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336 in every cubic centimetre

ghosts from the first second of time 👻, and about 24 million of them are inside you right now.

They're older than the oldest light, they go through planets as if they weren't there, and nobody has ever caught one. Here's how we know they're real anyway.

Start reading

Cup your hands together, like you're holding water.

The space inside them, maybe a hundred cubic centimetres of air, is crowded. Not with dust or germs. With tens of thousands of ghost particles that have been travelling since the universe was one second old.

They were there before your hands were. Before the Earth, the Sun, the first star, and even the first atom. They passed through your palms just now without touching a single one of your atoms, and they'll keep going for as long as the universe exists.

They're called relic neutrinos, and together they make up the cosmic neutrino background. There are more of them than of any other particle with mass that we know of. Nobody has ever caught one. Yet physicists know how many there are, how cold they are, roughly how fast they move, and even that they were there 380,000 years after the Big Bang, because they left a fingerprint on the oldest light in the sky.

This is the story of the most common thing you've never heard of. 👻

Chapter 1

A particle nobody could catch

In 1930 physics had a problem. When certain atoms decay, energy seemed to go missing, as if it just vanished. The physicist Wolfgang Pauli proposed what he called a "desperate remedy": maybe an invisible, very light particle was sneaking off with the missing energy. He announced it in a letter that began "Dear radioactive ladies and gentlemen", and skipped the meeting it was addressed to because he had a ball to go to.

The particle got its name a few years later, thanks to Enrico Fermi: neutrino, Italian for "little neutral one". It barely interacts with anything. A typical neutrino from the Sun could pass through a wall of lead a light-year thick. In 1934 two leading physicists calculated how shy it was and concluded there was "no practically possible way" to ever observe one.

Pauli reportedly bet an astronomer a case of champagne that nobody would. He lost. In 1956 a team led by Clyde Cowan and Frederick Reines parked a detector next to a nuclear reactor, which pours out an enormous stream of neutrinos, and caught a few. They sent Pauli a telegram. He replied: "Everything comes to him who knows how to wait." 🍾

☀️ Not those neutrinos

You may have heard that billions of neutrinos pass through your thumbnail every second. That's true, but those come from the Sun, and they whizz through at almost the speed of light. This page is about a different, much older crowd. They're slower, far colder, and around you there are about 150 of them for every one from the Sun.

Chapter 2

Leftovers from the first second

Rewind to when the universe was a fraction of a second old. Everything was a scorching soup at more than ten billion degrees. Light, electrons, their antimatter twins (positrons) and neutrinos were crammed together, crashing into each other constantly. In that crush, even neutrinos got bumped around.

But the universe was expanding fast, and the soup was thinning out. At about one second, the neutrinos' collisions became too rare to keep up. They stopped bumping into anything. Physicists call it decoupling. In plain words, the neutrinos left the party.

And they've been travelling ever since, for 13.8 billion years, without hitting a single thing. Every other particle we know of from back then has been scattered, absorbed or remade countless times. Not these.

To appreciate how old that is: the famous "afterglow of the Big Bang", the cosmic microwave background, was released when the universe was 380,000 years old. The neutrinos left at about one ten-trillionth of that age. They're the oldest untouched leftovers of the Big Bang that we can put a date on. 🕰️

Chapter 3

336 in every cubic centimetre

Here's the wild part: we can count them. The afterglow of the Big Bang is a nearly perfect bath of light at 2.7 degrees above absolute zero, and physics says exactly how many particles of light that temperature means: 411 in every cubic centimetre. The neutrinos were born in the same soup, so their number follows from the same arithmetic. For every 11 particles of light there are 9 neutrinos (counting their antimatter twins). That makes 336 in every cubic centimetre: a cube one centimetre on each side, smaller than a sugar cube. Spin it, then scale it up to the size of your body 👇

Now compare that with atoms. Ordinary matter is so spread out across the universe that, on average, there's one atom for every five cubic metres. So Big Bang neutrinos outnumber atoms by more than a billion to one.

Walls, planets and people don't keep them out, so the same crowd is inside everything. About 24 million of them are inside your body at this moment. By the time you finish this sentence, quadrillions have passed through you. You will never feel a single one.

Chapter 4

The colder twin

If the neutrinos and the light came from the same soup, you'd expect them to have the same temperature today. They don't. The neutrino background is colder: 1.95 degrees above absolute zero versus 2.73 for the light. Why?

Because of what happened a few seconds after the neutrinos left. The soup was still full of electrons and positrons, constantly being created and destroyed in pairs. As the universe cooled, it could no longer make new pairs, but the existing ones kept annihilating each other. Their energy had to go somewhere, and it went into light.

The neutrinos had already left the party, so they got almost none of it. The light got a warm boost that the neutrinos missed, and the gap has stayed ever since. The same boost made extra particles of light, which is why light ends up outnumbering the neutrinos 11 to 9 (Chapter 3). Do the arithmetic and the neutrinos come out at about 71% of the light's temperature (the cube root of 4/11, for the curious). Watch it happen:

Chapter 5

Once, 40% of everything

Tiny as they are, there were so many of them that for the universe's first few hundred years, neutrinos carried about 40% of all the energy in existence. Light carried most of the rest. Matter was a small minority. Slide through time:

Today matter and dark energy have taken over, and the neutrinos are a fraction of a per cent. But they still pull their weight. Even at the lightest masses physics allows, all the Big Bang neutrinos in the universe together weigh about half as much as all the stars in every galaxy, and 25 times more than all the Big Bang's light. Around 1980 some physicists thought these ghosts might be the universe's missing dark matter. Computer simulations showed that particles this fast would have built galaxies far too late, and the idea was dropped. At the lightest masses, the dark matter outweighs them about 200 times.

Chapter 6

Heard, not seen

So how do we know they're really there, if nobody has caught one? Because the universe recorded them.

The first clue is helium. The early universe's expansion speed depended on how much stuff was in it, and that set how much helium got made in the first three minutes. The helium we measure today fits three kinds of neutrino, the same number that particle colliders count in a completely different way.

The second clue is sharper. Before the afterglow was released, the young universe rang like a bell. Sound waves sloshed through the hot gas of light and matter, and when the light finally broke free, the pattern of those waves froze into it. Today we see it as a set of peaks in how the afterglow's brightness varies across the sky.

The neutrinos didn't join in the ringing; they had already left. They streamed ahead at nearly the speed of light, faster than sound could travel. But there were so many of them that their gravity tugged the sound waves along. The result is that the whole pattern is shifted, very slightly, as if the bell had been nudged:

In 2015 physicists spotted that shift in data from the Planck satellite. By 2025, with more data and more telescopes, it was measured at around 10 to 14 "sigma", which in physics means about as certain as it gets. Nothing else in standard physics leaves that particular fingerprint. 🔎 The ghosts were there, 380,000 years after the Big Bang, rushing past the sound.

Chapter 7

Slow ghosts

Here's a twist most people don't know. You might picture neutrinos as zipping along at the speed of light. Neutrinos from an exploding star do: in 1987 a burst of them kept pace with the star's light all the way to Earth (Nº 7 has that story). Most Big Bang neutrinos don't.

Neutrinos have mass, which we know because they change type as they travel, something only possible with mass (it won a Nobel Prize in 2015). The masses are absurdly small, at least a million times lighter than an electron, but only the lightest could be zero. (Nobody knows yet where those masses come from. The Higgs field, which gives electrons and quarks theirs, can't do it without some new ingredient: see Nº 5.) And the Big Bang neutrinos have cooled so much in 13.8 billion years that for at least two of the three types, the mass now matters. The heaviest have slowed down to a few thousand kilometres a second. Slide the mass and watch them cross a galaxy 👇

About 3,000 kilometres a second is more than 15 times faster than our fastest spacecraft, but slow for a ghost: it takes one about ten million years to cross our galaxy. That's still about six times too fast for the Milky Way's gravity to hold on to, though. They just stream through. So the crowd around you is close to the cosmic 336: at the lightest masses, only a few per cent more. Being this slow also makes their "1.95 degrees" a label, not a thermometer reading: it describes how their momenta are spread, but the heavy ones now move as lazily as a gas at a few hundredths of a degree (Nº 17 collects more temperatures that are labels, some of them negative).

And here's the trick that being slow plays on our intuition. You might think these ancient particles come from the very edge of the observable universe, even farther away than the afterglow. Light-speed ones would. But the heavier ones were slowed down by the expansion of space long ago, so the ones arriving here today set off much closer:

Chapter 8

Three scales that don't quite agree

How heavy is a neutrino? Three completely different methods are closing in, and right now they're squeezing it from both sides.

  • Shape-shifting sets a minimum: the three masses must add up to at least 0.059 electronvolts (about 10−37 kilograms).
  • A lab in Germany called KATRIN weighs neutrinos directly from radioactive decays and sets a maximum more than twenty times higher: about 1.4 electronvolts for all three together (none of them can weigh more than about 0.45). Its final answer is expected in 2027.
  • Maps of the universe weigh them by how they change the universe's expansion and how much they smooth out the cosmic web. They set a maximum of about 0.06: barely above the minimum. Adding the South Pole Telescope's data pushed it slightly below the minimum; a July 2026 analysis that also uses that telescope puts it right at the minimum, and the telescope's own newest analysis eases it back a little, to about 0.07.

Put all three on one scale and try a weight of your own. Drag the line 👇

That leaves almost no room. Either neutrinos are as light as physics allows, or something in our picture of the universe is slightly off, or one of the measurements has a hidden error. One suspect is dark energy, which might be changing over time (Nº 1 has the latest on that hint). Physicists expect to know which within a few years. 🔍

Chapter 9

How do you catch a ghost?

You can't make a Big Bang neutrino hit something hard enough to notice. It packs about a billion times less punch than the neutrinos we already know how to catch. So physicists turn to a trick that dates back to 1962: a radioactive atom as bait.

Tritium, a heavy form of hydrogen, decays on its own by spitting out an electron. Very rarely, a passing Big Bang neutrino gets absorbed instead and triggers the same decay. When that happens, the electron comes out with a tiny bit too much energy, more than any normal decay could give it. Spot those overachieving electrons and you've caught a ghost.

The catch is the numbers. A hundred grams of tritium would catch only four to eight ghosts a year, depending on details of the neutrino nobody knows yet. In the same year, it would produce about a million billion billion ordinary decays, and hundreds of millions of them would land close to the ghosts' energy. To see them, your detector has to measure energy with a precision that nobody has achieved yet. Try it: sharpen the detector until the ghosts' spike pokes out of the slope.

A project called PTOLEMY plans to spread the tritium on graphene, a sheet of carbon one atom thick. A hundred grams would need about half a square kilometre of it. And there's a quantum snag: pinning the tritium to a surface makes its motion fuzzy, thanks to Heisenberg's uncertainty principle, and that blurs the electrons' energies by more than the effect you're trying to see. Physicists are still arguing over how to get around that. A first test machine is being built under a mountain in Italy. Why bother? A caught ghost would be a direct message from the first second, and it could help tell us how heavy neutrinos are and even whether each one is its own antiparticle.

Chapter 10

The oldest thing you'll ever touch

Let's add up the bill. 🧾

👻 Ghost receipt

Inside you right nowa 70-litre human24,000,000
Their total weightat the lightest allowed masses< 1 electron
Inside the whole Earthtotal weight13 micrograms
Per atom in the universeon average> 1 billion
Ever caught0

older than the oldest light ✦ lighter than an electron

Twenty-four million particles from the first second of time are inside you, and if neutrinos are as light as physics allows, together they weigh less than a single electron. At those masses the whole Earth holds about 13 micrograms of them, less than a grain of salt.

Right now, while you read this, they're passing through your eyes, your hands, the screen, the floor, the planet.

Each one left the Big Bang when the universe was a second old, before there were atoms to make anything out of.

It has been travelling ever since, slowing down, cooling off, untouched by every star and galaxy it passed.

And it doesn't stop at you. It will keep going long after the last star has burned out.

You are a brief stop on the oldest journey in the universe.

Physicists have worked out how many there are and how cold they are, felt their pull on the young universe and heard them in the echo of the Big Bang. What nobody has done yet is catch one. It's one of the hardest measurements anyone has ever proposed, and maybe the most beautiful.

As Pauli said, everything comes to him who knows how to wait. The ghosts have been waiting for 13.8 billion years.

Nº 4 · ∫ Full version

Three hundred and thirty-six

Every cubic centimetre of the universe, including the one in front of your nose, holds about three hundred and thirty-six neutrinos left over from the first second after the Big Bang. They outnumber atoms by more than a billion to one. They have been travelling since before the first atomic nuclei were assembled, and about twenty-four million of them are inside you as you read this. No experiment has ever caught one. We know they are there anyway.

This page works out how many there are and why, why they are colder than the light from the Big Bang, how slow they are now, how the oldest light in the universe already recorded their passage, what they say about the neutrino's mass, and what it would take to catch one.

This is the ∫ Full version, with the equations, caveats and sources. New to the idea? Start with the ✨ Simple version.

Part IThe sea you sit in

Chapter 1The most common thing with mass

Start with something better known. The universe is filled with the cooled-down light of the Big Bang, the cosmic microwave background (CMB). Its spectrum is the most perfect blackbody ever measured, at a temperature of 2.7255 K.1 A blackbody at temperature T contains a fixed number of photons per unit volume:

nγ = (2ζ(3)/π2) (kBT/ħc)3 ≈ 410.7 cm−3 ζ(3) ≈ 1.202 is Apéry's constant. With T = 2.7255 K this gives 410.7 photons in every cubic centimetre of the universe.

Alongside those photons is a second, invisible sea. For every 11 CMB photons there are 9 neutrinos and antineutrinos, released when the universe was about one second old. Chapters 3 and 4 explain where the ratio comes from. Each of the three neutrino mass states contributes 112 per cubic centimetre, counting neutrinos and antineutrinos together:

nν = 3 × (3/11) nγ ≈ 336 cm−3 The textbook value, which assumes the neutrinos stopped interacting abruptly. A full Standard-Model calculation, in which they pick up a little extra heat as they let go, gives 339.5 cm−3, about 1% more.2

That is the number in the title. A real sugar cube is about 3 to 5 cubic centimetres, so the space it occupies holds over a thousand (about 1,000 to 1,700) of these neutrinos at any moment.

Compare that with ordinary matter. The CMB measures the cosmic density of baryons (protons and neutrons) to better than one per cent: Ωbh2 = 0.0224, which works out to 0.25 baryons per cubic metre.3 So on average relic neutrinos outnumber baryons by about 1.3 billion to one, and atoms by even more, since a helium atom holds four baryons. Of all the particles we know of, only the CMB photons are more numerous, and photons are massless. Oscillation experiments prove that at least two of the three mass states have mass, and those two alone outnumber atoms more than a billion to one. So relic neutrinos are the most numerous particles with mass that we know of.

None of this needs empty space. Relic neutrinos interact so feebly that walls, planets and people are almost perfectly transparent to them, so the same density fills the room you are sitting in. A 70-litre human body contains about 24 million of them at any instant (this page's arithmetic: 336 × 70,000 cm3). They are not the neutrinos usually meant when people say "billions pass through your thumbnail every second". Those come from the Sun: about 65 billion per square centimetre per second,4 but only about 2 per cubic centimetre at any one moment, because they travel at essentially the speed of light. The Big Bang's neutrinos are about 150 times more crowded, and most of them are much slower (Chapter 7).

WhatRelic neutrinosCMB photons*Atoms (actual)
1 cm3 of intergalactic space3364112.1 × 10−7
A sugar cube (≈4 cm3)≈1,300≈1,600≈3 × 1023
A person (≈70 litres)2.4 × 1072.9 × 107≈7 × 1027
The Earth3.6 × 10294.4 × 1029≈1.3 × 1050
The observable universe1.2 × 10891.4 × 1089≈7 × 1079

This page's arithmetic. *CMB photons in the same volume of open space: unlike neutrinos, they are absorbed by matter, so none are inside a person or a planet. The atoms column counts nuclei: with a quarter of the mass in helium, 2.5 × 10−7 baryons per cm3 make 2.1 × 10−7 atoms. Inside the Sun, the Earth or a person, atoms win, because matter is concentrated there. Averaged over the universe, the ghosts win by nine orders of magnitude. The observable-universe row uses a comoving radius of 46 billion light-years.

Figure 1🎲 Try it

One cubic centimetre of empty space

Neutrino masses

Playback

Number densities today: relic neutrinos 336 cm−3 (112 per mass state, neutrinos and antineutrinos together; 339.5 in the full Standard-Model calculation), CMB photons 411 cm−3 (from T = 2.7255 K), solar neutrinos about 2 cm−3 at Earth's distance (flux ÷ c), and baryons 2.5 × 10−7 cm−3 on average (from Ωbh2 = 0.0224), which make 2.1 × 10−7 atoms because a quarter of the mass is helium. In the animation every particle moves in a straight line at its own speed: relic neutrino momenta are drawn from the frozen Fermi–Dirac distribution (Tν = 1.945 K), so speeds follow from the chosen masses; time runs 109 to 1011 times slower than reality. The count inside the cube fluctuates by about its square root. This page's simulation.Each dot is one particle, moving at its real speed relative to the others, in extreme slow motion. Light zips straight through; the heavier Big Bang neutrinos barely crawl. Every cubic centimetre of the universe holds about 336 of them right now, including the space your hand is in. Open space also holds 411 particles of Big Bang light, but solid matter soaks those up, so none get inside your hand. Averaged over the universe, atoms are the rare ones.

Chapter 2A particle that could never be found

The neutrino began as a confession of desperation. In the late 1920s, beta decay seemed to break energy conservation: the electron emitted by a decaying nucleus came out with a spread of energies instead of a single value. On 4 December 1930 Wolfgang Pauli wrote an open letter to a physics meeting in Tübingen, addressed "Dear radioactive ladies and gentlemen". In it he proposed a "desperate remedy": a light, neutral particle, emitted along with the electron, that carries off the missing energy.5 He could not attend in person because of a ball in Zürich.

Pauli is often quoted as lamenting that he had "done a terrible thing" by postulating a particle that could never be detected. No contemporary record of that sentence exists; it comes from much later retellings. A better-sourced version has him telling the astronomer Walter Baade that he had predicted something that could never be found, and Baade betting him a case of champagne that it would be.6 The worry itself was real. Enrico Fermi, who had popularised the name "neutrino" ("little neutral one"), built the theory of beta decay around it in 1934.7 That same year Hans Bethe and Rudolf Peierls calculated how weakly it should interact and concluded that there was "no practically possible way of observing the neutrino".8

It took a nuclear reactor. In 1956 Clyde Cowan, Frederick Reines and colleagues detected antineutrinos from the Savannah River reactor through inverse beta decay.9 They sent Pauli a telegram. His reply, preserved in the CERN archive, reads: "Thanks for message. Everything comes to him who knows how to wait."10 By Reines's account, Pauli paid up, though the theorists drank the champagne without him and Cowan.6

The relic neutrinos have a separate history. In 1953 Ralph Alpher, James Follin and Robert Herman worked out how neutrinos would fall out of equilibrium in a hot early universe. Their calculation implies a background of neutrinos colder than the radiation background by the factor derived in Chapter 4.11 In 1962 Steven Weinberg proposed detecting a cosmic neutrino sea through its effect on beta decay right at the end of the spectrum, the idea behind every modern capture experiment (Chapter 9).12 In 1966, a year after the CMB's discovery, Semyon Gershtein and Yakov Zeldovich used the relic neutrinos' number density to set the first cosmological limit on the neutrino's mass.13

1930
Pauli's letter proposes the neutrino as a "desperate remedy".
1934
Fermi's theory of beta decay; Bethe and Peierls doubt it can ever be seen.
1953
Alpher, Follin and Herman: the relic neutrino background.
1956
Cowan and Reines detect reactor antineutrinos.
1962
Weinberg: look for the neutrino sea at the end of a beta spectrum.
1966
Gershtein and Zeldovich: relic neutrinos cap the neutrino mass.
1998–2002
Super-Kamiokande and SNO: neutrinos oscillate, so they have mass (Nobel Prize 2015).14,15
2013–2025
The CMB counts about three neutrino species (Planck 2013); their free-streaming "phase shift" is found at 4.5σ in 2015 and at about 10–14σ in 2025 (Chapter 6).

Chapter 3One second old

In the first second, the universe was a hot, dense soup of photons, electrons, positrons and neutrinos at a temperature of over ten billion kelvin. Particles collided constantly and shared one temperature. Neutrinos stayed in the soup only through the weak interaction, whose rate per neutrino scales steeply with temperature, while the expansion rate falls more gently:

Γ ~ GF2T5   versus   H = 1.66 √g* T2/MPl Γ is the weak scattering rate per neutrino and H the expansion rate, with g* = 10.75 counting photons, electrons, positrons and three neutrino species. Setting Γ = H gives T ≈ 1.5 MeV, about 1.7 × 1010 K (this page's estimate, with order-one factors dropped).

Because Γ/H falls as T3, the transition is fast. Within a factor of a few in temperature, neutrinos go from colliding many times per expansion time to almost never. Detailed calculations put the decoupling of electron neutrinos at about 1.9 MeV and of muon and tau neutrinos at about 3 MeV; the electron neutrinos hang on slightly longer because they also have charged-current interactions with electrons.16 In the radiation era, time and temperature are tied together:

t ≈ 0.74 s × (1 MeV / T)2 For g* = 10.75. So decoupling happens between about 0.1 and 1 second after the Big Bang.

From that moment on, the neutrinos were free. They have not scattered off anything since. Each one has simply travelled, its momentum stretched by the expansion of space, for 13.8 billion years. Their momentum distribution still has the Fermi–Dirac shape it had when they let go, with a temperature that falls as 1/a, where a is the scale factor.2

Older than the light. The CMB photons kept scattering off free electrons until hydrogen formed, about 380,000 years after the Big Bang. The neutrinos were released about 1013 times earlier, at a redshift of about 1010. They are the oldest particle background whose age we know; dark matter may be older still, but nobody yet knows what it is or when it formed. A background of primordial gravitational waves, if there is one, would also predate the neutrinos, but none has been seen. Even that one would carry the neutrinos' mark: Steven Weinberg calculated in 2004 that free-streaming neutrinos damp the gravitational waves that entered the horizon during the radiation era, cutting their squared amplitude by 35.6%.17

Chapter 4Four elevenths

If nothing else had happened, the neutrinos and the photons would have cooled side by side and shared one temperature today: the neutrinos' 1.95 K. Something else did happen, a few seconds later.

Electrons and positrons were being created from pairs of photons and destroying each other at equal rates, as long as the temperature was well above the electron mass, 0.511 MeV. As the universe cooled through that scale, pair creation switched off but annihilation didn't. Between about 0.5 and 0.05 MeV, from roughly three seconds to about ten minutes after the Big Bang, almost all the electrons and positrons annihilated.

Their energy, and their entropy, went into the photons. The neutrinos had already decoupled and got almost none of it. The bookkeeping uses the conservation of entropy per comoving volume in the photon–electron plasma:

g*s(aT)3 = constant:   (11/2)(aT)3before = 2(aTγ)3after Before annihilation, the plasma's entropy degrees of freedom are 2 for photons plus 7/8 × 4 for electrons and positrons (two spin states each), giving 11/2. Afterwards only the photons' 2 remain.

The photons end up warmer, relative to the neutrinos, by the cube root of 11/4:

Tν / Tγ = (4/11)1/3 ≈ 0.714   ⇒   Tν ≈ 1.945 K today The same factor fixes the number density. Per mass state, neutrinos plus antineutrinos give n = (3/4)(4/11) nγ = (3/11) nγ = 112 cm−3: the 3/4 comes from Fermi–Dirac versus Bose–Einstein statistics, the 4/11 from the cube of the temperature ratio.

Figure 2🌡️ Try it

Why the ghosts are colder: the 4/11 split

Time after the Big Bang
Neutrino ÷ photon temperature
Today, that ratio means

Top: a comoving box of the plasma, with particle numbers in proportion (45 neutrinos and antineutrinos of three species, 20 photons and 30 electrons and positrons at first; the photons' comoving number grows by 11/4 to 55, giving today's 11 : 9 ratio). Neutrinos scatter until about 1–3 MeV and then stream freely; photons keep scattering. Bottom: temperatures multiplied by the scale factor a, so a gas that simply cools as space stretches stays flat. Electron–positron pairs annihilate as T falls below mec² ≈ 0.511 MeV; their entropy goes to the photons, which end up (11/4)1/3 ≈ 1.401 times warmer than the already-decoupled neutrinos. Instantaneous decoupling assumed; the small leakage of heat into neutrinos gives Neff = 3.044 instead of 3. Times use t ≈ 2.42 s · g*−1/2 (MeV/T)2, this page's approximation.Press play. The neutrinos (green) stop bumping into things at about 1 second and fly off in straight lines. A few seconds later, electrons and their antimatter twins annihilate and dump their energy into light, making extra photons, but not extra neutrinos. Count the dots at the end: 55 photons for 45 neutrinos, the same 11 : 9 as in today's sky. Ever since, the ghost gas has been colder than the afterglow: 1.95 K versus 2.73 K today.

The real decoupling was not perfectly sudden. The neutrinos were still interacting a little when the annihilations began, and they caught a small share of the heat, mostly in their high-momentum tail. Corrections from the thermodynamics of the hot electron plasma (finite-temperature QED) and from flavour oscillations change the result slightly. The standard way to express this is the effective number of neutrino species, which measures the neutrinos' energy density in units of one ideal, abruptly decoupled species:

ρν = (7/8)(4/11)4/3 Neff ργ,   Neff = 3.0440 ± 0.0002 The Standard-Model prediction from three independent precision calculations.18 (A 2023 calculation gave 3.043; a 2024 check found the correction behind the difference about thirty times smaller.) Neff is not "3.044 species"; there are three. The extra 0.044 is mostly that leaked heat, plus about 0.01 from QED effects in the plasma.

So the neutrino background is a frozen snapshot of the moment just before electrons and positrons disappeared. Its temperature is 1.945 K, and its number density is set by the same arithmetic that sets the photons'.

Part IIHeard, not seen

Chapter 5Forty per cent of everything

Before about 50,000 years, when matter took over, the universe's energy was mostly radiation. With Neff = 3.044, relic neutrinos carried

ρν / (ργ + ρν) = 0.691 / 1.691 ≈ 41% Of all the radiation's energy after electron–positron annihilation. Before it, the share was 21/43 ≈ 49%. This page's arithmetic from the formula in Chapter 4.

That gravitational heft is why the early universe "felt" the neutrinos, and why we can still measure them (Chapter 6). As space expanded, the picture changed. Radiation energy dilutes as a−4, matter as a−3. Neutrinos began as radiation, but each mass state became non-relativistic once its typical momentum, 3.15 kBTν, fell below its mass. For a 0.05 eV neutrino that happened at a redshift of about 94. Today at least two of the three mass states are non-relativistic, and their energy density is just mass times number:2

Ωνh2 = Σmν / 93.12 eV Σmν is the sum of the three masses. The value 93.12 eV includes the extra heat of Chapter 4; an abrupt decoupling would give 94.07 eV.

Oscillation experiments set a floor on that sum (Chapters 7 and 8): Σmν ≥ 0.059 eV. Even at the floor, Ων ≈ 0.0014 for h = 0.674. That makes the relic neutrinos at least 0.4 per cent of all matter, and the slow ones are a mild form of "hot dark matter". It also gives them some surprising rankings (this page's arithmetic):

  • They outweigh the CMB by at least 25 times. Photons outnumber them 11 to 9, but carry only Ωγh2 = 2.5 × 10−5.
  • Across the universe, they weigh about half as much as all the stars19 (Ωstars ≈ 0.0027). They would weigh as much as the stars if Σmν = 0.12 eV, and about twelve times more at the laboratory upper limit.
  • Inside our galaxy, the opposite. Stars are concentrated in galaxies and relic neutrinos are spread almost evenly, so within about 200 kpc of the Milky Way's centre, the neutrinos at their minimum masses weigh only about 6 million solar masses (ignoring clustering), about 1/8,000 of the galaxy's 5 × 1010 solar masses of stars.20

For a few years around 1980 the relic neutrinos were a leading candidate for the dark matter. In 1980 a Moscow tritium experiment reported an electron-neutrino mass of a few tens of electronvolts, enough for the relic neutrinos to outweigh all the atoms in the universe many times over.21 Computer simulations soon showed that such fast-moving, "hot" dark matter builds the cosmic web from the top down, with the largest sheets forming first and galaxies too late.22 The mass claim was not confirmed, and cosmology turned to slow, "cold" dark matter. With today's cosmological limits the relic neutrinos are at most about 0.6 per cent of the dark matter (about 1.5 per cent if dark energy evolves), and about half a per cent at the minimum masses (this page's arithmetic).

Figure 3🥧 Try it

What the universe is made of, then and now

Neutrinos
Light (photons)
Matter
Dark energy

Shares of the total energy density in flat ΛCDM (Planck 2018: h = 0.674, Ωm = 0.315, Ωγh2 = 2.47 × 10−5, Neff = 3.044). Each neutrino's energy is approximated as √(p̄2 + m2) with mean momentum p̄ = 3.15 kTν; masses follow the oscillation splittings for the chosen lightest mass and ordering. Markers: matter–radiation equality, the release of the CMB, the heaviest neutrino state turning non-relativistic, and dark energy overtaking matter. "Zoom into the small" plots the same shares on a log scale. This page's calculation.For the universe's first few hundred years, these ghosts carried about 40% of all the energy there was. Today they're a fraction of a per cent. Zoom in to see the twist: once the heavier ones slowed down, they started to outweigh the Big Bang's light, and today they weigh at least 25 times more than all of it.

Chapter 6Heard in the afterglow

The relic neutrinos have never been detected directly. They have been detected indirectly in two ways, and the stronger is now a measurement at well over ten standard deviations. A third effect, on the growth of structure, is still being searched for.

1. They sped up the expansion

Extra radiation makes the early universe expand faster. That changes how much helium forms in the first three minutes, because the neutron-to-proton ratio freezes out earlier: each extra neutrino species raises the helium mass fraction by about 0.013.23 It also changes the CMB: more radiation means more damping of the small-scale ripples (the "damping tail"). Both effects measure the radiation density, and both find about three neutrino species:

DataNeff
Standard Model prediction3.044
Planck 2018 + lensing + BAO32.99 ± 0.17
Planck + ACT DR6 + lensing + DESI DR1 (2025)242.86 ± 0.13
Planck + ACT + SPT-3G (2026)252.82 ± 0.12
Big Bang nucleosynthesis + CMB232.90 ± 0.14

A universe with no relic neutrinos (Neff = 0) is ruled out at more than 15σ.2 The two newest CMB combinations sit about 1.4 and 2 standard deviations below 3.044. Nobody thinks that is significant yet, but it is the kind of thing the next generation of telescopes will settle.

Particle physics counts them too, in a completely different way. Every type of light neutrino that the Z boson can decay into adds to the Z's "invisible" decay rate, which the LEP collider at CERN measured precisely in the 1990s. With a 2019 correction to how LEP measured its luminosity (its rate of collisions), the count is Nν = 2.9963 ± 0.0074.26 The two counts need not have agreed: the Z counts the neutrino types it can decay into, and Neff counts the energy of everything relativistic in the early universe. One comes from Z bosons made in a collider, the other from radiation in the first seconds and at 380,000 years. Both say three.

2. They outran the sound

Counting radiation doesn't prove that the extra radiation is neutrinos. Something subtler does. Before the CMB was released, the photons and baryons formed a single fluid in which sound waves rang. Their pattern froze into the CMB as its famous peaks. The neutrinos, already decoupled, did not take part in the sound; they streamed freely at nearly the speed of light, faster than the sound speed, at most c/√3. Their gravity pulled the sound waves slightly ahead, which shifts the peaks by nearly the same phase:27,28

δφ ≈ 0.191π × εν,   εν = ρν/(ργ + ρν) ≈ 0.41 A shift of the peaks to larger angular scales by roughly 20–25 in multipole ℓ (this page's estimate; the exact size depends on ℓ). For the standard adiabatic initial conditions, nothing else in standard physics produces this signature.

In 2015 Brent Follin, Lloyd Knox and colleagues found the shift in Planck's temperature data at 4.5σ.29 A 2025 reanalysis with the full Planck data finds it at about 10σ, and at about 14σ adding the ACT and SPT telescopes.30 The same shift has also been seen, more weakly, in the distribution of galaxies through baryon acoustic oscillations: at about 2σ in 2019, and at about 4σ in DESI's first-year data combined with Planck, with an amplitude about 2.7 times the predicted one, though with large uncertainties; DESI's second-year data see it at 2.6σ on their own.31,32,33 The interpretation is direct: whatever this extra radiation is, it streams freely, as decoupled neutrinos should. Fluid-like or self-interacting alternatives are disfavoured.2

Figure 4🔊 Try it

Heard, not seen: neutrinos shift the echo of the Big Bang

Toy model

Top left, a sketch (not to scale): one point-like overdensity in the plasma. The photon–baryon sound wave spreads at less than c/√3 (the baryons slow it, to about 0.45c by the time the CMB is released), decoupled neutrinos stream ahead at c, and their gravity pulls the sound shell slightly outward; the dashed circle is where it would be without free-streaming neutrinos. Bottom: a toy CMB temperature spectrum with peaks near ℓn ≈ ℓA(n − φ/π), ℓA = 301, an envelope fitted by eye to the shape of the measured spectrum, and the free-streaming phase shift δφ ≈ 0.191π · Rν (Bashinsky & Seljak 2004; Baumann et al. 2016), where Rν = ρν/(ργ + ρν). Thick grey: the same toy without free-streaming neutrinos (Neff = 0); on wider screens each peak is labelled with its shift from it. Top right: the window marked below, magnified; drag the window along the spectrum (or focus it and use the arrow keys). Damping-tail and amplitude effects of Neff are left out. Not a fit to data.Clap once and watch. The sound ring spreads through the hot gas; the neutrinos race ahead at light speed and their gravity tugs the sound a little further out. That nudge moves every peak in the pattern of the afterglow by about the same small amount: compare the coloured curve with the thick grey one, a universe without the ghosts. Slide to zero neutrinos and watch the peaks move back.

3. They smooth out the cosmic web

Massive neutrinos are too fast to fall into small potential wells, so they don't cluster on small scales and they slow the growth of the matter that does. The linear matter power spectrum on small scales is suppressed by about ΔP/P ≈ −8fν, where fν is the neutrinos' share of the matter.34 At the minimum mass that is about 3.5% (this page's arithmetic). This effect is how cosmology hopes to weigh the neutrino (Chapter 8).

Chapter 7Slow ghosts

"Neutrino" conjures a particle at the speed of light. Energetic ones do keep pace: the two dozen from supernova SN 1987A, with about 10 to 40 MeV each, matched its light's speed to about 2 parts in a billion over 168,000 light-years (Nº 7). Relic neutrinos mostly aren't. Their momentum is set by the 1.945 K temperature: on average

⟨p⟩c = 3.15 kBTν ≈ 5.3 × 10−4 eV The mean of a relativistic Fermi–Dirac distribution, which the neutrinos keep in shape forever after decoupling.

That is far smaller than the neutrino masses. Oscillation experiments don't measure the masses themselves, only the differences of their squares: Δm221 = 7.49 × 10−5 eV2 and |Δm231| = 2.51 × 10−3 eV2.35 Even if the lightest neutrino weighed nothing, the other two would weigh at least 8.7 meV and 50 meV in the "normal ordering", or about 49 and 50 meV in the "inverted ordering". So at least two of the three relic mass states are non-relativistic today. In that limit the mean speed is simply

⟨v⟩/c ≈ 0.53 meV / m About 3,200 km/s for 50 meV, 18,000 km/s for 8.7 meV, and 350 km/s at the laboratory upper limit of 0.45 eV. This page's arithmetic, matching the Particle Data Group's formula.2

Two consequences repair common misstatements.

  • "1.95 K" is a label, not a thermometer reading. It describes the momentum distribution. The heavy states' kinetic energies correspond to a gas at only about 0.03 K (for 50 meV), a hundred times colder than the CMB. (Nº 17 collects other temperatures that are labels, some of them negative.)
  • Their wavelength is about 2.3 mm, whatever their mass. The de Broglie wavelength is h/p, and the momentum is fixed by the temperature. Neutrinos of one mass state and one helicity (56 per cubic centimetre) are about 2.6 mm apart on average, so the relic background is a marginally quantum gas, with de Broglie wavelengths almost as long as the gaps between them.

Could the Milky Way capture them? Estimates of the local escape speed range from about 450 to 550 km/s.36 For 50 meV, only about 1% of relic neutrinos are slower than that; for 0.1 eV, about 5–7%. Detailed simulations find that clustering changes the local density by less than 1% for 10 meV and raises it by about 7–12% for 50 meV and 27–50% for 100 meV; the lower values come from a 2023 study that reconstructs the real distribution of matter around us.37,38 So most relic neutrinos stream straight through the galaxy, crossing its disc in about ten million years.

Figure 5🐢 Try it

Slow ghosts: how fast is a Big Bang neutrino today?

Typical speed
Wavelength (de Broglie)Size of each ghost's quantum wave
Slow enough to be held by the Milky Way

Top: a sketch of relic neutrinos of the chosen mass crossing a Milky-Way-sized galaxy, seen from above; speeds and the escape speed are to scale, the galaxy's gravity is a simple smooth model with a flat rotation curve (230 km/s), and time runs at two million years per second. The count in the picture is lower than the share below, because the escape speed falls with distance from the centre. Bottom: the speed distribution of one mass state today, from the frozen Fermi–Dirac momentum distribution with Tν = 1.945 K (kTν = 1.68 × 10−4 eV), neglecting gravitational clustering; hover, tap or focus it (then use the arrow keys) for the share slower than a given speed. "Slow enough to be held by the Milky Way" counts neutrinos slower than a local escape speed of 500 km/s, the middle of current estimates (about 450–550 km/s); it is only a rough guide: gravitational clustering, ignored here, raises the local density well above it for the heavier masses (Chapter 7). This page's calculation.Slide the mass and watch the galaxy. The lightest ghosts flash straight through; heavier ones crawl along at a few thousand km/s, and only the very slowest get caught by the galaxy's gravity and circle it. Nobody knows the exact masses yet.

They come from closer than the CMB, not from behind it. It is tempting to picture the neutrino background as a deeper look than the CMB, from a "last scattering surface" one second after the Big Bang. For massless neutrinos that is true, but barely: they would have travelled only about 280 Mpc farther than the CMB's light. Massive neutrinos were slowed by the expansion and have travelled much less. A 50 meV relic neutrino with typical momentum has come about 2.6 Gpc (comoving), a fifth of the 13.9 Gpc to the CMB's last scattering surface; the slowest have come less than half as far (this page's arithmetic, following Dodelson and Vesterinen39). The relic neutrinos you would catch were born far away, but they are not the most distant thing in view.

Figure 6🗺️ Try it

Where does a relic neutrino come from?

Drag to turn
The ghost's trip
The CMB light's trip
Distance travelled since the first second
Distance to the CMB's origin13.9 Gpc45 billion light-years, comoving
Became slow (non-relativistic)

Spheres centred on us, to scale in comoving distance: where the CMB's light set off (13.9 Gpc), where a massless neutrino set off (280 Mpc farther), and where a neutrino of the chosen mass with the mean momentum set off: χ = ∫ v(a) da / (a2H), with v = pc/√(p2 + m2) and p = 5.28 × 10−4 eV / a, in flat ΛCDM (Planck 2018). "Play" moves a CMB photon and the neutrino along their paths on a logarithmic clock from 1 second to today. Slower neutrinos in the distribution come from closer still; deflection by structure is ignored. This page's calculation, following Dodelson & Vesterinen (2009).The big sphere is where the oldest light we can see set off. The green sphere is where a Big Bang neutrino reaching you today started from. Press play: the light races in from the edge, while the heavier neutrino covers most of its trip early on and then crawls for billions of years. It comes from much closer than you'd think.

Chapter 8Weighing the ghost

Three very different kinds of measurement are closing in on the neutrino mass from opposite sides.

From below: oscillations. The mass differences force Σmν ≥ 0.059 eV in the normal ordering and ≥ 0.099 eV in the inverted one.35 Which ordering nature chose is not yet known. In September 2026 the JUNO reactor experiment in China reported a first indication of normal ordering at about 2σ when combined with accelerator data, in a preprint not yet refereed.40

From above, in the laboratory: KATRIN. The Karlsruhe Tritium Neutrino experiment measures the shape of tritium's beta spectrum in the last few tens of electronvolts below its endpoint, where a neutrino mass would shave the spectrum off. Its 2025 result, from 259 days of data, bounds the effective electron-neutrino mass to mβ < 0.45 eV (90% confidence).41 KATRIN finished taking data on 26 October 2025 after a thousand measurement days; its final result, with an expected sensitivity near 0.3 eV, has not yet been published; the collaboration aims to release it in 2027.42 A different technique is already working on a small scale: Project 8 measures each electron's energy from the microwave radiation it gives off while circling in a magnetic field. Its first tritium measurement, published in 2023, set mβ < 155 eV, and its long-term goal is about 40 meV, using atomic rather than molecular tritium.43

From above, in the sky: cosmology. The expansion history, CMB lensing and the suppression of structure in Chapter 6 together give the sharpest limits. Planck 2018, combined with baryon acoustic oscillations, gave Σmν < 0.12 eV.3 Combining the DESI survey's 2025 baryon acoustic oscillation measurements with the CMB tightens this to Σmν < 0.064 eV at 95% confidence, assuming dark energy is a cosmological constant.44,33 A July 2026 DESI analysis, which adds the shape of the Lyman-alpha forest correlations and a CMB combination that includes the ACT and South Pole telescopes, gives 0.059 eV, the normal-ordering floor itself; it is still a preprint.45

These upper limits sit at or just above the normal-ordering floor and below the inverted one. With a different statistical treatment the 2025 DESI analysis gives an upper limit of 0.053 eV, below the floor.33 Several groups noticed that if you let the data choose a formally "negative" neutrino mass, they prefer one.46 That does not mean neutrinos have negative mass. It means the data show less of the neutrinos' expected effect than even the lightest allowed neutrinos should cause, if the rest of the cosmological model is right: the expansion history measured by DESI points to slightly less matter than the CMB predicts, and the CMB is lensed slightly more than expected. Both play a part; how much each matters is still debated. One leading suspect is the CMB's optical depth: if gas ionised by the first stars scattered slightly more of the CMB's light than Planck's large-angle polarization measurements suggest, the preference for "negative" masses largely goes away.46,47

The tension is about 2–3σ and it depends on the model. DESI's data hint, at about 3σ, that dark energy evolves (short of the 5σ discovery standard; see Nº 1); if it does, the limit relaxes to about 0.16 eV and the tension disappears.44,45 Assuming a cosmological constant, adding the South Pole Telescope's data to Planck, ACT and DESI gave 0.055 eV (0.048 eV in the first version of that analysis, posted in 2025); a new lensing analysis from the same telescope, posted as a preprint in August 2026, relaxes it to 0.072 eV.25,48 One of three things is true. The neutrino masses sit right at the edge of what oscillations allow, the cosmological model needs fixing, or there is a systematic error somewhere. KATRIN's final result, with a sensitivity near 0.3 eV, can weigh in only if the masses are large; JUNO's verdict on the ordering and the next generation of CMB and galaxy surveys should tell which within a few years.

Figure 7⚖️ Try it

Weighing the ghost: the squeeze on the neutrino masses

Drag the line
Who objects?
The three masses, normal ordering
The three masses, inverted ordering
All relic neutrinos vs all stars

The sum of the three masses, Σmν, on a log scale. Oscillations set the floors (normal ordering ≥ 0.059 eV, inverted ≥ 0.099 eV). KATRIN bounds the effective electron-neutrino mass, mβ < 0.45 eV (90% CL), shown here as Σmν ≲ 3 × 0.45 eV for nearly equal masses. Cosmological upper limits are 95%: Planck 2018 (TT,TE,EE+lowE+lensing+BAO); DESI DR2 with CMB, for a cosmological constant or for evolving (w0wa) dark energy; and Planck + ACT + SPT-3G with DESI DR2 (Camphuis et al. 2026), for a cosmological constant. Dotted rows ("Show 2026 preprints"): a July 2026 DESI analysis that adds the shape of the Lyman-alpha forest correlations (0.059 eV, or 0.17 eV with evolving dark energy) and an SPT-3G lensing analysis (0.072 eV, or 0.21 eV), both preprints; the shaded range uses only published limits. The individual masses follow from the sum and the NuFit-6.0 splittings; the comparison with stars uses Ωνh2 = Σmν/93.12 eV, h = 0.674 and Ωstars ≈ 0.0027 (this page's arithmetic).Drag the line to pick a total weight for the three kinds of ghost, and see which experiments object. Shape-shifting experiments (the "Oscillations" rows) set the floors on the left: the total can't be smaller. The KATRIN lab sets a ceiling far to the right. Maps of the universe say the total can't be much bigger than the lower floor, and adding the South Pole Telescope pushed the limit lower still, though its newest analysis loosens it a little. Either the masses sit right at the edge, something in cosmology needs fixing, or a measurement is off. The button adds two 2026 results that other scientists have not yet reviewed.

Part IIICatching one

Chapter 9The capture trick

Detecting a neutrino normally means giving it something to hit. Relic neutrinos carry so little momentum, about 5 × 10−4 eV/c, that scattering off anything would leave no measurable trace. Weinberg's 1962 idea avoids the problem: use a nucleus that is already unstable.12 Tritium decays by emitting an electron and an antineutrino, with a total kinetic energy of Q ≈ 18.6 keV. A relic neutrino can instead be absorbed:

νe + 3H → 3He + e− No energy threshold: the reaction is allowed even for a neutrino at rest. The electron comes out with kinetic energy Q + mν.49

Ordinary beta decay can give the electron at most Q − mν, because the emitted antineutrino must carry at least its rest mass. If the three masses are nearly equal, captured relic neutrinos make a line of electrons a gap of 2mν above the end of the ordinary spectrum: 0.1 eV for 50 meV, out of 18,600 eV. In general each mass state gives its own line at Q + mi, weighted by its electron-flavour content; at the lightest masses allowed, 98% of captures land within about 10 meV of the endpoint (Figure 8). The challenge is the numbers. For 100 grams of tritium, the expected capture rate is about 4 per year for Dirac neutrinos, or 8 per year if neutrinos are their own antiparticles (Majorana).50 These figures assume the neutrinos are non-relativistic; a nearly massless lightest state narrows the difference. Meanwhile the same 100 grams undergoes 3.6 × 1016 ordinary decays every second.

fraction of decays within the last δ of the spectrum ≈ 2.9 × 10−13 × (δ / 1 eV)3 For a massless neutrino, from the allowed beta spectrum of tritium. This page's calculation. In the last 0.1 eV that is about 3 × 108 decays per year from 100 g, against 4 captures.

The ordinary electrons never reach the capture line, but a detector with imperfect energy resolution smears them upward. Separating four events from the tail of 3 × 108 requires an energy resolution better than the neutrino mass itself: tens of millielectronvolts.

Figure 8🎣 Try it

Catching a ghost: the tritium trick

Your detector

Nature's unknowns

Inverted: two heavy mass states and one light.Majorana: the neutrino is its own antiparticle; slow ones are caught twice as often.

Ghosts caught
Ordinary decays in the same window
Verdict

Electrons from tritium near the endpoint Q (the endpoint for a massless neutrino), per year, on a log scale. Each mass state i contributes a beta spectrum ending at Q − mi and a capture line at Q + mi, both weighted by its electron-flavour content |Uei|2 ≈ 0.68, 0.30, 0.022 (NuFit-6.0); the masses follow the oscillation splittings for the chosen lightest mass and ordering. Capture rates for 100 g: about 4 per year if all states are slow Dirac neutrinos, 8 if Majorana (Long, Lunardini & Sabancilar 2014); a fast (nearly massless) Dirac state is captured at the Majorana rate. The endpoint fraction is from the allowed beta spectrum. A Gaussian whose standard deviation is the chosen resolution smears everything (the full width at half maximum is 2.35 times larger). The verdict estimates the years of data needed for a 5σ signal in a ±1σ window around the clearest line: 25B/S2 for S captures and B ordinary decays per year, but at least the time to collect about five captures. "Run" draws the year's captures at random (Poisson). This page's estimate; real proposals face further smearing (e.g. from tritium bound to graphene, 0.3–0.7 eV by Cheipesh et al.).Tritium decays all the time. Very rarely, a tritium atom absorbs a Big Bang neutrino and kicks out an electron with a tiny bit too much energy. Run the detector for a year: make it sharp enough and those few electrons stand out from the billions of ordinary ones. Make it blurry and they vanish. With the lightest masses allowed, the ghosts' electrons sit so close to the end of the ordinary ones that even a razor-sharp detector struggles.

The PTOLEMY collaboration proposes doing it with tritium bound to graphene, using electromagnetic filtering and microcalorimeters.51 The scale is daunting. Fully tritiated single-layer graphene holds about 0.19 mg of tritium per square metre, so 100 grams needs about half a square kilometre of it (this page's arithmetic).

In 2021 Yevheniia Cheipesh, Vadim Cheianov and Alexey Boyarsky raised a deeper problem. Tritium bound to a surface is localised, so by the uncertainty principle its momentum is uncertain. That spreads the electron energies by about 0.3–0.7 eV, an order of magnitude more than the resolution needed.52 PTOLEMY's response models different bonding geometries and proposes mitigations. Other authors find that particular effect smaller than first claimed, but point to further smearing from the host material.53 As of 2026 a PTOLEMY demonstrator is under construction at Italy's Gran Sasso laboratory, aimed first at measuring the neutrino mass; no relic-neutrino data exist.54

Tritium experiments have already set limits. Using its first runs, KATRIN constrained any local overdensity of relic neutrinos to less than about 1011 times the standard prediction (twice that if neutrinos are Dirac particles), improving on earlier experiments at Los Alamos and Troitsk.55 Cosmological arguments favour a local density within a few times the average, and the Pauli exclusion principle allows at most about a hundred times even for masses near 1 eV,56 so this ceiling sits ten orders of magnitude above where the answer must be. It is the best laboratory limit so far.

Chapter 10Whispers, winds and resonances

Capture is the most promising idea, but not the only one. The others show how far below every instrument the relic neutrinos lie.

  • A torque on a magnet. In 1975 Leo Stodolsky pointed out that an electron's spin energy shifts slightly in a sea of neutrinos, provided neutrinos and antineutrinos are not exactly balanced.57 If neutrinos outnumber antineutrinos only as slightly as matter outnumbers antimatter, the shift is about 10−47 eV per electron. A 2023 analysis argues that neutrinos reflecting off the Earth create a local imbalance that boosts such effects by roughly 105 (for torques) to 108 (for forces), still orders of magnitude beyond current instruments.58
  • A wind on a mirror. We move through the unclustered relic neutrinos at roughly 370 km/s, our speed relative to the CMB. That creates a "neutrino wind" whose tiny push on a test mass lies many orders of magnitude below what even gravitational-wave interferometers can sense.59
  • A dip in the highest-energy neutrinos. A neutrino with energy MZ2/2mν would annihilate on a relic neutrino through the Z boson, carving an absorption dip into the cosmic neutrino spectrum.60 For a 50 meV relic that resonance sits at about 8 × 1022 eV (this page's arithmetic). The most energetic neutrino ever detected, KM3NeT's 2023 event, had about 2 × 1017 eV,61 and the most energetic cosmic rays about 2–3 × 1020 eV.62 A related route, cosmic rays kicking relic neutrinos up to energies neutrino telescopes can see, is being refined; a 2026 preprint argues that a network of future telescopes could reach the standard density, if the lightest neutrino weighs around 0.1 eV or more. That would make the three masses add up to at least 0.3 eV: allowed by KATRIN, but well above today's cosmological limits (Chapter 8), so it would pay off only if those limits are wrong.63

Even the calendar doesn't help. For dark-matter searches, Earth's orbit makes the signal rise and fall over the year. For neutrino capture, the rate doesn't depend on the neutrinos' speed. The only annual change comes from the Sun's gravity focusing the slow ones, a small effect.64

Chapter 11Ceilings

Gathering the limits in one place shows how strange this background is. All figures are this page's arithmetic unless a source is given, and use the minimum masses (normal ordering).

QuantityValue
Age of the relic neutrinos when released≈1 second
Age of the CMB when released≈380,000 years (1013× later)
Relic neutrinos per baryon (cosmic average)≈1.3 billion
Relic neutrinos inside you≈24 million
Their combined mass≈0.9 electron masses
Relic neutrinos crossing your body each second≈1016dominated by the lightest state, if it is nearly massless; ≈5 × 1014 if all three weigh about 0.05 eV
Their mass inside the whole Earth≈13 micrograms
Their mass in a cubic light-year≈1019 kg, a quarter of the moon Mimas
Wavelength of each one≈2.3 mm
Captures per year, 100 g of tritium≈7 (Dirac) or 8 (Majorana) at these masses; 4 or 8 if all three are non-relativistic50
Best laboratory limit on their local density< 1011 × the prediction55

One of these deserves a moment. The 24 million relic neutrinos inside you weigh, together, less than one electron. Your body holds about 2 × 1028 electrons; the oldest particles in it add up to less than one more. And the familiar line that "a neutrino could pass through a light-year of lead" turns out to be roughly right for a solar neutrino: at 1 MeV, scattering coherently off whole lead nuclei gives a mean free path of about half a light-year (scattering off electrons alone would allow about 40). A relic neutrino carries about a billion times less momentum than that, and no detector built so far has registered a single one.

The open questions are now sharp ones.

  • What are the absolute masses, and in which order? JUNO and the next CMB and galaxy surveys will narrow it down; KATRIN and its successors test the larger masses directly.
  • Is the tension between cosmology and oscillations real?
  • Where do their masses come from? The Higgs mechanism, which gives the electron and the quarks their masses (Nº 5), cannot give neutrinos theirs without some new ingredient; some of the leading ideas would also make neutrinos their own antiparticles.
  • Are neutrinos their own antiparticles? Neutrinoless double-beta decay has not been seen; the strongest search bounds the relevant mass below 28–122 meV.65 For the non-relativistic states, the answer doubles or halves the capture rate.
  • Is the background exactly as predicted, with Neff = 3.044 and the full phase shift? So far the CMB says it is, within about 5–10 per cent; the galaxy-survey measurement of the phase shift is still rough and comes out somewhat high.

And can anyone ever catch one? Perhaps not with tritium on graphene, perhaps with something nobody has thought of yet. The precedent is encouraging. In 1934 there was "no practically possible way" of observing the neutrino itself, and it took twenty-two years and a nuclear reactor. The relic background was predicted in 1953. Its free-streaming fingerprint, the phase shift, was found in 2015 and measured at more than ten standard deviations in 2025. Its first direct detection would be one of the lowest-energy measurements ever attempted in physics, and the oldest untouched travellers in the universe are passing through the experiment the whole time.

Chapter 12Glossary and sources

Relic neutrinos (cosmic neutrino background, CνB)
Neutrinos and antineutrinos that decoupled from the hot early universe about a second after the Big Bang and have travelled freely since.
Decoupling
The moment a particle's collisions become too rare to keep up with the expansion, so it stops sharing the plasma's temperature.
Mass states vs flavours
Neutrinos are made and detected as flavours (electron, muon, tau) but travel as three mass states, each a mixture of flavours. Relic neutrinos long ago separated into mass states, each with 112 per cm3.
Neff
The effective number of neutrino species: the radiation energy density beyond photons, in units of one abruptly decoupled neutrino species. Standard Model: 3.044.
Normal and inverted ordering
Whether the lone mass state set apart by the larger splitting is the heaviest (normal) or the lightest (inverted).
Dirac and Majorana
Whether the neutrino is distinct from its antiparticle (Dirac) or the same particle (Majorana).
σ
Standard deviations: a measure of how rarely chance alone would produce a result this strong if there were no real effect. Physicists conventionally call 5σ a discovery.

Sources

  1. D. J. Fixsen, "The temperature of the cosmic microwave background," ApJ 707, 916 (2009), arXiv:0911.1955.
  2. J. Lesgourgues and L. Verde, "Neutrinos in cosmology," in F. Takahashi et al. (Particle Data Group), Int. J. Mod. Phys. A 41, 2630011 (2026).
  3. Planck Collaboration, "Planck 2018 results. VI. Cosmological parameters," A&A 641, A6 (2020), arXiv:1807.06209.
  4. N. Vinyoles et al., "A new generation of standard solar models," ApJ 835, 202 (2017), arXiv:1611.09867; Borexino Collaboration, "Comprehensive measurement of pp-chain solar neutrinos," Nature 562, 505 (2018).
  5. W. Pauli, letter of 4 December 1930 ("Liebe Radioaktive Damen und Herren"), Pauli Archive, CERN; English translation in L. M. Brown, "The idea of the neutrino," Physics Today 31(9), 23 (1978).
  6. H. Pietschmann, "Neutrino: past, present and future" (George Marx Memorial Lecture, 2005; arXiv 2006), physics/0603106.
  7. E. Fermi, "Versuch einer Theorie der β-Strahlen. I," Z. Phys. 88, 161 (1934).
  8. H. Bethe and R. Peierls, "The 'neutrino'," Nature 133, 532 (1934).
  9. C. L. Cowan Jr., F. Reines, F. B. Harrison, H. W. Kruse and A. D. McGuire, "Detection of the free neutrino: a confirmation," Science 124, 103 (1956).
  10. Pauli Archive, CERN, letters 2296 and 2297 (14 and 15 June 1956).
  11. R. A. Alpher, J. W. Follin Jr. and R. C. Herman, "Physical conditions in the initial stages of the expanding universe," Phys. Rev. 92, 1347 (1953).
  12. S. Weinberg, "Universal neutrino degeneracy," Phys. Rev. 128, 1457 (1962).
  13. S. S. Gershtein and Ya. B. Zeldovich, "Rest mass of muonic neutrino and cosmology," JETP Lett. 4, 120 (1966).
  14. Super-Kamiokande Collaboration, "Evidence for oscillation of atmospheric neutrinos," Phys. Rev. Lett. 81, 1562 (1998), hep-ex/9807003.
  15. SNO Collaboration, "Direct evidence for neutrino flavor transformation from neutral-current interactions in the Sudbury Neutrino Observatory," Phys. Rev. Lett. 89, 011301 (2002), nucl-ex/0204008.
  16. A. D. Dolgov, "Neutrinos in cosmology," Phys. Rept. 370, 333 (2002), hep-ph/0202122.
  17. S. Weinberg, "Damping of tensor modes in cosmology," Phys. Rev. D 69, 023503 (2004), astro-ph/0306304.
  18. J. J. Bennett et al., "Towards a precision calculation of Neff in the Standard Model II," JCAP 04 (2021) 073, arXiv:2012.02726; J. Froustey, C. Pitrou and M. C. Volpe, JCAP 12 (2020) 015, arXiv:2008.01074; K. Akita and M. Yamaguchi, JCAP 08 (2020) 012, arXiv:2005.07047; M. Cielo, M. Escudero, G. Mangano and O. Pisanti, Phys. Rev. D 108, L121301 (2023), arXiv:2306.05460; M. Drewes et al., JCAP 06 (2024) 032, arXiv:2402.18481.
  19. M. Fukugita and P. J. E. Peebles, "The cosmic energy inventory," ApJ 616, 643 (2004), astro-ph/0406095.
  20. J. Bland-Hawthorn and O. Gerhard, "The Galaxy in context," ARA&A 54, 529 (2016), arXiv:1602.07702.
  21. V. A. Lyubimov, E. G. Novikov, V. Z. Nozik, E. F. Tretyakov and V. S. Kosik, "An estimate of the electron-neutrino mass from the beta spectrum of tritium in the valine molecule," Phys. Lett. B 94, 266 (1980).
  22. S. D. M. White, C. S. Frenk and M. Davis, "Clustering in a neutrino-dominated universe," ApJ 274, L1 (1983).
  23. B. D. Fields, P. Molaro and S. Sarkar, "Big-bang nucleosynthesis," in F. Takahashi et al. (Particle Data Group), Int. J. Mod. Phys. A 41, 2630011 (2026); T.-H. Yeh, J. Shelton, K. A. Olive and B. D. Fields, JCAP 10 (2022) 046, arXiv:2207.13133.
  24. E. Calabrese et al. (ACT), "The Atacama Cosmology Telescope: DR6 constraints on extended cosmological models," JCAP 11 (2025) 063, arXiv:2503.14454.
  25. E. Camphuis et al. (SPT-3G), "SPT-3G D1: CMB temperature and polarization power spectra and cosmology from 2019 and 2020 observations of the SPT-3G Main field," Phys. Rev. D 113, 083504 (2026), arXiv:2506.20707.
  26. P. Janot and S. Jadach, "Improved Bhabha cross section at LEP and the number of light neutrino species," Phys. Lett. B 803, 135319 (2020), arXiv:1912.02067.
  27. S. Bashinsky and U. Seljak, "Signatures of relativistic neutrinos in CMB anisotropy and matter clustering," Phys. Rev. D 69, 083002 (2004), astro-ph/0310198.
  28. D. Baumann, D. Green, J. Meyers and B. Wallisch, "Phases of new physics in the CMB," JCAP 01 (2016) 007, arXiv:1508.06342.
  29. B. Follin, L. Knox, M. Millea and Z. Pan, "A first detection of the acoustic oscillation phase shift expected from the cosmic neutrino background," Phys. Rev. Lett. 115, 091301 (2015), arXiv:1503.07863.
  30. G. Montefalcone, B. Wallisch and K. Freese, "Free-streaming neutrinos and their phase shift in current and future CMB power spectra," JCAP 08 (2025) 051, arXiv:2501.13788.
  31. D. Baumann et al., "First constraint on the neutrino-induced phase shift in the spectrum of baryon acoustic oscillations," Nature Phys. 15, 465 (2019), arXiv:1803.10741.
  32. A. M. Whitford et al. (DESI), "Constraining the phase shift of relativistic species in DESI BAOs," MNRAS 538, 1980 (2025), doi:10.1093/mnras/staf394, arXiv:2412.05990.
  33. W. Elbers et al. (DESI), "Constraints on neutrino physics from DESI DR2 BAO and DR1 full shape," Phys. Rev. D 112, 083513 (2025), arXiv:2503.14744.
  34. W. Hu, D. J. Eisenstein and M. Tegmark, "Weighing neutrinos with galaxy surveys," Phys. Rev. Lett. 80, 5255 (1998), astro-ph/9712057; J. Lesgourgues and S. Pastor, "Massive neutrinos and cosmology," Phys. Rept. 429, 307 (2006), astro-ph/0603494.
  35. I. Esteban et al., "NuFit-6.0: updated global analysis of three-flavor neutrino oscillations," JHEP 12 (2024) 216, arXiv:2410.05380.
  36. A. J. Deason et al., "The local high-velocity tail and the Galactic escape speed," MNRAS 485, 3514 (2019), arXiv:1901.02016; H. H. Koppelman and A. Helmi, A&A 649, A136 (2021), arXiv:2006.16283; L. Necib and T. Lin, ApJ 926, 189 (2022), arXiv:2102.02211.
  37. P. Mertsch et al., "Neutrino clustering in the Milky Way and beyond," JCAP 01 (2020) 015, arXiv:1910.13388.
  38. W. Elbers et al., "Where shadows lie: reconstruction of anisotropies in the neutrino sky," JCAP 10 (2023) 010, arXiv:2307.03191.
  39. S. Dodelson and M. Vesterinen, "Cosmic neutrino last scattering surface," Phys. Rev. Lett. 103, 171301 (2009), arXiv:0907.2887.
  40. JUNO Collaboration, "Measurement of neutrino oscillation parameters at JUNO and indication of the neutrino mass ordering," arXiv:2609.37895 (2026, preprint); first results: "Measurement of reactor neutrino oscillation with the first JUNO data," Nature 654, 343 (2026), arXiv:2511.14593.
  41. KATRIN Collaboration, "Direct neutrino-mass measurement based on 259 days of KATRIN data," Science 388, 180 (2025), arXiv:2406.13516.
  42. Max Planck Institute for Nuclear Physics, "1000 days of neutrino mass measurements" (27 October 2025); A. Schwemmer for KATRIN, Rencontres de Noirmoutier (4 June 2026), indico.ijclab.in2p3.fr; C. Wiesinger for KATRIN, Neutrino 2026, Irvine (23 June 2026), indico.global.
  43. Project 8 Collaboration, "Tritium beta spectrum measurement and neutrino mass limit from cyclotron radiation emission spectroscopy," Phys. Rev. Lett. 131, 102502 (2023), arXiv:2212.05048; "The Project 8 neutrino mass experiment," Snowmass 2021 white paper, arXiv:2203.07349 (2022).
  44. DESI Collaboration, "DESI DR2 Results II: measurements of baryon acoustic oscillations and cosmological constraints," Phys. Rev. D 112, 083515 (2025), arXiv:2503.14738.
  45. DESI Collaboration, "DESI DR2 Results IV: Alcock–Paczyński measurements from the Lyman alpha forest and cosmological constraints," arXiv:2607.27410 (2026, preprint).
  46. N. Craig, D. Green, J. Meyers and S. Rajendran, "No νs is good news," JHEP 09 (2024) 097, arXiv:2405.00836; D. Green and J. Meyers, Phys. Rev. D 111, 083507 (2025), arXiv:2407.07878; W. Elbers et al., "Negative neutrino masses as a mirage of dark energy," Phys. Rev. D 111, 063534 (2025), arXiv:2407.10965.
  47. G. P. Lynch and L. Knox, "What's the matter with Σmν?," Phys. Rev. D 112, 083543 (2025), arXiv:2503.14470; T. Jhaveri, T. Karwal and W. Hu, "Turning a negative neutrino mass into a positive optical depth," Phys. Rev. D 112, 043541 (2025), arXiv:2504.21813.
  48. Y. Omori et al. (SPT-3G), "SPT-3G D1: quadratic-estimator CMB lensing reconstruction and cosmology," arXiv:2608.31136 (2026, preprint).
  49. A. G. Cocco, G. Mangano and M. Messina, "Probing low energy neutrino backgrounds with neutrino capture on beta decaying nuclei," JCAP 06 (2007) 015, hep-ph/0703075.
  50. A. J. Long, C. Lunardini and E. Sabancilar, "Detecting non-relativistic cosmic neutrinos by capture on tritium: phenomenology and physics potential," JCAP 08 (2014) 038, arXiv:1405.7654.
  51. S. Betts et al., "Development of a relic neutrino detection experiment at PTOLEMY," arXiv:1307.4738 (2013); PTOLEMY Collaboration, "Neutrino physics with the PTOLEMY project," JCAP 07 (2019) 047, arXiv:1902.05508.
  52. Y. Cheipesh, V. Cheianov and A. Boyarsky, "Navigating the pitfalls of relic neutrino detection," Phys. Rev. D 104, 116004 (2021), arXiv:2101.10069.
  53. PTOLEMY Collaboration (A. Apponi et al.), "Heisenberg's uncertainty principle in the PTOLEMY project: a theory update," Phys. Rev. D 106, 053002 (2022), arXiv:2203.11228; S. Nussinov and Z. Nussinov, Phys. Rev. D 105, 043502 (2022), arXiv:2108.03695.
  54. PTOLEMY demonstrator status: TAUP 2025 conference talk, and GSSI Science Fair talk (February 2026), indico.gssi.it; R. Ammendola et al. (PTOLEMY), JINST 21 (2026) P04009, arXiv:2512.19437.
  55. KATRIN Collaboration, "New constraint on the local relic neutrino background overdensity with the first KATRIN data runs," Phys. Rev. Lett. 129, 011806 (2022), arXiv:2202.04587.
  56. M. Bauer and J. D. Shergold, "Limits on the cosmic neutrino background," JCAP 01 (2023) 003, arXiv:2207.12413.
  57. L. Stodolsky, "Speculations on detection of the 'neutrino sea'," Phys. Rev. Lett. 34, 110 (1975).
  58. A. Arvanitaki and S. Dimopoulos, "Cosmic neutrino background on the surface of the Earth," Phys. Rev. D 108, 043517 (2023), arXiv:2212.00036.
  59. V. Domcke and M. Spinrath, "Detection prospects for the cosmic neutrino background using laser interferometers," JCAP 06 (2017) 055, arXiv:1703.08629.
  60. T. J. Weiler, "Resonant absorption of cosmic-ray neutrinos by the relic-neutrino background," Phys. Rev. Lett. 49, 234 (1982); B. Eberle, A. Ringwald, L. Song and T. J. Weiler, "Relic neutrino absorption spectroscopy," Phys. Rev. D 70, 023007 (2004), hep-ph/0401203.
  61. KM3NeT Collaboration, "Observation of an ultra-high-energy cosmic neutrino with KM3NeT," Nature 638, 376 (2025).
  62. Telescope Array Collaboration, "An extremely energetic cosmic ray observed by a surface detector array," Science 382, 903 (2023), arXiv:2311.14231; D. J. Bird et al. (Fly's Eye), "Detection of a cosmic ray with measured energy well beyond the expected spectral cutoff due to cosmic microwave radiation," ApJ 441, 144 (1995).
  63. G. Herrera, S. Horiuchi, X. Qi and I. M. Shoemaker, "The cosmic neutrino background is within reach of future neutrino telescopes," arXiv:2601.09790 (2026, preprint).
  64. B. R. Safdi, M. Lisanti, J. Spitz and J. A. Formaggio, "Annual modulation of cosmic relic neutrinos," Phys. Rev. D 90, 043001 (2014), arXiv:1404.0680.
  65. KamLAND-Zen Collaboration, "Search for Majorana neutrinos with the complete KamLAND-Zen dataset," Phys. Rev. Lett. 135, 262501 (2025), arXiv:2406.11438.