Dark Matter is a place holder for an anomaly, essentially for a problem where galaxies spin faster than they should (according to our normal laws that serve us well day to day). The leading theory to explain it is a ‘new’ type of matter – one that only interacts weakly with normal matter. Theorists like this solution because it helps explain other things such as the way galaxies are seeded and the general ‘clumpyness’ of the structure of the universe.
However it may just as well be that we misunderstand how gravity works on larger scales. We tend to think of atoms a bit like solar systems, the old Rutherford model. But in some ways they are more like mini galaxies, with stuff held within ‘arms’ of strange stuff moving around in strange ways – certainly strange if you want to see particles as fixed balls of stuff. In fact, with particles things are so strange that most physicists have stopped trying to understand it. The fact that the maths is so reliable and drives the modern world of mobile phones etc has lead to a famous response to those trying to understand whats actually happening of “shut up and calculate”.
Its possible that galaxies behave differently simply because of their scale (just as atoms behave differently at the very small scale). The combination of the supermassive black hole at the centre (still something of a mystery itself) combined with the sheer mass of the galaxy produces its own dynamics. Maybe the whole thing pulls space itself around due to some critical limit of gravity. Or maybe there is some version of fluid dynamics where the stars and planets are a bit like water molecules in a whirlpool.
The area I find compelling to explain dark matter (and a couple of other areas) is extra dimensions. The maths of string theory point this way, although they can be tweaked in so many ways that the physics gets lost. The fact that gravity is so weak would make perfect sense if it leaked between dimensions. Galaxies could spin so fast if matter/energy in other dimensions was ‘holding them together’ in some way. And there other speculative hints around, such as quasi crystals.
Maybe even areas of quantum mechanics such as entanglement can make more sense with extra dimensions (although this is considered a ‘hidden variable’ interpretations which many view as ruled out). To me it seems like there is some kind of connection between extra dimensions and Bohm’s enfolded holographic universe. Logically these are opposite theories – but they could also be two sides of the same coun.
We sometimes have trouble understanding where we stand as observers – but I will save diving into ontology and epistemology for another time.