Though she be but little, she is fierce!
– William Shakespeare, writing about neutrinos

For something as ubiquitous as they are, neutrinos still keep many secrets. We don’t know what their masses are, and there’s even some uncertainty about how many neutrino flavors (types) are out there. They change from one flavor to another, according to rules we’re still working out. These mysteries linger because neutrinos are very easy to make, but hard to detect and impossible to confine. They’re electrically neutral, meaning that they can’t be trapped or steered by magnetic fields, and even the densest of solids is like a loose net to a neutrino. Neutrino detection is something I may post about later (since that’s the chapter of my book I’m working on currently), but another aspect of the particles has potential implications for the very structure of the Universe.

Before I get going too far, a quick neutrino overview is in order. Neutrinos are electrically neutral elementary particles that interact primarily through the weak nuclear force. According to the Standard Model of particles and interactions, there are three flavors of neutrino: electron, mu, and tau neutrino. (Those flavors correspond to the three types of low-mass charged elementary particles: electrons, muons, and tauons.) However, the Standard Model predicts that neutrinos should be precisely massless, while experiments have shown neutrinos have a small mass — the characteristic that allows them to change flavor, the phenomenon known as neutrino oscillation. Since the Standard Model can’t explain neutrino mass, that opens up some interesting possibilities for new physics — and cosmology.

Before the cosmos became transparent about 380,000 years after the Big Bang, ordinary matter was a dense, hot plasma. During that epoch, neutrinos could affect the properties of the plasma and the expansion rate of the Universe, depending on their masses and numbers. The Universe we observe places limits on some neutrino properties: if neutrinos were too massive, or came in too many varieties, or behaved in fundamentally different ways, we wouldn’t be here to talk about them. Beyond human-centric arguments, we also can count galaxies and estimate their masses, both things that place constraints on what neutrinos can be like.

It may seem odd that an elementary particle could have such a profound effect on something as big as a galaxy. However, we have to remember that neutrinos move close to the speed of light — making them somewhat like photons in terms of their gravitational behavior — and very numerous. No experiment has ever found a significant difference between neutrino speed and the speed of light, which means neutrinos will escape all but the strongest of gravitational fields. If neutrinos are too massive, they behave more like ordinary matter when the cosmos was dense, but that also could suppress the formation of early galaxies and galaxy clusters. Too-heavy neutrinos would carry away mass and energy as the proto-galaxy formed, preventing it from becoming dense enough to ignite star formation. Counting the numbers and masses of galaxies therefore places an upper limit on the neutrino mass: neutrinos must be sufficiently low mass to be consistent with the Universe we observe.

That upper limit is surprisingly stringent: according to conservative estimates, if you take one of each of the neutrino flavors and added their masses up, the total is less than 1/1000 of the electron mass. I’m someone who deals in pretty extreme numbers regularly, but a mass that tiny still boggles my mind, not least since the lightest neutrino mass is probably at least a factor of 10 smaller. Because neutrinos are so low mass, many analyses of cosmological data either assume they’re massless, or don’t include their properties among the adjustable parameters when trying to fit observational data.

It’s not crazy: if you look at the big cosmological observations — cosmic microwave background, baryon acoustic oscillations, the large-scale distribution of galaxies and galaxy clusters, etc. — you find you can describe everything pretty well with just six numbers.[1] Those six parameters are part of the concordance model of cosmology, which also includes the basic ingredients of cosmic flatness, inflation, dark matter, and dark energy. However, “pretty well” isn’t always good enough, and with the advent of precision measurements, some nagging discrepencies between different observations popped up. The one that got the most attention was the small but statistically significant difference in the measurements of the Hubble parameter, which is the expansion rate of the Universe: estimates from cosmic microwave background experiments were noticeably different from those using galaxies.

Mark Wyman, Douglas Rudd, Ali Vanderveld, and Wayne Hu argued in a recent paper that neutrinos could help solve the problem. Or rather, they proposed that using neutrino properties to expand the parameter space would help match theory to observation. After all, there’s no inherent reason to think those six parameters are the only ones we get: it’s a convenience, not a hard rule. The new paper added two of three new numbers that can be varied to fit the cosmological data: the effective number of neutrino flavors and either the total mass of the three standard neutrino flavors or the mass of a hypothetical fourth neutrino.

The effective number of neutrino flavors is kind of an odd concept, since it isn’t necessarily the same as the actual number of flavors. It doesn’t even need to be a whole number! Any extra fraction over the whole number indicates the presence of particles that behave relativistically, but aren’t necessarily neutrinos. That could include electrons and positrons that annihilate in the hot cosmic plasma, or I suppose even dark matter particles that move close to light speed, if any exist. (I reserve the right to name my next band “Hot Cosmic Plasma”.) The Standard Model predicts a value slightly over 3 for the effective number of neutrinos, which is consistent so far with the six-parameter concordance model, but only barely.

By contrast, the existence of one or more additional neutrino flavors is easier to grasp. If these extra flavors don’t interact directly with ordinary matter — something called sterile neutrinos — they would be noteworthy primarily by their absence. We’d see them indirectly in the form of missing energy or missing neutrinos, if the normal (active) neutrino flavors oscillate into sterile neutrinos. Experiments haven’t ruled out sterile neutrinos yet, and they could be much more massive than their active cousins (albeit still less massive than electrons).

Using eight parameters instead of six, Wyman and colleagues found they could correct some of the disagreements between the CMB results and galaxy measurements. The best fits to the data in their simulations (using a standard cosmological software package called CosmoMC) included a slightly higher effective number of neutrinos, and either a larger maximum neutrino mass or the existence of a sterile neutrino. (The effect of either increasing the total mass of all neutrino flavors or adding a sterile neutrino is similar, so it’s distinctly possible both could be true, but it’s hard to check them simultaneously.) The numbers they found are consistent with particle physics experiments and measurements of the large-scale structure of the Universe.

Of course, just because this scheme works doesn’t mean it’s the best or only solution to the tension between CMB and galaxy measurements. However, it has the advantage of simplicity: no new physics is necessarily required. Even if we end up requiring a sterile neutrino, it’s a fairly minimal addition to the physics we know. Neutrinos already provide some hints about the physics we know exists beyond the Standard Model; it’s possible they could help us resolve a cosmological predicament too.