Hi everybody. We haven’t talked about dark matter for some time. Which is why today I want to tell you how my opinion about dark matter has changed over the past twenty years or so. In particular, I want to discuss whether dark matter is made of particles or if not, what else it could be. Let’s get started.
First things first, dark matter is the hypothetical stuff that astrophysicists think makes up eighty percent of the matter in the universe, or 24 percent of the combined matter-energy. Dark matter should not be confused with dark energy. These are two entirely different things. Dark energy is what makes the universe expand faster, dark matter is what makes galaxies rotate faster, though that’s not the only thing dark matter does, as we’ll see in a moment.
But what is dark matter? 20 years ago I thought dark matter is most likely made of some kind of particle that we haven’t measured so far. Because, well, I’m a particle physicist by training. And if a particle can explain an observation, why look any further? Also, at the time there were quite a few proposals for new particles that could fit the data, like some supersymmetric particles or axions. So, the idea that dark matter is stuff, made of particles, seemed plausible to me and like the obvious explanation.
That’s why, just among us, I always thought dark matter is not a particularly interesting problem. Sooner or later they’ll find the particle, give it a name, someone will get a Nobel Prize and that’s that.
But, well, that hasn’t happened. Physicists have tried to measure dark matter particles since the mid 1980s. But no one’s ever seen one. There have been a few anomalies in the data, but these have all gone away upon closer inspection. Instead, what’s happened is that some astrophysical observations have become increasingly difficult to explain with the particle hypothesis. Before I get to the observations that particle dark matter doesn’t explain, I’ll first quickly summarize what it does explain, which are the reasons astrophysicists thought it exists in the first place.
Historically the first evidence for dark matter came from galaxy clusters. Galaxy clusters are made of a few hundred up to a thousand or so galaxies that are held together by their gravitational pull. They move around each other, and how fast they move depends on the total mass of the cluster. The more mass, the faster the galaxies move. Turns out that galaxies in galaxy clusters move way too fast to explain this with the mass that we can attribute to the visible matter. So Fritz Zwicky conjectured in the 1930s, that there must be more matter in galaxy clusters, just that we can’t see it. He called it “dunkle materie” dark matter.
It’s a similar story for galaxies. The velocity of a star which orbits around the center of a galaxy depends on the total mass within this orbit. But the stars in the outer parts of galaxies just orbit too fast around the center. Their velocity should drop with distance to the center of the galaxy, but it doesn’t. Instead, the velocity of the stars becomes approximately constant at far distance to the galactic center. This gives rise to the so-called “flat rotation curves”. Again you can explain that by saying there’s dark matter in the galaxies.
Then there is gravitational lensing. These are galaxies or galaxy clusters which bend light that comes from an object behind them. This object behind them then appears distorted, and from the amount of distortion you can infer the mass of the lens. Again, the visible matter just isn’t enough to explain the observations.
Then there’s the temperature fluctuations in the cosmic microwave background. These fluctuations are what you see in this skymap. All these spots here are deviations from the average temperature, which is about 2.7 Kelvin. The red spots are a little warmer, the blue spots a little colder than that average. Astrophysicists analyze the microwave-background using its power spectrum, where the vertical axis is roughly the number of spots and the horizontal axis is their size, with the larger sizes on the left and increasingly smaller spots to the right. To explain this power spectrum, again you need dark matter.
Finally, there’s the large scale distribution of galaxies and galaxy clusters and interstellar gas and so on, as you see in the image from this computer simulation. Normal matter alone just does not produce enough structure on short scales to fit the observations, and again, adding dark matter will fix the problem.
So, you see, dark matter was a simple idea that fit to a lot of observations, which is why it was such a good scientific explanation. But that was the status 20 years ago. And what’s happened since then is that observations have piled up that dark matter cannot explain.
For example, particle dark matter predicts a density in the cores of small galaxies that peaks, whereas the observations say the distribution should be flat. Dark matter also predicts too many small satellite galaxies, these are small galaxies that fly around a larger host. The Milky Way for example, should have many hundreds, but actually only has a few dozen. Also, these small satellite galaxies are often aligned in planes. Dark matter does not explain why.
We also know from observations that the mass of a galaxy is correlated to the fourth power of the rotation velocity of the outermost stars. This is called the baryonic Tully Fisher relation and it’s just an observational fact. Dark matter does not explain it. It’s a similar issue with Renzo’s rule, that says if you look at the rotation curve of a galaxy, then for every feature in the curve for the visible emission, like a wiggle or bump, there is also a feature in the rotation curve. Again, that’s an observational fact, but it makes absolutely no sense if you think that most of the matter in galaxies is dark matter. The dark matter should remove any correlation between the luminosity and the rotation curves.
Then there are collisions of galaxy clusters at high velocity, like the bullet cluster or the el gordo cluster. These are difficult to explain with particle dark matter, because dark matter creates friction and that makes such high relative velocities incredibly unlikely. Yes, you heard that correctly, the Bullet cluster is a PROBLEM for dark matter, not evidence for it.
And, yes, you can fumble with the computer simulations for dark matter and add more and more parameters to try to get it all right. But that’s no longer a simple explanation, and it’s no longer predictive.
So, if it’s not dark matter then what else could it be? The alternative explanation to particle dark matter is modified gravity. The idea of modified gravity is that we are not missing a source for gravity, but that we have the law of gravity wrong.
Modified gravity solves all the riddles that I just told you about. There’s no friction, so high relative velocities are not a problem. It predicted the Tully-Fisher relation, it explains Renzo’s rule and satellite alignments, it removes the issue with density peaks in galactic cores, and solves the missing satellites problem.
But modified gravity does not do well with the cosmic microwave background and the early universe, and it has some issues with galaxy clusters.
So that looks like a battle between competing hypotheses, and that’s certainly how it’s been portrayed and how most physicists think about it.
But here’s the thing. Purely from the perspective of data, the simplest explanation is that particle dark matter works better in some cases, and modified gravity better in others. A lot of astrophysicist reply to this, well, if you have dark matter anyway, why also have modified gravity? Answer: Because dark matter has difficulties explaining a lot of observations. On its own, it’s no longer parametrically the simplest explanation.
But wait, you may want to say, you can’t just use dark matter for observations a,b,c and modified gravity for observations x,y,z! Well actually, you can totally do that. Nothing in the scientific method that forbids it.
But more importantly, if you look at the mathematics, modified gravity and particle dark matter are actually very similar. Dark matter adds new particles, and modified gravity adds new fields. But because of quantum mechanics, fields are particles and particles are fields, so it’s the same thing really. The difference is the behavior of these fields or particles. It’s the behavior that changes from the scales of galaxies to clusters to filaments and the early universe. So what we need is a kind of phase transition that explains why and under which circumstances the behavior of these additional fields, or particles, changes, so that we need two different sets of equations.
And once you look at it this way, it’s obvious why we have not made progress on the question what dark matter is for such a long time. There’re just the wrong people working on it. It’s not a problem you can solve with particle physics and general relativity. It a problem for condensed matter physics. That’s the physics of gases, fluids, and solids and so on.
So, the conclusion that I have arrived at is that the distinction between dark matter and modified gravity is a false dichotomy. The answer isn’t either – or, it’s both. The question is just how to combine them.