When I talk about uncovering the nature of dark matter as a particle, I mean that we would like to know the basic properties of the dark matter particle (or particles) such as its mass and the type of interactions it possess. As I mentioned in the previous post, available interactions with ordinary matter are very much constrained, but is possible that dark matter is part of a rich dark sector with its own forces. For instance, one could think of dark matter as being 'charged' and interact with each other via a Coulomb-like interaction, just as electrons/protons interact with each other. Of course, this charge is not the ordinary charge but it only affects particles in the dark sector. See for example this paper for an example of the modeling of this idea.
These type of 'self-interactions' between dark matter particles are allowed by observations to a significant level. They can be large enough to impact the formation and evolution of galaxies. The proposal of self-interacting dark matter (SIDM) became in fact quite popular at the turn of the millennium with a famous paper by D. Spergel and P. Steinhardt as a way to modify the standard CDM paradigm and obtain predictions that were seemingly in better agreement with the observed inner dynamics of galaxies.
The SIDM idea attracted me specially since it might be possible to look for signatures of non-gravitational dark matter interactions in the observed properties of galaxies, a possibility that is absent in the CDM model. I will talk more about SIDM and galaxies in the next post.