Quantum mechanics is incredibly successful at describing the small scales of reality, but it's usually However, there are some fringe cases where
its distinct features manifest on scales we can observe—in things like superfluids,
or the interiors of collapsed stars. But it’s also possible that our entire galaxy
is filled with a reverberating quantum mechanical wave that literally holds the galaxy together—and
in fact explains all the dark matter that we see across the universe. And this isn’t even a fringe theory. It’s axionic dark matter. Around 80% of the mass of the universe seems
to be this completely invisible stuff we call dark matter. Several lines of evidence tell us that there
must be an unseen gravitational influence out there. For example, it’s needed to hold galaxies
together and even to allow galaxies to form in the first place. Although we can’t directly detect dark matter,
we can see how it behaves. It acts like a bunch of low-temperature particles
that barely interact with anything except via gravity. This “cold dark matter” model is the CDM
in our Lambda-CDM model of cosmology, and it’s been pretty successful in explaining
how the tiny density fluctuations in the cosmic microwave background collapsed under gravity
to form the types of structures we see in the universe today. The mainstream hypothesis is that cold dark
matter is some kind of exotic particle—something outside the standard model of particle physics
and not yet detected in our particle experiments. And the main-mainstream version of such a
particle is called the WIMP - which stands for weakly interacting massive particle - and
there are many speculative candidates for the type of particle that could behave in
the way needed for the CDM model. For now, all you need to know about WIMPs is that they can form gravitationally bound structures, known as dark matter “halos”, through
a process called virialization. Imagine a spherical “cloud” of WIMPs collapsing
under its own gravity, as might have existed in the very early universe. The particles will fall towards the center
of mass, pass through it due to their weakly-interacting nature, and come out the other side on chaotic
orbits. They’ll end up flying around the halo with
random orbits which give them an effective “pressure” that keeps the halo “puffy”
and supported against further gravitational collapse. Dark matter halos can be formed in this way
in many different sizes, ranging from a small fraction of a galaxy to entire clusters of
galaxies; and it’s within these halos that galaxies, themselves, can form. As I mentioned, in cosmological simulations
the CDM model does a pretty nice job of reproducing the structure of the universe we see today,
on scales all the way from individual galaxies to giant galaxy clusters and the filaments
of the cosmic web. But we have reasons to be concerned about
the WIMP model. For one thing, despite decades of effort we’ve
never been able to detect a WIMP particle. That doesn’t rule anything out - for example,
WIMPs may be too massive to be created by current particle colliders. But there’s another reason to wonder if
WIMPs are really the answer - and that’s because the standard cold dark matter model
doesn’t quite do a perfect job of explaining structure formation. It appears to miss some of the smaller scale details, and I’ll come back to exactly how it fails. Fortunately, there’s another compelling
candidate for dark matter that could solve some of these problems. The candidate particle is the axion. We’ve talked previously about this ultra-light
hypothetical particle, but we haven’t talked about how the axion could explain dark matter. And we should, because it’s exceptionally
weird, and involves the quantum nature of these particles becoming manifest on galactic
scales. All particles are really wave-like on the
smallest scales. Quantum field theory describes every particle
as a localized vibration in its own quantum field. The size-scale of that vibration is defined
by the de Broglie wavelength, which gets smaller as the momentum of the particle increases. But momentum depends on mass, and so massive
particles tend to have very short de Broglie wavelengths. That means we don’t observe their wave-like
nature on human scales - there they just act like particles. That’s how the massive WIMP particles are
supposed to behave. But the lower the mass of the particle, the
longer its de Broglie wavelength. In principle, that wavelength could reach
human, or even astronomical scales. What would that even look like? Let’s try to imagine it. To start with, we’ll think about WIMP-like
dark matter. How close together would those particles be? Let’s say the mass of each dark matter particle
is around 1 GeV — roughly the mass of a proton — we would need about 1 of these
particles per cubic meter on average in order to produce the amount of excess gravity not
explained by visible matter. So there would be WIMPs in the room with you right now, but those WIMPs are really far apart from each other compared to their own
tiny de Broglie wavelengths. If they also only interact by short-range
forces then WIMPs basically never bump into each other. That’s what we need for a dark matter particle—something
that very rarely interacts even with itself. Now, imagine that we could tune the mass of
the dark matter particles. The lower the mass, the more dark matter particles
we need to produce the gravity that we observe out there. The particles end up closer together. But at the same time, their de Broglie wavelengths
increase. Once the mass drops below a meV or so - around
a millionth that of an electron - we start to run into some interesting effects. If these particles are slow moving, as expected
for cold dark matter, then their de Broglie wavelengths are around the same as their separation. The quantum wavefunctions of the particles
start to overlap. Now we’re in the realm of quantum mechanics. As we’ve seen in recent episodes, the behavior
of overlapping quantum particles depends on their type. Fermions will repel each other - which would
rule them out as weakly-interacting. But boson wavefunctions can comfortably overlap,
so the particles can still ignore each other, just like dark matter is supposed to. Let’s keep going. As we reduce the mass of these bosons even
further, the overlapping vibrations will blend together into one seamless, coherently oscillating
field. Think about ripples in a pool that have reflected
off the edges until you can’t see the original sources and the surface is a pattern of resonant
oscillations. At a certain low mass - around one thousandth of an electron volt - any trace of individual dark matter particles will have vanished and we’re left with a
dark matter field that behaves as a pure wave. Now, if you’ve been keeping up with recent Space Time episodes, you might recall what happens when you have a fluid of non-interacting bosons
with overlapping wavefunctions. You get a Bose-Einstein condensate, manifesting
as a superfluid. Because the particles of a superfluid can’t
interact, they can’t exchange energy, which means they have no friction. They flow perfectly, with zero viscosity. And that’s what axionic dark matter would
be—a superfluid. For example, if the axion predicted by quantum
chromodynamics has a mass of around 10^-5 eV, it would have formed in sufficient numbers
in the early universe to account for all of the dark matter and to exist in this superfluid
state.. But if dark matter is a superfluid, how does
it actually behave? Remember that modeling dark matter as regular
particles works pretty well. This new type of dark matter would need to
do at least as good a job as WIMPs for us to consider them as a valid alternative. But this type of dark matter would behave
very differently to a WIMP. For example, the picture I painted earlier
of WIMPs falling towards the center and ending up in random orbits doesn’t work for the
axion superfluid. Instead, imagine some clouds of axionic dark
matter in the early universe as simple spherical waves like ripples. These would fall towards each other under
the influence of gravity, and, as they collide, create rippling vibrations that pass through
each other and interfere, just like the ripples on a pond. But as these waves get all mixed
up and pulled back into the growing gravitational well, they create interference patterns
of increasing complexity as the waves overlapped. What we’re left with is a messy, bubbling
interference pattern of gravitationally bound dark matter waves sloshing around in the shape
of a halo. That doesn’t sound anything like a WIMP
dark matter halo, but it turns out that this slosh of axion superfluid will have the same
density distribution. It’s dense towards the center of the halo,
and then drops in density as you go out in the same way as regular cold dark matter. That means it potentially has exactly the
same gravitational field. That’s especially true if your axion type
is of the more standard breed in which the mass is around 10^-5 eV. The typical size of the bubbly structure in
axion dark matter is of order the de Broglie wavelength, which is a few hundred meters
or less for more standard types of axion. On the scale of even a solar system, this
type of axionic dark matter would look very smooth, and its gravitational effect would
be pretty much indistinguishable from WIMP dark matter. This isn’t a coincidence. The large-scale average behavior of wavy axion
dynamics is mathematically identical to the large-scale average behavior of WIMP dynamics
because both of these systems can broadly be described as cold, collisionless fluids
with no significant interactions apart from gravity. So if WIMP and axion dark matter look the
same, and WIMPs do a good job of explaining the evolution of structure in the universe,
then axionic dark matter is also a viable model. So why choose axions over WIMPs? For one thing it’s good to explore all the
possible alternative explanations. And maybe this explains why no WIMP has ever
been detected—it would be because they don’t exist. On the other hand, the fact that axionic dark
matter can very closely resemble WIMP dark matter makes it difficult to discriminate
between the two. There’s another reason to consider axionic
dark matter over WIMPs—and that’s because it may do an even better job at explaining
the structures we see in the universe. While cold dark matter models like WIMPs predict
the large scale structure and the number of big galaxies in the universe very well, historically
they’ve struggled to reproduce the finer details of structure formation. For example, CDM models predict that galaxies
should have very high densities at their centers. They also predict that there should be lots
of smaller clumps of matter like dwarf galaxies and satellite galaxies. CDM models make these predictions precisely
because the dark matter in CDM models is cold—which means its particles have lower speeds and
tend to fall towards the center of their gravitational wells. In most of our simulations, CDM models give
you a lot of small galaxies and give you large galaxies with a high concentration of stuff
in the center. But in the real universe we don’t see nearly
as many small structures as seen in most simulations. Also we see that in real large galaxies, density increases towards the center but then flattens out, rather than producing a steep central
cusp. Now I will say that newer simulations have
been able to explain some of these discrepancies—for example, by better simulating the role of
“regular” matter in structure formation. But another potential fix is to use axionic
dark matter. The axions that we’ve been talking about
are very light at 10^-5-ish eV, but if we could tune that mass down even more—to a
ridiculous 10^-20 eV or so—then the structures produced by this dark matter would start to
look different to regular cold dark matter. A dark matter axion with such a low mass has
an enormous de Broglie wavelength—perhaps thousands of light years long. In that case, the smallest structures such
dark matter could form would also be thousands of light years. It would be harder to make small galaxies,
and it would be harder for this dark matter to clump up in the centers of large galaxies—making
the model more consistent with what we observe in our actual universe. Axionic dark matter with such extremely low
masses gives us so-called Fuzzy Dark Matter, with a wavey, fuzzy nature apparent on astronomical
scales. This sort of dark matter wouldn’t just help
with our structure formation problems, it would actually be detectable because it should
lead to a grainy structure from galactic-scale interference patterns. There are proposals for detecting this, for
example by looking for its effect in gravitational lensing. There’s nothing conclusive yet, but upcoming
giant surveys have a hope of spotting fuzzy dark matter if its real. By the way, there’s a semi-reasonable motivation
for proposing such extremely light axions—they are actually predicted by string theory. So now we just need string theory to be right. Like I said, it’s not clear that the cold
dark matter model actually fails, but to dig into the potential issues with the glorious
Lambda-CDM cosmological model we’re going to need another episode. Which we’ll get to soon. In the meantime, rest assured that dark matter
will keep doing its good work, whether as WIMPs or overlapping oscillations of an invisible
superfluid that stitches together our galactic space time.
