The Cosmic Neutrino Background: The Oldest Relic

The Oldest Thing in the Room

Hold out your hand. The cubic centimetre of air just above your palm contains roughly 336 neutrinos that have been travelling, untouched, since the universe was one second old. They are not passing through from some distant source. They are simply there, everywhere, a cold fossil gas filling every volume of space in the cosmos.

This is the cosmic neutrino background — the CνB, or relic neutrino background. It decoupled from the primordial plasma about one second after the Big Bang, at a temperature near 10¹⁰ K, and the expansion of space has since cooled it to roughly 1.95 K. That makes it 380,000 years older than the cosmic microwave background, which was not released until atoms formed and the universe turned transparent to light. The CνB is the oldest relic in existence.

And nobody has ever detected it. We are certain it exists, we can quote its temperature to three significant figures, and it remains entirely unseen. That tension is the story.

What Happened at One Second

In the first fraction of a second, neutrinos were ordinary participants in a dense plasma, created and destroyed through weak reactions like e⁺ + e⁻ ⇄ ν + ν̄ fast enough to stay in thermal equilibrium with everything else.

Equilibrium is a race between two rates. The weak interaction rate falls steeply as the universe cools, roughly as T⁵, while the expansion rate falls more slowly. There comes a moment when a neutrino can no longer find a partner before the universe has doubled in size. For neutrinos that moment arrives near 1 MeV, about 10¹⁰ K, when the universe is approximately one second old.

After that, nothing. Because the weak force is so feeble, the neutrinos have essentially not interacted since; their momenta have simply been stretched by the expansion of space. The photons, meanwhile, stayed trapped, scattering off free electrons for another 380,000 years.

Why the Neutrinos Ended Up Colder Than the Light

Here is the elegant part. If both backgrounds had cooled identically from the same bath, both would sit at 2.725 K today. They do not, because of one short episode just after neutrino decoupling.

Once the temperature fell below the electron rest-mass energy of 0.511 MeV, electrons and positrons could no longer be replenished and annihilated into photons. All of that energy went into the light. The neutrinos, already decoupled, got none of it, and the gap has been frozen in ever since.

Entropy conservation fixes its size exactly. Count the effective degrees of freedom in the coupled bath before annihilation: 2 for the photon plus 7/4 each for the electron and positron, giving 11/2. Afterwards only the photons remain, with 2. The comoving entropy is unchanged, so the neutrinos end up colder by

T_ν / T_γ = (4/11)^(1/3) ≈ 0.7138

Put the measured 2.725 K into that and you get T_ν ≈ 1.95 K. The number is not fitted to anything. It falls out of entropy bookkeeping and the mass of the electron.

1 · Decoupling timeline 2 · Relic mass and PTOLEMY

Cosmic time 1 s

Cosmic Neutrino Background vs Cosmic Microwave Background

The two backgrounds are siblings born 380,000 years apart, and setting them side by side is the quickest way to see what each is good for.

	Cosmic microwave background	Cosmic neutrino background
Released at	380,000 years	about 1 second
Temperature then	about 3,000 K	about 10¹⁰ K
Temperature now	2.725 K	about 1.95 K
Density now	about 411 photons/cm³	about 336 neutrinos/cm³
Detected	1965, by accident	never, directly

The CMB is a photograph of the universe at 380,000 years, the surface where the plasma turned transparent. Everything earlier hides behind it. The CνB, if we could read it, would be a photograph taken at one second, from deep inside that opaque region — the only relic field that could in principle be read from before the Big Bang’s first minute. The trade is brutal: the earlier the relic, the feebler it is when it arrives.

How We Know It Is There Without Seeing It

Undetected is not unevidenced. Free-streaming neutrinos contribute to the radiation density of the early universe, which sets the expansion rate, which controls both the primordial element abundances and the shape of the CMB anisotropies. That contribution is parameterised by N_eff, the effective number of neutrino species. The Standard Model predicts 3.044 — slightly above three because decoupling was not instantaneous. Planck 2018 combined with baryon acoustic oscillation data measures N_eff = 2.99 ± 0.17, and Big Bang nucleosynthesis agrees independently. Remove the neutrino background from the model and the fit fails badly.

A sharper fingerprint followed. Because neutrinos stream freely while the photon–baryon fluid oscillates, they drag the CMB acoustic peaks very slightly out of position. In 2015 that phase shift was measured for the first time, and the neutrino temperature it implied was 1.96 ± 0.02 K against a prediction of 1.95 K.

Massive neutrinos leave a third mark. Moving fast and refusing to clump, they smooth the growth of small-scale structure in a way dark matter does not, by an amount that scales with the summed mass. DESI DR2 baryon acoustic oscillations combined with CMB data give Σm_ν < 0.064 eV at 95 per cent confidence — tight enough to sit in mild tension with the roughly 0.059 eV floor that neutrino oscillation experiments require for the normal mass ordering. That tension is model-dependent and unresolved.

Why Direct Detection Is Brutally Hard

Neutrinos are hard to catch at the best of times, and cross-sections grow with energy, which is why detectors chase the energetic ones. Relic neutrinos go the wrong way. Their mean momentum today is about 3.15 k T_ν, or roughly 0.53 meV — a fraction of a millielectronvolt, some ten orders of magnitude below the solar neutrinos that existing detectors see. Scattering fails twice over: the interaction probability is vanishingly small, and any recoil would be far too tiny to register.

So the trick is not to scatter them but to absorb them. Neutrino capture on a beta-unstable nucleus, ν_e + ³H → ³He⁺ + e⁻, has no energy threshold at all. It is energetically downhill however slow the neutrino is, because the tritium is already unstable. Every other method needs the neutrino to bring energy. Capture needs only that it arrive.

PTOLEMY: A Hundred Grams of Tritium

The threshold-free idea goes back to Weinberg in 1962 and was developed into a concrete proposal by Cocco, Mangano and Messina in 2007. PTOLEMY — the Princeton Tritium Observatory for Light, Early-Universe, Massive-Neutrino Yield — is the experiment built around it.

The signature is beautiful. Ordinary tritium beta decay produces electrons up to an endpoint of 18.57 keV. A captured relic neutrino produces an electron about 2m_ν above that endpoint, because the neutrino’s rest mass is delivered rather than carried away. The signal is an isolated peak in a region where ordinary decay can put nothing.

The catch is that word “nothing”. Finite resolution smears the beta spectrum across the endpoint, and 100 g of tritium yields around 10²⁴ beta decays per year against a handful of captures. The requirement is that the full-width-half-maximum resolution Δ satisfy Δ < 0.7 m_ν. PTOLEMY targets Δ ≈ 50 meV, so it is sensitive only to neutrinos heavier than about 70 meV. If the lightest neutrino is lighter — and the cosmological bound hints it may be — the peak stays buried.

Hence the design: atomic tritium implanted on graphene to suppress molecular broadening, a transverse-drift electromagnetic filter, and cryogenic microcalorimeters. A demonstrator with roughly a gram of tritium has been under construction and test at Gran Sasso, aimed first at direct mass sensitivity in the manner of KATRIN, whose current limit is 0.45 eV. Relic physics is envisaged for the 2030s. That is a plan, not a schedule.

What Reading It Would Actually Tell Us

A capture peak would do more than confirm a prediction. Its position would give the absolute neutrino mass directly, assuming nothing about whether the neutrino is its own antiparticle. Its height would measure the local relic density, which gravitational clustering should have concentrated around the Milky Way by a factor nobody has measured. The rate itself differs by a factor of two between Dirac and Majorana neutrinos. And any anomaly — an unexpected temperature, an asymmetry between neutrinos and antineutrinos — would be direct evidence about one second after the Big Bang, an epoch no other observation can touch.

One Second, Still Streaming

The figure of 336 per cubic centimetre is not an estimate of something far away. It is the density of ancient particles inside your lungs right now, each carrying an unaltered memory of a moment when the universe was hot enough that atomic nuclei could not survive.

We have calculated their temperature to three figures from the mass of the electron and a ratio of degrees of freedom. We have seen their shadow in the spacing of the microwave background’s peaks. We have used their reluctance to clump to put a ceiling on their own mass. What we have never done is touch one. The oldest thing in the universe is also the one thing we are sure of and have never met — and whether that changes in the 2030s depends on a number the universe has so far declined to tell us.