Watch the first three minutes of the universe—adjust baryon density to see how light element abundances change
Big Bang Nucleosynthesis (BBN) is one of the three pillars of Big Bang cosmology, along with the cosmic microwave background and the expanding universe. During the first few minutes after the Big Bang, the universe was hot and dense enough for nuclear reactions to synthesize light elements from primordial protons and neutrons. BBN successfully predicts the observed abundances of deuterium (D), helium-3 (³He), helium-4 (⁴He), and lithium-7 (⁷Li) with only one free parameter: the baryon-to-photon ratio η, which is now independently measured from CMB observations.
At temperatures above ~1 MeV (t < 1 second), neutrons and protons are kept in equilibrium via weak interactions: n + νₑ ↔ p + e⁻ and n + e⁺ ↔ p + ν̄ₑ. When the temperature drops below 1 MeV, the weak interaction rate falls below the Hubble expansion rate, and the neutron-to-proton ratio freezes out at n/p ≈ 1/7. Neutrons then decay (half-life ~10 minutes), so by the time BBN starts, n/p ≈ 1/7 to 1/8.
To build heavier nuclei, we must first form deuterium: p + n → D + γ. However, deuterium has a low binding energy (2.2 MeV), and at high temperatures photons constantly photodissociate it: D + γ → p + n. Even though the universe cools below the deuterium binding energy fairly quickly, the enormous photon-to-baryon ratio (η⁻¹ ~ 10⁹) means there are still enough high-energy photons in the tail of the blackbody distribution to destroy deuterium. Only when T drops to ~0.07 MeV (about 1/30 of the binding energy) does the deuterium abundance become substantial. This "deuterium bottleneck" is the key delay in BBN.
Once deuterium survives, the reaction chain proceeds rapidly: D(p,γ)³He, D(d,n)³He, ³He(d,p)⁴He, ³He(α,γ)⁷Be, etc. Almost all remaining neutrons end up in ⁴He because it is the most tightly bound light nucleus (28.3 MeV binding energy). The final ⁴He mass fraction is Yₚ ≈ 2(n/p)/(1 + n/p) ≈ 0.25 (or 25% by mass). This is remarkably insensitive to η: varying η by a factor of 2 changes Yₚ by less than 1%. However, it is sensitive to the expansion rate during BBN, which depends on the number of relativistic species (especially neutrinos).
BBN cannot proceed beyond ⁷Li (with tiny amounts of ⁷Be that later decays to ⁷Li) because there are no stable nuclei with mass 5 or 8. The reaction ⁴He + ⁴He → ⁸Be is blocked because ⁸Be decays in 10⁻¹⁶ seconds. Similarly, ⁴He + p → ⁵Li is blocked. These "mass gaps" prevent further synthesis. The universe must wait billions of years for stars to form and bridge the mass gaps via triple-alpha (⁴He + ⁴He + ⁴He → ¹²C) and other stellar nucleosynthesis processes.
Observations of metal-poor HII regions (dwarf galaxies) give Yₚ = 0.245 ± 0.003 (24.5% by mass). BBN predicts Yₚ ≈ 0.247 for the CMB-measured η = 6.1 × 10⁻¹⁰, in excellent agreement. This was one of the first major successes of Big Bang cosmology. The near-constancy of Yₚ across different galaxies (with different metallicities) confirms a primordial origin. Stars add a little helium, but most helium was made in the first three minutes.
Deuterium is extremely sensitive to η: higher baryon density means more D is burned into ⁴He, so D/H decreases with increasing η. Observations of high-redshift quasar absorption systems (where gas is pristine) give D/H = (2.5 ± 0.1) × 10⁻⁵. This pins down η = (6.1 ± 0.1) × 10⁻¹⁰, in remarkable agreement with the CMB. Deuterium is the "baryometer" of the universe. Unlike helium, deuterium is only destroyed in stars, never created, so the observed value is a lower limit on the primordial abundance.
Helium-3 is produced in BBN with ³He/H ≈ 10⁻⁵, but stellar processing both creates and destroys it, making the observed abundance uncertain. Solar system measurements give ³He/H ≈ 1.4 × 10⁻⁵, consistent with BBN plus some stellar production. ³He is less useful as a cosmological probe than D or ⁴He, but it provides a consistency check.
BBN predicts ⁷Li/H ≈ 5 × 10⁻¹⁰ for η = 6.1 × 10⁻¹⁰, but observations of metal-poor halo stars give ⁷Li/H ≈ 1.6 × 10⁻¹⁰, about 3 times lower. This is the "lithium problem," one of the few unsolved puzzles in BBN. Proposed solutions include: stellar depletion of lithium via mixing into hot layers, systematic errors in stellar temperature measurements, or (more speculatively) new physics such as decaying particles or additional neutrino species. The lithium discrepancy remains an active area of research.
The BBN predictions depend on the expansion rate of the universe during nucleosynthesis, which is set by the Friedmann equation: H² ∝ ρ_total. At T ~ 1 MeV, the energy density is dominated by photons and relativistic species (neutrinos, electrons, positrons). The standard model has three neutrino families (Nν = 3). If there were additional relativistic species (e.g., a fourth neutrino, or light dark matter), the expansion rate would be faster, giving less time for neutrons to decay, and thus more ⁴He. BBN constrains Nν = 2.9 ± 0.3, consistent with the Standard Model. This was the first evidence for three (and only three) neutrino species, before direct measurements at LEP collider. BBN is a precision test of particle physics in the early universe.
Vary η (baryon-to-photon ratio): Increase η and watch deuterium abundance drop while lithium rises. Notice helium-4 barely changes (only ~1% variation). This explains why D/H is the best baryometer: it's maximally sensitive to η. The CMB measurement η ≈ 6 × 10⁻¹⁰ agrees perfectly with deuterium.
Neutrino number Nν: Increase Nν from 3 to 4. The universe expands faster, so there's less time for neutrons to decay before BBN starts. This means more neutrons survive, and thus more ⁴He is produced. BBN constrains Nν = 3.0 ± 0.3, consistent with three neutrino families. This was historically important before LEP directly measured Z boson decays.
The deuterium bottleneck: Watch the abundances plot carefully. Notice how deuterium stays near zero until T ~ 0.07 MeV, then suddenly rises. This delay allows more neutrons to decay, which is why faster expansion (more Nν) leads to more ⁴He. The bottleneck is caused by photodissociation: D + γ → p + n.
Freeze-out of reactions: In the reaction rate plot, watch when different reaction rates drop below the Hubble rate H. When a reaction rate Γ < H, that reaction freezes out and its products lock in. The D(p,γ)³He and D(d,n)³He rates drop at T ~ 0.05 MeV, ending helium synthesis.
Compare with observations: Enable "Show observations" to see measured abundances from quasar absorption (D), HII regions (⁴He), and halo stars (⁷Li). The lithium problem is visible: theory predicts ~3× more ⁷Li than observed. This is the only significant discrepancy in BBN.
BBN was first proposed by George Gamow, Ralph Alpher, and Robert Herman in the 1940s. Alpher and Herman predicted the CMB in 1948 based on BBN calculations. However, their work was largely ignored until the 1960s, when Fred Hoyle, Roger Tayler, and others revived BBN and showed it predicted Yₚ ≈ 0.25. The observational confirmation came in the 1970s with measurements of helium in HII regions and deuterium in interstellar gas. By the 1980s, BBN was firmly established as a pillar of cosmology. Today, precision measurements of D/H from quasar absorption systems provide the tightest constraint on the baryon density, rivaling (and agreeing with) the CMB.
For more, see: Cyburt et al. (2016), "Big Bang Nucleosynthesis: Present status" (Reviews of Modern Physics) for a comprehensive review, or Weinberg, "The First Three Minutes" for an accessible popular account of the early universe and BBN's role in confirming the hot Big Bang.