Big Bang Nucleosynthesis (BBN) describes the formation of the lightest atomic nuclei in the first few minutes after the Big Bang, when the universe was a hot, dense plasma of protons, neutrons, electrons, and photons. During this epoch — between roughly 10 seconds and 20 minutes after t = 0 — the temperature dropped from about 10 MeV to below 0.1 MeV, allowing protons and neutrons to fuse into deuterium, helium-3, helium-4, and trace amounts of lithium-7. The predicted primordial He-4 mass fraction of ~25% and the tiny D/H ratio of ~2.5 × 10−5 are among the most precise tests of the Hot Big Bang model.
This simulator traces the key phases: the n/p ratio freezes out at T ≈ 0.8 MeV when weak interactions can no longer maintain equilibrium; deuterium forms but is instantly photodissociated until T ≈ 0.07 MeV (the deuterium bottleneck); then rapid fusion locks nearly all neutrons into He-4 within minutes. You can adjust the baryon density parameter Ωbh² to see how it shifts the predicted hydrogen, deuterium, helium, and lithium abundances on the live log-scale abundance plot.
Why does helium-4 make up about 25% of all ordinary matter?
When the n/p ratio froze out at about 1/7, one neutron was available for every seven protons. He-4 has two neutrons and two protons, so virtually all available neutrons were incorporated into He-4 nuclei. The He-4 mass fraction Yp ≈ 2×(n/p)/(1 + n/p) ≈ 2×(1/7)/(1 + 1/7) ≈ 0.25. This 25% fraction has been confirmed by spectroscopic observations of old, metal-poor stars and HII regions, matching BBN predictions to within 1%.
What is the deuterium bottleneck?
Deuterium (D = p + n) can only survive once the universe cools below about 0.07 MeV (roughly 80,000 MK), when the photon bath is no longer energetic enough to photodissociate it. Before this moment, any deuterium formed is immediately destroyed, delaying He-4 synthesis despite the temperature being low enough in principle. This bottleneck lasts until t ≈ 200–400 seconds and is sensitive to baryon density: higher density pushes synthesis to earlier times and lower D/H abundances.
How does baryon density affect primordial abundances?
Higher baryon density Ωbh² means more protons and neutrons per photon, so fusion reactions proceed faster. This lowers the final D/H and He-3/H abundances (more of these intermediates burn into He-4) while slightly increasing Yp and raising Li-7/H. The observed D/H ≈ 2.5 × 10−5 in quasar absorption spectra pins Ωbh² = 0.0224 ± 0.0001, in excellent agreement with the CMB value from Planck satellite data.
Standard BBN predicts Li-7/H ≈ 5 × 10−10 for the observed baryon density, but spectroscopic measurements of old halo stars (Spite plateau) find Li-7/H ≈ 1.6 × 10−10 — about three times lower. This discrepancy, known as the "cosmological lithium problem", persists after accounting for known stellar depletion mechanisms. Proposed explanations include lithium diffusion into stellar cores, new physics beyond the Standard Model, or as-yet unidentified nuclear reaction rates.
The active nucleosynthesis window lasted approximately from t ≈ 10 seconds (when T ≈ 3 MeV and n/p began freezing) to t ≈ 20 minutes (T ≈ 0.03 MeV) when the universe had cooled too much for nuclear reactions to proceed. By this point the universe's nuclear composition was essentially fixed: ~75% hydrogen (by mass), ~25% helium-4, ~0.003% deuterium, trace helium-3 and lithium-7. All heavier elements were made later in stars.
There are no stable nuclei with mass numbers 5 or 8, creating a gap that prevents the chain reactions needed to build carbon (mass 12) and heavier nuclei. The triple-alpha process that bridges this gap in stars requires helium densities and temperatures achievable only in stellar cores, not in the rapidly cooling and dilute Big Bang plasma. Carbon, oxygen, and all elements beyond lithium are products of stellar nucleosynthesis and supernova explosions.
Three main observational pillars support BBN: (1) the He-4 mass fraction Yp ≈ 0.245 measured in metal-poor extragalactic HII regions; (2) D/H ≈ 2.5 × 10−5 observed in quasar absorption-line systems at high redshift, where deuterium has not been destroyed by stellar processing; and (3) the baryon density from CMB anisotropies (Planck 2018: Ωbh² = 0.02237) agrees to within 0.2% with the value inferred from deuterium observations.
George Gamow proposed in 1946 that element synthesis occurred in the hot early universe ("Alpher-Bethe-Gamow" paper, 1948 — Bethe was added for alphabetical fun). Ralph Alpher and Robert Herman made quantitative predictions and in 1948 predicted the existence of a relic thermal radiation field at a temperature of ~5 K — a prediction vindicated by Arno Penzias and Robert Wilson's discovery of the CMB in 1965. Fred Hoyle, who coined the term "Big Bang" mockingly, nevertheless made crucial contributions to understanding He-4 synthesis.
Below T ≈ 0.8 MeV (about 9 billion kelvin, t ≈ 2.6 seconds), the weak-interaction rates maintaining equilibrium between protons and neutrons (p + e− ↔ n + νe) fall below the Hubble expansion rate. After freeze-out, the n/p ratio is set by the Boltzmann factor exp(−Δm/Tfreeze) where Δm = 1.293 MeV is the neutron-proton mass difference. The ratio at freeze-out is ~1/6, declining slightly to ~1/7 by the onset of synthesis due to neutron decay (τn = 880 s).
The n/p freeze-out temperature depends on the Hubble expansion rate at that epoch, which in turn depends on the total radiation energy density — including all relativistic species. Extra neutrino flavours (or any other light, weakly interacting particles) would speed up expansion, leading to an earlier and higher freeze-out n/p ratio and thus more He-4. BBN constrains the effective number of neutrino species to Neff = 2.99 ± 0.17, consistent with exactly three families (electron, muon, tau) as established by LEP experiments at CERN.
The very slight matter-antimatter asymmetry — roughly one extra baryon per billion photons (the baryon-to-photon ratio η ≈ 6 × 10−10) — meant that virtually all antimatter annihilated with matter before BBN began at t ≈ 10 s. BBN therefore produced only ordinary (matter) nuclei. The origin of this asymmetry (baryogenesis) is one of the outstanding unsolved problems in cosmology, requiring CP violation beyond what is observed in the Standard Model.
This model recreates the physics of Big Bang Nucleosynthesis (BBN), the process by which protons and neutrons fused into the first atomic nuclei during the first twenty minutes of the universe. It traces the neutron-to-proton freeze-out, the deuterium bottleneck, and the resulting primordial abundances of hydrogen, deuterium, helium-3, helium-4 and lithium-7, derived from a simplified analytic treatment of the radiation-era temperature-time relation and equilibrium-style reaction equations. Everything updates live as you change the baryon-to-photon ratio, expressed here through the baryon density parameter Ωbh².
A particle field visualises protons, neutrons and light nuclei forming as the plasma cools, alongside a log-scale abundance chart plotting H, He-4, D/H, He-3/H, Li-7/H and the n/p ratio against time, plus a phase timeline marking freeze-out, the deuterium bottleneck and helium-4 synthesis.
Drag the Baryon density Ωbh² slider to see how it shifts the final abundances, use the Time slider to jump to any moment between roughly 0.01 s and 17 minutes, adjust Speed to slow or accelerate the animation, and use Play/Pause or Reset to control playback.
In 1948 Ralph Alpher and Robert Herman used BBN calculations to predict a relic radiation temperature of around 5 K — seventeen years before that cosmic microwave background radiation was actually detected.
Ωbh² sets the density of ordinary matter relative to radiation. Raising it speeds up fusion, lowering the final deuterium and helium-3 abundances whilst slightly raising the helium-4 and lithium-7 fractions, matching the trends predicted by standard BBN theory.
Once the temperature drops below about 0.8 MeV, weak interactions become too slow to keep protons and neutrons in equilibrium, so the ratio freezes out near 1/6 and thereafter falls only slowly as free neutrons decay, exactly as the timeline panel labels.
Deuterium nuclei form continuously but are destroyed by energetic photons until the universe cools past roughly 0.07 MeV. This delay, shown as its own phase band, holds up helium-4 synthesis even though the temperature would otherwise allow it sooner.
Almost every free neutron ends up bound inside a helium-4 nucleus once synthesis proceeds, so the final mass fraction depends almost entirely on the frozen-out n/p ratio, which the "He-4 Yp" readout tracks live as you move the Time slider.
It reproduces the standard predicted Li-7/H abundance, but does not include the observational discrepancy seen in old halo stars, which remains a separate, unresolved puzzle in real BBN research rather than part of this simplified model.