Using the Universe to calculate the mass of a dark matter candidate

This year, the Large Hadron Collider has produced more than 10 times the data that it generated in the previous year's run. While most of that hasn't been analyzed yet, none of the data looked at so far contains an obvious sign of one of the Universe's big mysteries: a dark matter particle. With each year's failure to turn up a WIMP (weakly interacting massive particle), it gives us a little more motivation to consider alternatives.
One of the more compelling alternatives is a particle called an axion. Axions were first proposed to solve a different problem in physics, one involving the forces that pulls quarks and gluons together to form things like protons and neutrons. But if axions exist and have mass, they would seem to have the properties needed to produce the effects we ascribe to dark matter.
One nice thing about axions is that, since they have to perform another role, their properties are a bit constrained. Now, a team of researchers have used that fact to calculate the mass we should expect an axion to have. The input parameters to that calculation? Nothing more than the Universe itself.
The whole endeavor, undertaken by a large European team, involves what's called an equation of state. That's a physicist's way of describing the necessary equations to describe a physical system from a certain perspective. So, for example, you can create equations of state that describe a large gas cloud in terms of thermodynamics, or in terms of gravity. But the idea is that the equation of state provides a complete description.
If axions exist, they should be part of the equation of state for quantum chromodynamics (QCD), the branch of physics that describe the interactions among quarks and gluons. Axions help break the time symmetry of QCD, making it play nice with other areas of physics. So, to get some hint of the axions' properties, you just need to calculate an equation of state of a system where axions are involved. And, conveniently, we have one: the first instants of the Universe's existence.
Immediately after the Big Bang, the Universe was so energetic that matter couldn't form the protons and neutrons that make up the foundation of our every day experience. Instead, the entire Universe was filled with a soup of quarks and gluons (as well as other particles), a condition that can only be produced in particle accelerators. During the Universe's expansion, things cooled enough for this soup to condense into the protons and neutrons we have today. This transition, which took place throughout the entire Universe, is what the team used as their equation of state. That equation of state should provide a value that's related to the mass of the axion.
(Technically, what they were looking at is the breaking of the time symmetry—the one mediated by the axions—which happened around the same time in the Universe's existence. But the paper's description of this was phrased as "The underlying Peccei-Quinn U(1) symmetry is spontaneously broken—which can happen pre-inflation or post-inflation—and an axion field A acts as a massless Goldstone boson of the broken symmetry." So we'll go with the approximation above.)
Needless to say, performing a QCD calculation for the entire Universe is pretty computationally intense. So, the researchers identified the two major computational bottlenecks and found workarounds to both of them. Rather impressive workarounds. For one aspect of the calculations, they note that the traditional route has a cost that scales to the eight power of one of the terms. Their replacement for it scales with the same term to the zeroth power. As they understate in the paper, "the reduction in CPU time is tremendous."
In fact, the team spent so much time describing the calculations and the physics behind them in the body of the paper that they forgot to bother to mention the results that it produced. You have to look at the label for one of their graphs to find it. In any case, if our understanding of the early Universe is correct, axions have a mass somewhere between 50 micro-electronVolts and 1,500 μeV.
That's still a pretty large range, but it definitely means that axions are light (as expected). But it can be used by cosmologists to determine whether axions really can produce all the observed effects of dark matter. And it can be used by experimentalists to limit their search for these particles.
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