# Why Is There Dark Matter?

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.

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### 53 Responses to Why Is There Dark Matter?

1. Michael says:

Interesting overview. Two questions:

1. Do you have a source of Martin Rees’ article? Is it this one: https://www.bigquestionsonline.com/content/why-does-dark-matter-matter ?

2. Dark matter appears to us through its effects. Are there serious arguments arguing for or ruling out dark matter to be another, new type of matter or a (yet unknown) interaction of known matter?

2. Derrick says:

What do you think of “Massive Primordial Black Holes from Hybrid Inflation as Dark Matter and the seeds of Galaxies”? http://arxiv.org/abs/1501.07565

3. Ryan Reece says:

Great article Sean! As I’m sure you know, but one might add, the possibility of additional gauge symmetries is rather rich, even if one is constrained and motived by the apparent unification of the SM gauge couplings at high energies. Many Grand Unified Theories start with higher gauge groups that can be broken into direct products of gauge groups that can include the Standard Model, SU(3)xSU(2)xU(1), in addition to other gauge groups (with or without SUSY). Theses additional gauge groups, may as well be considered “dark” if our Standard Model particles don’t have any (significant) couplings to them (because of the broken symmetries). In other words, if one is motivated by gauge theory and apparent unification, then I completely agree it’s no surprise we have dark matter (given all the interesting caveats we don’t know about symmetries could break in the early universe).

Those interested in more could look here:

Maybe someone has better contemporary references for how GUTs can populate WIMP dark matter.

Seems like it’s possible for us to have reach to these dark sectors in colliders or direct detection, but it’s also possible that there’s plenty of ways to make very weakly interacting dark matter that we could never touch experimentally.

One of the best reasons I’ve heard around that we should be able to detect or produce dark matter is that since the dark:SM ratio is about 85%:15%, one could argue that the big bang produced order the same amount of dark matter as SM matter, so the dark-SM coupling cannot be too small or they wouldn’t equilibrate and would freeze-out at even more different amounts. Maybe that’s naive.

4. Sean Carroll says:

Michael– I don’t know where to find the Rees article, but it was from years (decades) ago. Dark matter can’t just be an interaction of ordinary matter, since it’s located where the ordinary matter isn’t.

Derrick– I haven’t read it. There are many, many dark matter candidates.

Ryan– It’s no surprise there are dark particles, but I think it’s at least a little surprising that they are stable, massive, and dissipationless. Wouldn’t be able to quantify that degree of surprise, though. Hopefully we will detect or make it, and then we’ll have a lot more to go on!

5. Elizabeth M says:

I have not found much discussion on this possible explanation of “dark matter”, although to me the question begs to be asked. The presence of matter distorts space-time’s curvature. The rate of time’s passage changes along this curvature. Could “dark matter” and it’s apparent pull within galaxies be attributed to the variance of time’s passage from, for instance, the dense galactic center to its rarified outer edges? Wouldn’t different rates of time’s passage also help account for gravitational lensing of light, as well? Light would bend towards a “slower” rate of time. Space-times is NOT a uniform stage upon which the universe is orchestrated, rather space-time is intimately connected, warping and bending accordingly. That topological warping and bending of space-time demonstrates the presence of matter by providing different frames for time’s passage. Please excuse me if I am totally confused, but space-time become more difficult to grasp the closer one looks at it..

6. Ken K says:

First we were not the center of our world. Then we learn we’re not the center of our solar system. Then we find out our galaxy isn’t special; and now we learn the dominant matter in the universe doesn’t even care to interact with us.

7. Jshobe says:

But MOND does not account for the suspicion that dark matter has been found far away from galaxies through its gravitational lensing of light.

8. Sean – Thanks for providing criteria that models of dark matter should meet.

Dark matter consists of 5 copies of Standard Model particles. Each of the now-6 clones (the ordinary-matter copy and the 5 dark-matter copies) includes its own photons. The clones share gravitons. None of the non-graviton bosons in any clone interacts directly with fermions in any other clone. (The word directly recognizes that indirect interactions via gravity are possible.) The mass of a particle associated with one clone is the same as the mass of the counterpart particles associated with the other clones.

To what extent might such a model conflict with physics data?
To what extent might such a model conflict with established or proposed theories?

Quantum Diaries refer to the cusp-core problem. It looks from this recent Astrobites that it is solved, i.e. “core DM” profiles reign (due to supernova dilution of galaxy cores). CDM is now better at predicting core profiles than alternatives (at least of the interacting et cetera DM kind).

http://astrobites.org/2015/06/12/the-labor-of-outflows-against-dark-matter-halo/

10. Chris Longden says:

Thomas J. Buckholtz :

What you are describing is essentially a naive version of supersymmetry. Supersymmetry is not exactly as you describe, but there are reasons for those differences to do with the symmetries we know nature has. The idea of each standard model particle having a tower of partner particles is at the core of supersymmetry though, and indeed, it is considered a potential DM candidate – in particular the lightest supersymmetric particle, such as the partner of the neutrino perhaps.

I don’t know why you chose to have 5 copies of each SM particle – supersymmetry theoretically prefers powers of 2 (1,2,4,8… not more than that or you run in to spin > 2 particles which are a problematic) and of those, a single superpartner for each SM particle is the most experimentally reasonable as far as I know, with “extended” supersymmetry models with 2 or more partners having some issues to do with chirality.

Supersymmetry must also be broken – there can’t just be partner particles all over the place or we would detect them in particle accelerator experiments. The breaking of supersymmetry allows the partner particles to have higher masses than their SM counterparts, and hence be as of yet unproduced at the LHC. If the LHC does detect supersymmetric matter, then this will be a very promising avenue for dark matter researchers and will generate a lot of interest.

PS : Thanks to Sean for running this blog. And also for writing that GR book, from which I first obtained a serious understanding of the subject, and has served me well as I embark on a PhD in cosmology.

11. andrew says:

Prof. Carroll,
.
You’re slightly wrong about the coin tossing example.
.
In the coin tossing example, all sequences are equally probable if you believe the coin is fair – (1/2)^n. If you consider a single hypothesis of a fair coin, any result would be equally surprising. The sequence TTTTT.. is no more surprising than THHTH…
.
The correct procedure would be to consider a ratio of probabilities for a sequence for two rival hypotheses – a so-called Bayes-factor, and find whether eg a fair coin is favoured vs a biased coin. Your statements along the lines of
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“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..”
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neglect this important point.
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I’m using your simple example of coins because you make the same mistake when discussing DM. You consider a single theory (actually a union of all conceivable theories) and want to draw conclusions about whether something was surprising. I don’t think that makes sense. As well as the above issues, with DM data, the probability will actually be dimensional probability density – it makes no sense to ask whether it is big or small. Again, you ought to consider rival theories, take a ratio and ask the well-defined and scientific question, which theory is most probable given the DM data.

.
Of course, we’re all free to speak of what data we find surprising, but it’s misleading to suggest that this particular discussion is in principle meaningful in a probabilistic (or even scientific) framework.

12. ed says:

What is dark matter used for and why does it exist?

13. Chris – Thanks for your comment about my comment. Some thoughts:

I propose 6 copies of the Standard Model, based on the math on which I base some attempted research. An SU(7) symmetry pertains. I think the 48 generators correlate with 48 clones of the Standard Model. Further looking at the math indicates that there would be 8 units, each having gravitons and 6 clones of the Standard Model. The “other 7 units” would be dark energy particles. (Yes, there is a reason why the measured density of dark energy has yet to grow to be 7/8-ths of the total density. And, no, there need not be any time-dependent growth in the actual amount of any type of stuff. And, yes, there are new forces that would govern the rate of expansion of the universe.)

Regarding spin, limiting solutions (in the math I use) to spins not exceeding 2 proves helpful in allowing me to limit the solutions I correlate with physics. (By the way, the math features isotropic pairs of isotropic quantum harmonic oscillators. And, yes, solutions correlate with all known elementary fermions, as well as with all known elementary bosons.)

Regarding supersymmetry, I don’t think my attempted research ‘goes in that direction.’ The math shows something other than a match between types of bosons and types of fermions. And, there seems to be no data-related need for having such a match.

I will be happy to discuss such further, perhaps ‘off-line (with regard to Prof. Carroll’s blogs and related comments)’. And, certainly, I welcome gaining insight or feedback.

14. Michael Balmer says:

enjoyed reading this,thank you,i contend Dark Matter to be” unused,uncharged ordinary matter”this is to say reverse engineer ordinary matter,it’s construct but mostly it’s acquisition of charges,i see DM as a field rather than particles (individual)of course a particle field but different in that one particle would be equal that of 10 protons but that is less of a point than the quantity that would be a field (uncountable) of course this field does not interact with an EMField and should always be found flanked by EMF and Matter fields and since the DMField doesn’t interact directly it does through it’s bosons and the acquisition of charge that would result in ordinary matter goes like this….y–>ve–>Wf–>Sf =m

15. John Barrett says:

If you wanted to start asking the big questions in a more respectable manner, you could try using abductive reasoning. Then if the shoe fits, wear it. Say you wanted to know if dark matter was a particle. You could start asking yourself questions, and you could see if it follows along with good abductive reasoning.

For instance, are there any known particles in the Standard Model that could be dark matter? No, there are no such particles. Then we found one counter example of where abductive reasoning fails. Therefore, dark matter is not a known particle.

The correct answer for what dark matter actually is would be able to pass almost every question you could throw at it with abductive reasoning. It could be possible that there may be one or two questions that would fail this test, but that would mean that there is something that is unknown or flawed in our reasoning or science. Therefore, dark matter could either be an unknown particle, or there is something flawed within the standard model or the method they are found using particle accelerators. Now if I had a list of 100 or 1,000 ways dark matter could fit within the standard model in some other way except this one, then I might consider that dark matter was a particle.

Say you wanted to abandon that line of reasoning and try different model to what dark matter could be. You could ask, “Does the discovery of dark matter indicate that there is a better theory of gravitation?”

Would a new theory of gravitation be “dark”? Yes, you can’t see gravity directly but only indirectly from the bending of light, in the same way dark matter is detected.

Would a new theory of gravitation be “cold”? Yes, empty space is a scaler, so any accurate theory of gravity wouldn’t allow for the force of gravity to heat up space.

Would a new theory of gravitation have “a goodly amount of it”? Yes, there is a “goodly” amount of matter in the universe that has mass.

Would a new theory of gravity say that the laws of gravitation remain stable? Yes, as far as we know the natural laws of the universe stay the same.

Would a new theory of gravity be dissipationless? Yes, it would have to be able to describe how the stars in galaxies remain in orbit where General Relativity does not.

Then you just keep asking every possible question to see if it fits, and if you end up getting all “yes’s” and not any “no’s”, then you have your answer. The more questions you ask and answer increases the probability of finding the correct solution. A single or very disproportionate number of “no(‘s)” in a line of questioning would indicate new physics is needed pertaining to that particular question.

16. Lou says:

What would one do with a bucket of dark matter

17. Avattoir says:

“Dark matter can’t just be an interaction of ordinary matter, since it’s located where the ordinary matter isn’t.”

Do you mean in the Pauli sense, that it’s displaced by ordinary matter? Or does each sort CLUMP?

And tho dark, given it’s still “matter”, does it have anything in the way of, or like, entanglement?

18. Shmi Nux says:

Elizabeth M: Yes, the “normal” relativistic effects have all been considered and accounted for. The “abnormal” effects, such as the modified gravity (MOND) models, have also been considered and found lacking by most experts. They are also contradicted by experimental evidence (gravitational lensing of some galactic collisions).

19. What do you think of “Massive Primordial Black Holes from Hybrid Inflation as Dark Matter and the seeds of Galaxies”? http://arxiv.org/abs/1501.07565

Note that the authors don’t claim that their PBHs constitute all, or even most, of the dark matter. As they correctly point out, this is ruled out by observational constraints.

They thus claim that there is more than one form of dark matter. One form would be the simplest case, but if there is evidence a) for PBHs and b) it is clear that they cannot be all the dark matter, then this leads to at least two forms of dark matter.

20. Nikola Milovic says:

Everything written above has nothing to do with the laws of nature and everything that someone forged on the basis of erroneous theories about the Big Bang, it is a great mistake and a misconception. In the universe, only that “dark” where science knows nothing about it, and it’s ether, which fills the infinite universe .From that ether was created substances and all types of energy, and what he does, “submerged” all entities of matter and energy that I call COSMOS (Cosmos should be distinguished from the universe, because it will be easier to understand the universe in general, and its structure.)
There is neither dark matter nor dark energy and how one can estimate the amount of any thing, if on no data. Who are those people who believe that BB was created 13.8 billion years ago, it looked like hours for mineral water, to spread in only one direction and that we are creating here, only no one knows how many years behind the “occupation” of our area where there are now.
The cosmos is finite, measurable and visible, as well as emerging and it will disappear, but never completely. Everything is in Cosmos, was formed from the ether under the command of the Absolute consciousness of the universe (ACU). Who owns your individual consciousness, he will understand what is ACU. It’s a wonder how many people “higher knowledge” does not understand who we are and where we got such attempt that do not respect nor we know what our formed as the last patent on this planet.

21. Colin Chambers says:

by removing a proton and a neutron from its atom equals dark matter, these particles exterior from its atom shell have no attraction with gravity to each other or all other atoms. The force of gravity is thus formed by contact between other atom shells. The strength of gravity field Will depend on the sizes of each atom Shell and the contact or the no contact each atom has between it’s self and neighbouring atoms (mass)…Jacktar

22. Kevin Henderson says:

Great post. Could a Maxwell’s demon explain why there is no dissipation? I think so, but then one is left pondering what and where are the little demons…

23. Steve Ruis says:

When we first got the idea that the universe was expanding (well, Hubble, anyway) the observation was that things were moving away from one another. Much later we find out that things are accelerating which makes no sense without additional components to the Universe.

Has anyone given consideration to space expanding as well as the material bits embedded into are moving away? The combination of the two effects would give the appearance of an accelerating expansion.

24. Derrick says:

Phillip — it is hard for me to understand your comment in relation the authors’ phrase, “producing abundances comparable to those of Dark Matter today,” from their abstract.

25. Peter Erwin says:

Having a particle be dark isn’t hard at all. All electrically-neutral particles are dark in this sense. Photons, gravitons, … [emphasis added]

Something’s a bit off about that particular statement, but I can’t quite put my finger on it…