Superfluid dark matter gets seriously into business

very dark fluid

Most matter in the universe isn’t like the stuff we are made of. Instead, it’s a thinly distributed, cold, medium which rarely interacts both with itself and with other kinds of matter. It also doesn’t emit light, which is why physicists refer to it as “dark matter.”

A recently proposed idea, according to which dark matter may be superfluid, has now become more concrete, thanks to a new paper by Justin Khoury and collaborators.

Astrophysicists invented dark matter because a whole bunch of observations of the cosmos do not fit with Einstein’s theory of general relativity.

According to general relativity, matter curves space-time and, in return, the curvature dictates the motion of matter. Problem is, if you calculate the response of space-time to all the matter we know, then the observed motions doesn’t fit the prediction from the calculation.

This problem exists for galactic rotation curves, velocity distributions in galaxy clusters, for the properties of the cosmic microwave background, for galactic structure formation, gravitational lensing, and probably some more that I’ve forgotten or never heard about in the first place.

But dark matter is only one way to explain the observation. We measure the amount of matter and we observe its motion, but the two pieces of information don’t match up with the equations of general relativity. One way to fix this mismatch is to invent dark matter. The other way to fix this is to change the equations. This second option has become known as “modified gravity.”

There are many types of modified gravity and most of them work badly. That’s because it’s easy to break general relativity and produce a mess that’s badly inconsistent with the high-precision tests of gravity that we have done within our solar system.

However, it has been known since the 1980s that some types of modified gravity explain observations that dark matter does not explain. For example, the effects of dark matter in galaxies become relevant not at a certain distance from the galactic center, but below a certain acceleration. Even more perplexing, this threshold of acceleration is related to the cosmological constant. Both of these features are difficult to account for with dark matter. Astrophysicists have also established a relation between the brightness of certain galaxies and the velocities of their outermost stars. Named “Baryonic Tully Fisher Relation” after its discoverers, it is also difficult to explain with dark matter.

On the other hand, modified gravity works badly in other cases, notably in the early universe where dark matter is necessary to get the cosmic microwave background right, and to set up structure formation so that the result agrees with what we see.

For a long time I have been rather agnostic about this, because I am more interested in the structure of fundamental laws than in the laws themselves. Dark matter works by adding particles to the standard model of particle physics. Modified gravity works by adding fields to general relativity. But particles are fields and fields are particles. And in both cases, the structure of the laws remains the same. Sure, it would be great to settle just exactly what it is, but so what if there’s one more particle or field.

It was a detour that got me interested in this: Fluid analogies for gravity, a topic I have worked on for a few years now. Turns out that certain kinds of fluids can mimic curved space-time, so that perturbations (say, density fluctuations) in the fluid travel just like they would travel under the influence of gravity.

The fluids under consideration here are usually superfluid condensates with an (almost) vanishing viscosity. The funny thing is now that if you look at the mathematical description of some of these fluids, they look just like the extra fields you need for modified gravity! So maybe, then, modified gravity is really a type of matter in the end?

I learned about this amazing link three years ago from a paper by Lasha Berezhiani and Justin Khoury. They have a type of dark matter which can condense (like vapor on glass, if you want a visual aid) if a gravitational potential is deep enough. This condensation happens within galaxies, but not in interstellar space because the potential isn’t deep enough. The effect that we assign to dark matter, then, comes partly from the gravitational pull of the fluid and partly from the actual interaction with the fluid.

If the dark matter is superfluid, it has long range correlations that give rise to the observed regularities like the Tully-Fisher relation and the trends in rotation curves. In galaxy clusters, on the other hand, the average density of (normal) matter is much lower and most of the dark matter is not in the superfluid phase. It then behaves just like normal dark matter.

The main reason I find this idea convincing is that it explains why some observations are easier to account for with dark matter and others with modified gravity: It’s because dark matter has phase transitions! It behaves differently at different temperatures and densities.

In solar systems, for example, the density of (normal) matter is strongly peaked and the gradient of the gravitational field near a sun is much larger than in a galaxy on the average. In this case, the coherence in the dark matter fluid is destroyed, which is why we do not observe effects of modified gravity in our solar system. And in the early universe, the temperature is too high and dark matter just behaves like a normal fluid.

In 2015, the idea with the superfluid dark matter was still lacking details. But two months ago, Khoury and his collaborators came out with a new paper that fills in some of the missing pieces.

Their new calculations take into account that in general the dark matter will be a mixture of superfluid and normal fluid, and both phases will make a contribution to the gravitational pull. Just what the composition is depends on the gravitational potential (caused by all types of matter) and the equation of state of the superfluid. In the new paper, the authors parameterize the general effects and then constrain the parameters so that they fit observations.

Yes, there are new parameters, but not many. They claim that the model can account for all the achievements of normal particle dark matter, plus the benefits of modified gravity on top.

And while this approach very much looks like modified gravity in the superfluid phase, it is immune to the constraint from the measurement of gravitational waves with an optical counterpart. That is because both gravitational waves and photons couple the same way to the additional stuff and hence should arrive at the same time – as observed.

It seems to me, however, that in the superfluid model one would in general get a different dark matter density if one reconstructs it from gravitational lensing than if one reconstructs it from kinetic measurements. That is because the additional interaction with the superfluid is felt only by the baryons. Indeed, this discrepancy could be used to test whether the idea is correct.

Khoury et al don’t discuss the possible origin of the fluid, but I like the interpretation put forward by Erik Verlinde. According to Verlinde, the extra-fields which give rise to the effects of dark matter are really low-energy relics of the quantum behavior of space-time. I will admit that this link is presently somewhat loose, but I am hopeful that it will become tighter in the next years. If so, this would mean that dark matter might be the key to unlocking the – still secret – quantum nature of gravity.

I consider this one of the most interesting developments in the foundations of physics I have seen in my lifetime. Superfluid dark matter is without doubt a pretty cool idea.