Could dark matter be super cold neutrinos?

Probably the greatest physics problems of the current generation are the cosmological questions. Thanks to the development of powerful new telescopes (many of them in space) in the last years of the twentieth century, startling new and unexpected results have pointed the way to new physics. These currently go under the names of "dark matter" and "dark energy", but those aren't real descriptions; rather they are suggestions for what might provide theoretical solutions to experimental anomalies. And, as naming often does, they guide our thinking into explorations of how to come up with new physics.

The problem that "dark matter" is supposed to resolve began in the 1970s with the observations of Vera Rubin. By making a careful analysis of the motion of stars in galaxies, she found an unexpected anomaly. As any first year physics student can tell you, Newton's law of gravitation tells you how planets orbit around the sun. The mass of the sun draws the planets towards it, bending their velocities ever inward in (nearly) circular orbits. The mathematical form of the law produces a connection between the distance the planets are from the sun and the speed (and therefore the period) of the planets.

That connection was known empirically before Newton to Kepler (Kepler'sthird law of planetary motion: the cube of the distance from the sun is proportional to the square of the planet's period). The fact that Newton's laws of motion together with his law of gravity explained that result was considered a convincing proof of Newton's theories.

A galaxy has a structure somewhat like that of a solar system. There is a heavy object in the center – a massive black hole – that is responsible for most of the motion of the stars in the galaxy. Rubin found that the speed of the stars around the center didn't follow Kepler's law. The far out stars were going too fast. This suggested that there was an unseen distributed mass that we didn't know about (or that Newton's law of gravity perhaps failed at long distances; In my opinion this option has not received enough attention, though that's for another post.).

Observations in the past thirty years have increasingly supported the idea that there is some extra matter that we can't see – and a lot of it. More than the matter that we do see. As a result, a growing number of physicists are exploring what might be causing this.

I saw a lovely colloquium yesterday about one such search. Carter Hall, one of my colleagues in the University of Maryland Physics Department, spoke about the LUX experiment. This explores the possibility that there is a weakly interactive massive particle (a "WIMP") that we don't know about – one that doesn't interact with other particles electromagnetically so it doesn't give off or absorb light, and it doesn't interact strongly (with the nuclear force) so it doesn't create pions or other particles that would be easily detectable in one of our accelerators. This would make it very difficult to detect. The experiment was a tour de force, looking for possible interactions of a WIMP with a heavy nucleus – Xenon. (The interaction probability goes up like the square of the nuclear mass so a heavy nucleus is much more likely to show a result.) The experiment was incredibly careful, ruling out all possible known signals. It found no results but was able to rule out many possible theories and a broad swath of the parameter space – eliminating many possible masses and interaction strengths. An excellent experiment.

But as I listened to this beautiful lecture, I wondered whether the whole community exploring this problem hadn't made the mistake of looking under the lamppost for our lost car keys. It's sort of wishful thinking to assume that the solution to our problem might be exactly the kind of particle that would be detectable with the incredibly large, powerful, and expensive tools that we have built – particle accelerators. These are designed to allow us to find new physics – in the paradigm we have been exploring for nearly a century: finding new sub-nuclear particles and determining their interactions in the framework of quantum field theory.

This reflects a discussion my friend Royce Zia and I have been having for five decades. Royce an I met in undergraduate school (at Princeton) and then became fast friends in grad school (at MIT). We spent many hours there (and since) arguing about deep issues in physics. We both started out assuming we wanted to be elementary particle theorists. That, after all, was where the action was. Quarks had just been proposed and there was lots of interest in the nuclear force and how to make sense of all the particles that were being produced in accelerators. But we were both transformed by a class in Many Body Quantum Theory given by Petros Argyres, a condensed matter theorist. In this class we saw many (non-relativistic) examples of emergent phenomena – places where you knew the basic laws and particles, but couldn't easily see important results and structures from those basic laws. It took deep theoretical creativity and insight to find a new way of looking at and rearranging those laws so that the phenomena emerged in a natural way.

There are many such examples. The basic laws and particles of atomic and molecular physics were well known at the time. Atoms and molecules are made up of electrons and nuclei (the structure of the nuclei is irrelevant for this physics – only their charge and mass matters) and they are well described by the non-relativistic Schrödinger equation. But once you had many particles – like in a large atom, or a crystal of a metal – there were far too many equations to do anything useful with. Some insight was needed as to how to rearrange those equations so that there was a much simpler starting point.

Three examples of this are the shell model of the atom (the basis of all of chemistry), plasmon oscillations in a metal (coherent vibrations of all the valence electrons in a metal together), and superconductivity (the vanishing of electrical resistance in metals at very low temperatures). Each of these were well described by little pieces of the known theory arranged in clever and insightful ways – ways that the original equations gave no obvious hint of in their structure.

I was deeply impressed by this insight and decided that this extracting or explaining phenomena from new treatments of known physics was just as important – as just as fundamental – as the discovery of new particles or new physical laws. Royce and I argued this for many hours and finally decided to grant both approaches the title of "fundamental physics" – but we decided they were different enough to separate them. So we called the particle physics approach "fundamental-sub-one" and the many-body physics approach "fundamental-sub-two". (Interestingly, both Royce and I went on to pursue physics careers in the f2 area, he in statistical physics, me in nuclear reaction theory.) In the decades since we had these arguments, physics has made huge progress in f2 physics – from phase transition theory to the understanding and creation of exotic (and commercially important) excitations of many body systems.

So yesterday, I brought my f2 perspective to listening to Carter talk about dark matter and I wondered: He was talking all about f1 type solutions. Interesting and important, but could there also be an f2 type solution? We already know about weakly interacting massive particles: neutrinos. They only interact via gravity and the weak nuclear force, not electromagnetically or strongly. 

Could dark matter simply be a lot of cold neutrinos? They would have to be very cold – travelling at a slow speed – or else they would evaporate. When we make them in nuclear reactions in accelerators they are typically highly relativistic – travelling at essentially the speed of light. The gravity of the galaxy wouldn't be strong enough to hold them.

That leads to a potential problem for this model. Whatever dark matter is, it has to have been made fairly soon after the big bang – when the universe was very dense, very uniform, and very hot -- hot enough to generate lots of particles (mass) from energy. (Why we believe this is too long a story to go into here.) So you would expect that any neutrinos that were made then would be hot – going too fast to become cold dark matter.

But suppose there were some unknown emergent mechanism in that hot dense universe -- a phase transition -- that squeezed out a cold cloud of neutrinos. Neutrinos interact with matter very weakly – and their interaction strength is proportional to their energy so cold neutrinos interact even more weakly than fast neutrinos. If there were a mechanism that spewed out lots of cold neutrinos, I expect they would interact too weakly with the rest of the matter to come to thermal equilibrium. If the equilibration time were, say, a trillion years, they would stay cold and, if their density were right, could serve as our "dark matter".

Most of the experimental dark matter searches wouldn't find these cold neutrinos. Searching for them at this point would have to be a theoretical exploration: Can we find a mechanism in hot baryonic matter that will produce a phase transition that spews out lots of cold neutrinos? I don't know of any such mechanism or where to start, but wouldn't it be fun to consider?