Cosmology
Cosmic Neutrino Background
Relic neutrinos from one second after the Big Bang
The cosmic neutrino background (CNB or CνB) is a faint sea of relic neutrinos that decoupled from the hot early universe roughly one second after the Big Bang — long before the photons of the cosmic microwave background broke free at 380,000 years. Ever since, these neutrinos have free-streamed across the cosmos, redshifting and cooling with the expansion of space to a present-day temperature near 1.95 K. They fill every cubic centimetre with about 336 particles and stand as the oldest accessible fossil of the universe's first second.
- Decoupling time~1 second after the Big Bang
- Decoupling temperature~10¹⁰ K (≈ 1 MeV)
- Present temperature1.95 K (vs 2.725 K CMB)
- Temperature ratioT_ν / T_γ = (4/11)¹ᐟ³ ≈ 0.714
- Number density~336 cm⁻³ (≈112 per flavour)
- Effective speciesN_eff ≈ 3.04
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Older than the oldest light
Look up at the cosmic microwave background (CMB) and you are seeing the universe as it was 380,000 years after the Big Bang — the moment electrons and protons combined into neutral hydrogen and photons could finally fly free. It is rightly called the oldest light we can see. But there is something older: a background of relic neutrinos that stopped talking to the rest of matter when the cosmos was just one second old. This is the cosmic neutrino background, and it is a snapshot of an era that arrived more than 10 trillion times sooner in cosmic time — a universe that was a million times hotter than the one the CMB shows us.
Neutrinos are the universe's most aloof particles. They carry no electric charge, are nearly massless, and feel only the weak nuclear force and gravity. In today's universe a neutrino can pass through a light-year of solid lead with only even odds of being absorbed. That same aloofness is precisely why the CNB exists: once the early universe cooled and thinned enough that weak interactions could no longer keep up, the neutrinos simply stopped colliding and have been coasting in straight lines ever since — free-streaming across more than 13.8 billion years.
Decoupling at one second
In the first fraction of a second, the universe was a seething plasma in thermal equilibrium: photons, electrons, positrons, neutrinos, and a trace of protons and neutrons, all colliding furiously. Neutrinos were held in this bath by weak reactions such as νₑ + e⁺ ⇌ ν̄ₑ + e⁻ and neutrino–nucleon scattering.
Whether a species stays coupled is a race between two rates. The interaction rate Γ falls steeply as the universe cools (roughly as T⁵ for weak processes), while the expansion rate — the Hubble parameter H — falls more gently (as T²). When Γ drops below H, particles can no longer find each other before space stretches them apart, and they decouple. For neutrinos this crossover happens at a temperature of about 1 MeV (≈10¹⁰ K), which the universe reached at an age of roughly one second. From that instant the neutrinos were on their own.
Why 1.95 K and not 2.725 K
The CNB is colder than the CMB today, and the reason is a beautiful piece of bookkeeping. Just after neutrinos decoupled, the universe cooled past the electron rest-mass energy (0.511 MeV). Electrons and positrons could no longer be produced from photon collisions, so they annihilated, e⁺ + e⁻ → 2γ. All of that energy and entropy was poured into the photon gas — but the neutrinos had already frozen out and received none of this reheating.
Conserving entropy through the annihilation gives a clean ratio between the two temperatures:
| Quantity | Photons (CMB) | Neutrinos (CNB) |
|---|---|---|
| Decoupling epoch | ~380,000 yr (recombination) | ~1 s (neutrino decoupling) |
| Decoupling temperature | ~3,000 K (≈0.26 eV) | ~10¹⁰ K (≈1 MeV) |
| Present temperature | 2.725 K | 1.95 K |
| Temperature relation | T_γ | T_ν = (4/11)¹ᐟ³ · T_γ |
| Number density (today) | ~411 cm⁻³ | ~336 cm⁻³ (all flavours) |
| Typical energy today | ~6 × 10⁻⁴ eV | ~5 × 10⁻⁴ eV (kinetic) |
The factor (4/11)¹ᐟ³ ≈ 0.714 multiplied by the measured CMB temperature of 2.725 K gives the famous CNB temperature of about 1.945 K. The ⁴⁄₁₁ comes from counting the relativistic degrees of freedom before and after e⁺e⁻ annihilation: photons (2 spin states) plus electrons and positrons (with a 7/8 fermion factor) heat up relative to the untouched neutrinos.
We can't see it — but we know it's there
No one has ever directly captured a relic neutrino. Their energies sit in the milli-electron-volt range, a million times feebler than the solar neutrinos that detectors like Super-Kamiokande and IceCube already struggle to catch. Yet the CNB leaves two unmistakable fingerprints on the universe.
- Big Bang nucleosynthesis (BBN). The neutrino sea sets the expansion rate during the first few minutes, which fixes the proton-to-neutron ratio frozen in at deuterium formation. The observed primordial abundances of helium-4, deuterium and lithium only fit if the early universe contained the energy density of three light neutrino species.
- The CMB power spectrum. A free-streaming relativistic background shifts the acoustic peaks and damps the tails of the CMB anisotropy. Planck measurements pin the effective number of neutrino species at N_eff ≈ 3.04 — beautifully consistent with the three known flavours plus a tiny correction for incomplete decoupling. The data even prefer a free-streaming (not tightly-coupled) component, exactly as relic neutrinos should be.
The hardest, most heroic idea for a direct detection is the PTOLEMY concept: capture relic electron-neutrinos on tritium nuclei via νₑ + ³H → ³He + e⁻, a neutrino-capture reaction that has no energy threshold. A captured relic neutrino would produce an electron just above the ordinary tritium beta-decay endpoint. The required energy resolution and the enormous tritium target make it one of the most demanding experiments ever proposed.
Relic neutrinos as hot dark matter
Neutrino oscillation experiments proved that at least two of the three neutrino mass states are nonzero, with the summed mass Σmν of at least about 0.06 eV. Because relic neutrinos are so numerous — outnumbering ordinary atoms by roughly a billion to one — even these whisper-light masses add up. Today most relic neutrinos have cooled below their rest-mass energy and move non-relativistically, drifting at a few hundred to a few thousand km/s.
That makes them a genuine, if minor, component of the cosmic matter budget — a form of hot dark matter. Their lingering speed lets them stream out of small gravitational wells, smoothing away structure on small scales. By measuring exactly how much small-scale clustering is suppressed, galaxy surveys and the CMB together place an upper bound on the summed neutrino mass of roughly Σmν < 0.1 eV — a particle-physics measurement extracted from maps of the largest structures in the universe.
Why the CNB matters
- Earliest fossil within reach. It records the universe at one second — a temperature regime no telescope of light can ever show us.
- Validates the hot Big Bang. The (4/11)¹ᐟ³ prediction and N_eff ≈ 3 are precision tests that the standard cosmology passes.
- A bridge to particle physics. The CNB ties neutrino mass, the number of light species, and the matter power spectrum into one story.
- An unsolved detection challenge. A direct measurement would open a brand-new observational window onto the first second of time.
Frequently asked questions
What is the cosmic neutrino background?
The cosmic neutrino background (CNB or CνB) is a relic sea of neutrinos left over from about one second after the Big Bang. At that moment the universe cooled enough that neutrinos stopped interacting with the hot plasma and began free-streaming. They have been redshifting and cooling ever since, now sitting at roughly 1.95 K and filling space at a density of about 336 neutrinos per cubic centimetre.
How is the cosmic neutrino background different from the CMB?
Both are relic backgrounds, but they decoupled at very different epochs. Neutrinos decoupled at about 1 second when the universe was ~10 billion K; photons decoupled at recombination ~380,000 years later at ~3000 K. So the CNB is a snapshot of an earlier, hotter universe than the cosmic microwave background. The CNB is also colder today — 1.95 K versus 2.725 K — because electron-positron annihilation reheated the photons after the neutrinos had already frozen out.
Why is the CNB temperature 1.95 K instead of 2.725 K?
Shortly after neutrino decoupling, the temperature dropped below the electron mass and electrons and positrons annihilated. That annihilation dumped entropy into the photon gas but not into the already-decoupled neutrinos. The result is that the neutrino temperature is lower by a factor of (4/11)¹ᐟ³ ≈ 0.714. Multiplying 2.725 K by that factor gives the CNB temperature of about 1.95 K.
Has the cosmic neutrino background been detected?
Not directly — relic neutrinos are far too low in energy to register in conventional detectors. But its existence is strongly confirmed indirectly. Big Bang nucleosynthesis and the detailed shape of the CMB power spectrum both require an extra relativistic component consistent with three neutrino species (the effective number N_eff ≈ 3.04). The PTOLEMY experiment proposes a direct capture using neutrino absorption on tritium, but it remains extraordinarily difficult.
Do relic neutrinos have mass, and does it matter?
Yes. Oscillation experiments prove neutrinos have nonzero mass (the sum of the three masses is at least ~0.06 eV). Because relic neutrinos are so numerous, even tiny masses make them a small but measurable component of the matter budget today — most are now non-relativistic and behave as a form of hot dark matter that suppresses small-scale cosmic structure. Cosmological surveys currently cap the summed neutrino mass at roughly 0.1 eV.
How many relic neutrinos are passing through me right now?
About 336 relic neutrinos and antineutrinos occupy every cubic centimetre of space, summed over all three flavours — roughly 112 per cm³ per flavour. Their typical speeds are a few hundred to a few thousand kilometres per second, so an enormous flux streams through your body every second. They almost never interact, which is exactly why they have survived untouched since the universe was one second old.