Chalnoth said:
It's difficult to write down a model where the right amount of dark matter is produced in the early universe if there are only gravitational interactions. I'm sure it's not impossible, but it's not easy.
Perhaps more importantly, we don't have any possibility of detecting a dark matter particle that only interacts gravitationally within the forseeable future. It's perfectly sensible to search for possible particles we do have the possibility of detecting in the mean time.
The difficulty is not so much in writing down a model where the right amount of dark matter is produced in the early universe, as it is writing down a model where the dark matter that is produced in the early universe gets distributed in that manner that we observe it to be distributed today when we infer its location from gravitational dynamics.
If a particle interacts solely via gravity, you have only two free parameters, its mass and its mean velocity, and in the case of "thermal dark matter" (i.e. models where all dark matter is created shortly after the big bang and then is stable after that), those two parameter are degenerate, because mean velocity is a function of "freeze out temperature" which is a function of particle mass.
On the up side, since we know the total amount of dark matter in the universe, and we can determine mean velocity and the number of dark matter particles in the universe simply by dividing by particle mass, that gives us a nice finite range of singlet dark matter models to investigate. And dark matter researchers have done just that.
We know for certain that the mean velocity of dark matter can't be too high, which is called "hot dark matter" because if it were there would be far less structure in the universe. In the case of thermal dark matter where mass and velocity are degenerate, that corresponds to dark matter particle masses on the order of 1 eV/c^2.
A number of investigators have concluded that "cold dark matter" is also ruled out because in simulations this produces the wrong shaped dark matter halos and too much structure (e.g. sub-halos and satellite galaxies). The masses associated with mean velocities that correspond to cold dark matter in a thermal dark matter model are on the order of 1 GeV/c^2 and up, with 100 GeV/c^2 having been the type specimen of cold dark matter. But, once dark matter is cold, simulations aren't terribly sensitive to just how cold it is over a wide mass range.
The investigators who have concluded that cold dark matter is ruled out favor "warm dark matter" as the key to reproducing the phenomenology that is observed with warm dark matter defined as mean velocities associated with masses in a thermal dark matter scenario on the order of single digit keV/c^2 masses.
In state of the art simulations as of two or three years ago, WDM totally stomps CDM in terms of how well it reproduces what is observed in real life. (N.B., both WDM and CDM qualify as CDM for purposes of the definition used in the lambdaCDM standard model of cosmology which has a quite broad definition of CDM compared to what people trying to pin down particular dark matter particle models use to define those terms.)
But, the last word has yet to be spoken in the CDM v. WDM debate, because the models used to simulate the two kinds of purely gravitational dark matter had some serious flaws and didn't adequately take into account the feedback effects between ordinary baryonic matter such as stars and planets and interstellar gas and dust, and dark matter. This is clearly a problem, because in real life, dark matter halo shapes are tightly correlated with the distribution of ordinary luminous matter in the system.
Considering gravitational feedback between ordinary matter and dark matter reduces the amount of difference between the shape of dark matter halos in CDM models and the shape of dark matter halos in WDM models, although there is also dispute over whether the ordinary matter feedback in the simulations is correctly modeled. There is also dispute over whether any of these models are valid because some of the assumptions made may be wrong or lack of good physical basis -- you have to insert a lot of assumed rules about the non-gravitational interactions (e.g. supernovas and active galactic nuclei) that play a part in the gravitational clumping of matter to make these models work because they are highly oversimplified versions of real life.
However, one real important conclusion that was reached quite a few years ago with these models is that singlet dark matter models (with or without self-interactions between dark matter particles via a Yukawa force carrying boson that only, or predominantly, interacts with dark matter with a strength on the same order of magnitude as the electromagnetic force) more closely reproduce the distribution of dark matter that we observe than models with multiple kinds of dark matter at different masses.
Now, this doesn't mean that there has to be only one possible kind of dark matter, any more than the Standard Model implies that there has to be only two possible kinds of ordinary baryonic matter (protons and neutrons) that are very similar to each other for many purposes (there are in fact, hundreds of possible hadrons, but almost all of them are unstable). But, it does mean that the one kind of dark matter particle, or multiple kinds of dark matter particles with nearly degenerate velocities and masses that can be modeled well as one kind of dark matter particle, must make the predominant contribution to the dark matter phenomena that we observe.
This line of reasoning is also corroborated by the fact that dark matter distributions can be accurately described over many orders of magnitude with toy models like MOND that have just one degree of freedom. This doesn't mean that MOND is correct by a long shot, but it does mean that if you need more degrees of freedom to describe the same data with a dark matter particle model that your model is probably too baroque. So one or two particle models are pretty much the only way to go.
The bottom line then is that the universe of possible dark matter particles that interact only via gravity has been pretty well explored, and that we are reasonably close to pinning down the best fitting singlet only gravitationally interacting dark matter particle model, and to pinning down the best fitting dark matter particle that only has self interactions with a boson of a particular coupling constant and mass model, based upon the empirically observed evidence, and to seeing which of the two is a better fit to the data.
Pretty much the only hold up to solving that problem is finding a way to do a simulation which is accurate enough that a consensus of dark matter theorists agree that it is accurate enough to distinguish between CDM and WDM and self-interacting DM models and between the DM distributions that we actually infer from the dynamics of luminous matter.
The more computing power we can throw at the problem, the less assumptions about the processes involved we have to write into the model and the easier it is for the model to make assumptions that are directly supported by observational evidence or well understood stellar and black hole dynamics. We can also improve the models by directly observing processes that are mere assumptions in the current models to calibrate those assumptions (e.g. what happens when two galaxies of particular relative sizes and shapes collide at particular angles and relative speeds and how common are different scenarios relative to each other). Most importantly, we have to make sure that we are modeling the feedback in gravitational interactions between ordinary matter and dark matter correctly. And, it would also help to have more precise descriptions of the shape of more dark matter halos in a wide variety of circumstances, which is tricky because sometimes a couple of parameters used to describe the shape of a dark matter halo are degenerate in most observations and the degeneracy can only be resolved with a few, particularly difficult to observe, data points that require expensive space telescopes to see.
Unfortunately, there are so many debatable points in current state of the art simulations, that there is a high probability that I will be dead, and a decent probability that my children will be dead, before this can be sorted out definitively.
Eventually, however, one of the three possible gravitation only models will be the winner, or, alternatively all three will be excluded by empirical evidence and we'll have to see if we can either come up with a dark matter model that interacts by some means in addition to gravity that has evidence to support it (such as dark matter annihilation signatures in cosmic rays), or a non-thermal dark matter model where dark matter is routinely created and destroyed and has a characteristic velocity and stable total quantity (like axion dark matter models), or come up with a gravity modification models that can fit the empirical evidence.
Or we might find that none of our models can recreate what we observe, in which case it is back to the drawing board. But, a null result that rules out all plausible models to modify gravity or have particle dark matter is pretty unlikely, because a handful of empirical phenomenological formulas can describe pretty much all observed dark matter phenomena and we just have to figure out how to come up with a model that sews them all together to produce those results.
As they say in the Publisher's Clearing House sweepstakes, one of these theories "may already be a winner" and we just don't know it yet, because we don't have enough data and computational power to confirm this conclusion.
