The second most abundant particles in the Universe are undetectable! [Starts With A Bang]

“These neutrino observations are so exciting and significant that I think we’re about to see the birth of an entirely new branch of astronomy: neutrino astronomy.” -John Bahcall

You’ve been around here long enough to know about the Big Bang. The vast majority of galaxies are speeding away from us, but more than that, the farther away they are from us, the faster they appear to be receding.

But it’s more than that; when you look at a distant galaxy, because the speed of light is finite, you’re actually looking at it in the distant past. Since all the galaxies are expanding away from one another, and galaxies that are farther away are expanding away at a faster rate, this led to the idea that the Universe was smaller, denser, and also hotter in the past.

Going backwards in time, because the Universe was hotter, it was once so hot that neutral atoms couldn’t even form: everything was a sea of ionized plasma, filled with nuclei, electrons, and radiation. (When the Universe cooled to form neutral atoms, that’s where the cosmic microwave background comes from.) Going even further back, you can imagine a Universe so hot that even the atomic nuclei can’t hold together against the intense bath of radiation; a high-enough energy photon will blast them apart into free protons and neutrons.

(And when the Universe finally cools enough to form stable nuclei, that’s where the primordial elements in the Universe come from.)

But going even farther back than that, we can find a time where the radiation in the Universe was so hot that all the particles that exist, along with their antiparticles, would be spontaneously created in particle-antiparticle pairs.

This includes all the quark/antiquark pairs, all the lepton/antilepton pairs, all the gluons and photons and the weak bosons, and any heretofore undiscovered particles that might exist at even higher energies than we currently understand. Back when the entire observable Universe — now nearly 100 billion light-years in diameter — was compressed into a space smaller than a single light-year across, these particle/antiparticle pairs all existed in great abundance, spontaneously creating and annihilating in (approximately) equilibrium.

But — as you can clearly see — that state doesn’t last for very long. As the Universe expands and cools, it becomes harder and harder to make new particle-antiparticle pairs, while the existing ones will continue to annihilate away into photons, or particles of light. Eventually, the chance of annihilating — dependent on their cross-section — will drop to such a low value that whatever exists at that time will be effectively “frozen in,” and as long as that particle is stable against decay, it will continue to exist to the present day.

We know of three such particles (and their antiparticles) that do this: the neutrinos!

Coming in three flavors to match the three types of lepton — electron, muon and tau — these are the lightest, lowest-mass particles known to actually have a non-zero mass. The upper limit on the mass of the heaviest neutrino is still more than 4 million times lighter than the electron, the next lightest particle.

And yet, neutrinos have an energy-dependent cross section that becomes extremely small at lower energies. By time the Universe is about a single second old, the neutrinos and anti-neutrinos stop interacting with one another, and simply continue to lose energy and cool with the expansion of the Universe. You may remember that this is the same thing that photons do once neutral atoms are formed, and that’s where the cosmic microwave background comes from.

Only, neutrinos are slightly different than photons. Even though they have the tiniest masses of anything we know, because we know where they come from (and what the Universe was like when they stopped interacting), we know they don’t do exactly the same thing. The cosmic microwave background (CMB) of photons has an energy spectrum like the one above, with a peak at a temperature of 2.725 Kelvin.

The cosmic neutrino background should have a slightly lower temperature at 1.96 Kelvin (because electrons/positrons hadn’t annihilated yet; that’s why the CMB is slightly hotter), but remember the important difference: unlike photons, neutrinos have a mass!

That mass, tiny though it may be, is still large compared to the amount of energy that corresponds to the thermal energy that’s left over from the early Universe. Depending on their mass (remember, there’s still some uncertainty), they’re moving at no more than a few thousand km/s today, and probably at just a few hundred km/s.

This is a really, really interesting number.

The mass-and-energy of these neutrinos tell us that they’ve fallen into the large-and-small-scale structures in the Universe, including in our own galaxy. They tell us that they’re a small percentage of the dark matter — about 0.3% of it — but cannot be all of it. (There’s about as much mass in neutrinos as there is mass in the form of stars currently burning through their fuel today. Not a lot, but still interesting!)

But what’s maybe most amazing about these neutrinos is that we have no idea how to experimentally detect them!

We can detect neutrinos, but only neutrinos with about a billion times the energy of these cosmic relics. Because of how quickly the cross-section falls off, we really have no hope for how to detect something with such a small signature. This is one of the last great untested predictions of the Big Bang, but one we’re unlikely to solve anytime soon. Despite the fact that there are hundreds of these neutrinos and antineutrinos per cubic centimeter, and despite the fact that they’re zipping around at (at least) hundreds of kilometers per second, the only interaction they can conceivably have with normal matter is via a nuclear recoil.

And a nucleus, compared to a neutrino, is large, to put it mildly. Detecting one of these recoils is more difficult than detecting the recoil of a supremely-heavily-loaded semi-truck when it collides with… a paramecium.

But there is one interesting thing we’ve learned about these neutrinos. You see, we’ve known for a long time that neutrinos are all left-handed, which is to say that their spin always opposes their momentum, or that they’re spin -½. On the other hand, anti-neutrinos are all right handed, their spin always points in the same direction as their momentum, or that they’re spin +½. All the other particles of half-integer-spin we know of have versions that are ±½, whether they’re matter or antimatter.

But not neutrinos. It’s fueled speculation that neutrinos might actually be their own antiparticles, making them a special type of particle known as a Majorana Fermion. But there’s a special type of decay that should happen if they are; so far, no dice on that decay, and because of that, the window on neutrinos being Majorana particles is closing.

So there you have it: there are some 10⁹⁰ neutrinos and anti-neutrinos left over from the Big Bang, making them the second most abundant particle in the Universe (after photons). There are more than a billion ancient neutrinos out there for each proton in the Universe. And yet, all of these relic neutrinos — making up the cosmic neutrino background (or CNB) — are completely undetectable to us. Not in principle, just in practice, as we don’t know how to make experiments sensitive enough (or even close) to search for this. If you want to know what you can do to win a Nobel Prize, come up with a way to detect them, and the Nobel Prize in physics will surely be yours!

Until then, enjoy some other neutrino fun facts, and marvel at what’s perhaps the last great unverified prediction of the Big Bang: a relic background of cosmic neutrinos!