Years ago I read an article by Martin Rees, in which he surveyed the options for what the dark matter of the universe might be. I forget the exact wording, but near the end he said something like “There are so many candidates, it would be quite surprising to find ourselves living in a universe without dark matter.”
I was reminded of this when I saw a Quantum Diaries post by Alex Millar, entitled “Why Dark Matter Exists.” Why do we live in a universe with five times as much dark matter as ordinary matter, anyway? As it turns out, the post was more about explaining all of the wonderful evidence we have that there is so much dark matter. That’s a very respectable question, one that I’ve covered now and again. The less-respectable (but still interesting to me) question is, Why is the universe like that? Is the existence of dark matter indeed unsurprising, or is it an unusual feature that we should take as an important clue as to the nature of our world?
Generally, physicists love asking these kinds of questions (“why does the universe look this way, rather than that way?”), and yet are terribly sloppy at answering them. Questions about surprise and probability require a measure: a way of assigning, to each set of possibilities, some kind of probability number. Your answer wholly depends on how you assign that measure. If you have a coin, and your probability measure is “it will be heads half the time and tails half the time,” then getting twenty heads in a row is very surprising. If you have reason to think the coin is loaded, and your measure is “it comes up heads almost every time,” then twenty heads in a row isn’t surprising at all. Yet physicists love to bat around these questions in reference to the universe itself, without really bothering to justify one measure rather than another.
With respect to dark matter, we’re contemplating a measure over all the various ways the universe could be, including both the laws of physics (which tell us what particles there can be) and the initial conditions (which set the stage for the later evolution). Clearly finding the “right” such measure is pretty much hopeless! But we can try to set up some reasonable considerations, and see where that leads us.
Here are the important facts we know about dark matter:
- It’s dark. Doesn’t interact with electromagnetism, at least not with anywhere near the strength that ordinary charged particles do.
- It’s cold. Individual dark matter particles are moving slowly and have been for a while, otherwise they would have damped perturbations in the early universe.
- There’s a goodly amount of it. About 25% of the energy density of the current universe, compared to only about 5% in the form of ordinary matter.
- It’s stable, or nearly so. The dark matter particle has to be long-lived, or it would have decayed away a long time ago.
- It’s dissipationless, or nearly so. Ordinary matter settles down to make galaxies because it can lose energy through collisions and radiation; dark matter doesn’t seem to do that, giving rise to puffy halos rather than thin galactic disks.
None of these properties is, by itself, very hard to satisfy if we’re just inventing new particles. But if we try to be honest — asking “What would expect to see, if we didn’t know what things actually looked like?” — there is a certain amount of tension involved in satisfying them all at once. Let’s take them in turn.
Having a particle be dark isn’t hard at all. All electrically-neutral particles are dark in this sense. Photons, gravitons, neutrinos, neutrons, what have you.
It’s also not hard to imagine particles that are cold. The universe is a pretty old place, and things tend to cool off as the universe expands. Massless particles like photons or gravitons never slow down, of course, since they always move at the speed of light, so they don’t lead to dark-matter candidates. Indeed, even particles that are very light, like neutrinos, tend to be moving too quickly to be dark matter. The simplest way to get a good cold dark matter candidate is just to imagine something that is relatively heavy; then it will naturally be cold (slowly-moving) at late times, even it was hot in the very early universe. Ordinary atoms do exactly that. It’s possible to have very low-mass particles that are nevertheless cold; axions are a good example. They were simply never hot, even in the early universe; we say they are non-thermal relics. But in the space of all the particles you can imagine being cold (in some ill-defined measure we are just making up), it seems easiest to consider particles that are heavy enough to cool down over time.
Getting the right amount of dark matter is tricky, but certainly not a deal-breaker. Massive particles, generally speaking, will tend to bump into massive anti-particles and annihilate into lower-mass particles (such as photons). If our dark matter candidate interacts too strongly, it will annihilate too readily, and simply be wiped out. Conversely, if it doesn’t interact strongly enough, we will be stuck with too much of it at the end of the day. The sweet spot is approximately the interaction strength of the weak nuclear force, which is why WIMPs (weakly interacting massive particles) are such a popular dark-matter candidate. Again, this certainly isn’t the only kind of possibility, but it seems very natural and robust.
We need our dark matter particles to be stable, and now we’re coming up against a bigger issue than before. There are plenty of stable particles in nature — photons, gravitons, neutrinos, electrons, protons. All the ones we know about are either massless (photons, gravitons), or they are the lightest kind of particle that carries some conserved quantity. Protons are the lightest particles carrying baryon number; electrons are the lightest particles carrying electric charge; neutrinos are the lightest particle carrying fermion number. All of these conserved quantities are the result of some symmetry of nature, following from Noether’s Theorem. So if you want your dark matter candidate to be relatively massive but also stable (or nearly), the most straightforward route is to have it carry some conserved quantity that follows from a symmetry. What quantity is that supposed to be? Symmetries don’t just grow on trees, you know. The most robust kinds of symmetries are gauge symmetries, which entail long-range forces like electromagnetism (associated with conservation of electric charge). So arguably the easiest way to make a stable, massive dark-matter particle would be to have it carry some analogue of electric charge. (This is exactly what Lotty Ackerman, Matt Buckley, Marc Kamionkowski and I did with our Dark Electromagnetism paper.) Axions, always wanting to be the exception to every rule, get around this by being so low-mass and so weakly-interacting that they do decay, but extremely slowly.
Finally, we’d like our dark matter particle to be dissipationless. And here’s the problem: if we follow the logic so far, and end up with a massive neutral particle carrying a new kind of conserved quantity associated with a gauge symmetry and therefore a long-range force, it tends to have dissipation. You can make magnetic fields, you can scatter and emit “dark photons,” you can make “dark atoms,” what have you. It’s not necessarily impossible to make everything work out, but it’s probably safe to say that you would expect dissipation if you knew your particle was coupled to photon-like particles but didn’t know anything else. There’s a straightforward fix, of course: if your particle is stable because of a global symmetry, rather than a gauge symmetry, then it isn’t coupled to any long-range forces. Protons are kept stable by carrying baryon number, which comes from a global symmetry. However, global symmetries are generally thought to be more delicate than gauge symmetries — it’s fairly easy to break them, whereas gauge symmetries are quite robust. Nothing stops us from imagining global symmetries that keep our dark matter particles stable; but it isn’t the first thing you might expect. Indeed, in the most popular WIMP models based on supersymmetry, there is a global symmetry called R-parity that is responsible for keeping the dark matter candidate stable. This is kind of a puzzle for such models; it wouldn’t be hard to imagine that R-parity is somehow broken, allowing the lightest supersymmetric particles to decay.
So should we be surprised that we live in a universe full of dark matter? I’m going to say: yes. The existence of dark matter itself isn’t surprising, but it seems easier to imagine that it would have been hot rather than cold, or dissipative rather than dissipationless. I wouldn’t count this as one of the biggest surprises the universe has given us, since there are so many ways to evade these back-of-the-envelope considerations. But it’s something to think about.