harvard-Radcliffe but it was a different, somewhat less insane, era around 2005. Just to avoid doubts: I didn't single out Lisanti because of some jokingly motivated, fake or real political correctness; this paper is a rare case in which she – despite her youth – is the senior leader and the three guys constitute her reverse harem of junior collaborators!
(11 pages including many figures)
OK, these four authors have looked not only at the galactic rotation curves but also at the vertical motion of the stars inside the galaxies, especially their dispersion. And they concluded that due to the new forces, the superfluid dark matter models almost universally predict vertical accelerations of the stars that are much higher than the observations.
When the superfluid dark matter model disagrees with observations, it's wrong. This simple statement is the key to science. It doesn't matter how ugly you are, how much money you have stolen from the taxpayers, how many journalists and Canadian hippies you have had romantic relationships with, or how many brainwashed morons are following your weblog.
Well, the word "kill" may be a bit too strong. Lisanti et al. have performed a Bayesian analysis and CDM is favored over the superfluid – by some 32-to-1 – when taking their vertical argument into account. It's still a very strong piece of evidence against the superfluid dark matter.
Unless there is a glitch in the argumentation by Lisanti et al., it is a powerful tool to quickly kill any generic wrong would-be "compromise" model of dark matter. It seems that every model that remains "fundamentally 3D rotationally symmetric" will fail the Lisanti test because such models unavoidably tie the 2D galactic curves and the motion in the third, perpendicular dimensions and the link seems not to be working – simply because the observed galactic 2D accelerations require much stronger extra forces than what the vertical accelerations seem to need or allow.
I feel that if you want some compromise model and you want it to be viable, it should better allow some separation of the axes – it should break the rotational symmetry, hopefully softly or spontaneously or by small holographic effects or whatever.
Also, I think that the people who are working on the "not really careful world-class models of dark matter" generally have lower standards and many of them seem to believe that the repetition of clichés about some correctly explained pattern is good forever. But that's not how science works. In science, one apparent success repeated 100 times isn't enough for the survival of the theory. Instead, one disagreement is enough to kill a theory, regardless of your obsession with the positive hype. And the alternative theories to regular dark matter are just too constraining.
If all other things are equal, it's better to have a more predictive, constrained theory but it's more important whether the predictions work. If some of them don't work, the theory has to be abandoned – and a less predictive theory is preferred over a highly constrained by excluded theory.