# 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. Gary Godfrey says:

Aside from providing the fun theoretical playground Sean talks about, the idea of Dark Matter was created to preserve the acceleration~1/r^2 of Newtonian Gravity in regions of very small accelerations. Without dark matter, Newtonian gravity fails to explain how constituents (gas, stars, or galaxies) in parts of all structures from 10^6 solar mass dwarf galaxies to 10^15 solar mass Galactic clusters can have the high velocities seen. DM is guaranteed to work. Just put in the right amount and distribution of DM in each structure to give the observed velocities and dispersion velocities that are observed for the real masses. Unfortunately, the required mix of DM and matter varies from structure to structure. Dwarf galaxies require 100’s of times more DM than real matter, spiral galaxies require DM be a few times more than real matter, and galactic clusters require 10’s of times more DM than real matter. Unique DM/matter ratio and radial distribution fit parameters are needed for each structure. Though not impossible, it strains credulity that these thousands of ratios and parameters can come from the stochastic assembly of non-interacting DM and matter into structures that obey the Tully-Fisher relation (v^4~Luminosity). Yet a simple modification of Newton’s law in regions of small acceleration, crafted to yield the Tully-Fisher relation, correctly explains the velocities in ALL structures except clusters of galaxies. This modification (called MOND) has only one universal constant which is the same for all structures. If DM is real, DM must be able to explain this simple empirical regularity.

Rightly so, we look for DM with all our experimental tools, but as yet no confirmed detection. The experiments increase in cost and sensitivity, and the infinite space of DM theoretical models becomes infinitesimally smaller. Can DM be disproved? Perhaps DM is more weakly interacting than any experiment we can afford to build … how will this process end?

A glimmer of hope to escape this dark future is KATRIN which, within a couple of years, will be able to measure the electron neutrino mass if >.2 eV. If KATRIN measures the neutrino mass to be 1-2 eV, this would explain the missing mass that MOND predicts in galactic clusters, and would explain the unseen material causing gravitational lensing in colliding clusters, like the Bullet Cluster. Cluster formation will need these massive neutrinos to cool the increased rate of structure formation caused by the MOND force law. These massive neutrinos would also eat into the 20% of the universe’s Omega budget attributed now to DM … making DM even more unlikely and providing a bright future for theorists to find GR’s successor.

2. Thomas J. Buckholtz:

Hoping I’m not violating posting rules, I came up with an idea quite similar to yours, except that instead of the 5 other copies of the Standard Model residing in our Universe, they would be sequestered on 5 parallel branes in a 5D bulk space, and only their gravitational effect would be felt. The raison d’ etre for their being exactly 6 types of Universes was that above the electroweak synthesis there are three forces in the Standard Model – Electroweak, QCD, Gravity. Without going into detail, it’s assumed that any one of these forces can transpose roles with any other one, which would be equivalent to a duality. By the permutation rule – N!, where N=3, there are six possible rearrangements of 3 elements. I noted that M-theory consists of 6 sub-theories (which are dual to each other), so thought that one of those corresponds to our Universe, with its particular set of particles and forces, while the other 5 reside on their own branes.

A more detailed description of this idea is at the bottom of the index page of my website under the heading “Supersymmetry with a Triplet Higgs”.

I’m not a physicist, just a retired engineering technician, so probably there’s probably a ton of holes in this idea. I guess we should probably correspond offline, if I can figure a way to send you my email address.

3. BobC says:

Let’s bring this discussion down to earth, and make it literal.

The best dark matter candidate is clearly “Trader Joe’s Dark Chocolate Peanut Butter Cups”.

Seriously, try them. They make it impossible to think about physics.

Well, I do wonder if WIMPS could have peanut-buttery cores…

4. Tom Andersen says:

Physics is in a sad state when Dark Matter and Dark Energy – 95% of all that is – needed to be discovered, rather than predicted. (Hindsight does not count).

To further underline the utter failure of modern physics we have a embarrassment of riches when we try to explain Dark Matter’s presence and properties.

Something is very wrong, and no one wants to come out and say it.

5. 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.

Maybe “an order of magnitude less” is “comparable”.

Look at their FIG. 1. Various constraints show that the density of PBHs is limited to, at best, 0.1 of the density of dark matter, in many mass ranges less than this.

6. zephirawtz says:

It all looks quite well until you write

“>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”.

This is actually not necessarily true. For example the scattering effects in the Earth atmosphere are all caused with very temporal density fluctuations. Yet they’re stable, because they’re exist in dynamic equilibrium and they do form as fast, as they annihilate. As I explained already here, many aspects of dark matter don’t fit well neither the particle, neither the field models. The dark matter may be more close to so-called “virtual particles”, which are usually responsible for effect like the Casimir force. In another discussion I explained, why the dark matter is close to AdS/CFT dual of Casimir field, which is also generated with (lack or disbalance of) virtual photons. (for further info)

7. Well, this is a highly informative article! I am trying to follow Sean Carroll’s articles as a layman in physics desperately trying to understand something of this crazy Universe around us. Being on this road for sometime now, I know that it is very hard for a layman to ask a question to a physicist that is both meaningful and relevant (both or either…). Anyway, if Sean could be generous enough, I would appreciate if he commented, even if very briefly, whether he thinks dark matter is more difficult than dark energy for physicists to come to grips with…

8. Neuroendocrinologist says:

Question: If dark matter is a massive particle that once was hot, would its temperature have contributed to the cosmic background radiation? And if so, is the CMB temperature consistent with such cooling?

9. marten says:

Dark matter is what you may expect to discover in the constellation of Taurus.

10. David Schroeder:

Thanks. It is good to learn of theories that correlate with a 5:1 or 5+:1 ratio of dark matter to ordinary matter. (If, as you suggest, you would like to have my e-mail address, click on the link above, find the link (in the upper right corner) to the “about” page, click that link, and look near the bottom of that page.)

11. Derrick says:

Phillip — how does 10% compare to the threshold in http://iopscience.iop.org/2041-8205/720/1/L67/pdf/2041-8205_720_1_L67.pdf ? Please see also the “possible tension” mentioned in http://arxiv.org/abs/1503.02317

12. Thomas:

Thanks for the information! I just looked at your site and can see that it’s very, very well done, and your idea for Dark Matter is intriguing and well thought out. I’m away from home at a casino, and am eager to join my brother soon on the slots, so will explore your site more thoroughly when I’m home later.

From reading the responses to Sean’s article, I can see that Dark Matter is a pretty intractable problem with many ideas to solve it. Possibly, something will show up in the current run of the LHC in the form of a particle(s) with all the right properties to explain all the data supporting its existence. What’s even more mind boggling, though, is that even after this puzzle is solved, there’s still the issue of Dark Energy, which is even a bigger chunk of the Universe.

13. Brett says:

How would you react to hard evidence that dark matter is not a particle? What evidence would it take? I’m seriously curious about this. I’ve had discussions with astronomers who refuse to believe that it isn’t a WIMP telling me:

“If we never find evidence that dark matter is a particle of some sort, then we’ll just have to continue on to the next step with the assumption that it is and accept that we’ll never be able to prove it.”

Am I wrong in thinking that this is an irrational and insane way to view the problem? I’m sure this psychological mechanism seems familiar. It’s what every group of people who have held back humanity over many centuries have done. It really shatters my confidence in humanity when I see scientists turning science into a religion.

14. Derrick says:

David — As Harvard astrophysicist Douglas Finkbeiner said, “Every hint of exotic dark matter particle properties has always been wrong.” http://www.wired.com/2013/01/musket-ball-dark-force/

That’s as true today as it was two years ago. Please see also http://www.newscientist.com/article/mg22630263.000-chasing-shadows-how-long-can-we-keep-looking-for-dark-matter.html

15. BilB says:

I just love it when physicists talk “dark” and dirty. It really gets the mind racing watching you guys tackle the big problem. I, for one, hang on every new thought and idea, so much done yet so far to go.

16. S.E. Grimm says:

I don’t think dark matter is hard to understand. Maybe it is for cosmologists, but not for physicists. That’s because dark matter represents quanta (Planck’s constant). The quanta is concentrated in a region but it is not already altered into rest mass. Just because the local physical conditions are not suitable to form matter. Thus, dark matter is “primordial” rest mass. Albeit it cannot force the scalar field to move quanta to the vector field. To express it in a simple way: dark matter is comparable with m in the equation E = mc2. This amount of quanta is far less concentrated than rest mass but the existence influences matter in the same way as normal rest mass.

17. Derrick:

Thanks for the links. Those were very thought provoking articles. Yes, I’ve noticed that candidates for Dark Matter, one after the other are shot down, either as a result of new data coming along, or some incompatibility with the Standard Model issue, that the original authors hadn’t considered.

18. Phillip — how does 10% compare to the threshold in http://iopscience.iop.org/2041-8205/720/1/L67/pdf/2041-8205_720_1_L67.pdf ? Please see also the “possible tension” mentioned in http://arxiv.org/abs/1503.02317

The former can produce tighter constraints under an additional assumption: DM consists of PBHs and WIMPs. Under this assumption, the constraints are better than 10 per cent.

The latter is concerned with supermassive black holes. However, we know that these cannot be a significant fraction of DM—not because of microlensing (the timescale would be too long), but because they would distort the images of jets of extragalactic radio sources. There was a paper on this by Lacy and Ostriker decades ago.

19. Derrick says:

Phillip — Lacy and Ostriker have been updated with regard to both the path of black holes within halos and the corresponding extent to which they acrete and emit due to accretion. Please see http://arxiv.org/abs/astro-ph/0501345

It won’t be long until we have empirical data on this, per http://arxiv.org/abs/1402.5975
and http://arxiv.org/abs/1301.5067

20. “Lacy and Ostriker have been updated with regard to both the path of black holes within halos and the corresponding extent to which they acrete and emit due to accretion.”

Are you claiming that most dark matter could consist of black holes?

21. J says:

I am.

22. I wanted to mention that the antecedent for the idea, described above, as a potential explanation for Dark Matter, was another, simpler, duality idea. This duality is encompassed within 1 of the 6 ‘global’ dualities, so is not the complete enchilada. But its dynamical effects are easier to explain in this partial form.

As it’s not even a page long, and quite informal, realistically it probably has as many holes as a kitchen strainer. But there’s perhaps an outside chance that it has a bearing on the Dark Matter problem, in the context of the larger theory.

It’s the very first link titled: “Dualities and Matter Waves”.

23. Being somewhat of a nitpicker as regards language, I always have a problem with the interrogative “why?’ in discussions of physics, why? for me implying purpose or intentionality. That aside, the question of how it is or might be that there is something out there that is currently labeled “dark matter” as well as “dark energy” is very important. But it ties back clearly to your lecture reported on in Symmetry.org regarding the field nature of particles. This is how. Quantum field theory (quantum dynamics, etc.) associates a unique field to every “particle.” Your lecture on fields suggests a turnabout, that the particles themselves are excitations of their own fields. I would take this reasoning one step further and posit, not many fields, but one field, electromagnetic in nature, that permeates all. Then the many fields of QFT, and your turnabout, become simply distortions of that primal field, and the unique particulate excitations we call particles can be seen as energy concentrations that themselves generate wider distortions. These wider, regional distortions around large energy distortions we call stars and galaxies manifest the effects attributed to the mysterious “dark matter.” I have tried to express this in significant detail in two books and my own blog at enquiriesnw.com. I think it leads to a far simpler cosmology than any other I have come across, and answers more questions. “Dark matter” is then a distortion in the field. The field itself is “dark energy.” No particles need to be employed.

24. Joseph Chi says:

Can anyone comment on the status of so-called “mirror matter” as a candidate for dark matter? I think it’s a fascinating concept, but as a non-physicist obviously cannot critically evaluate it.
Wikipedia: Mirror Matter