This simulation recreates Big Bang nucleosynthesis (BBN), the synthesis of the lightest nuclei during the first three minutes of the universe. Using a semi-analytic model, it plots how hydrogen, helium-4, deuterium, helium-3 and lithium-7 emerge as the cosmos cools through the MeV temperature range. The physics rests on neutron-proton freeze-out, the Saha-like deuterium bottleneck, and the relation Y_p ≈ 2(n/p)/(1+n/p) for the helium-4 mass fraction.
You control the baryon density Ω_b h² (0.005–0.040), which fixes the baryon-to-photon ratio η and the final abundances, and the neutron lifetime τ_n (820–920 s), which tweaks the surviving neutron fraction. Three views show abundances versus temperature, the temperature-time timeline T(t)≈1.5/√t MeV, and abundances scanned against η. BBN is one of the strongest pillars of the hot Big Bang, letting cosmologists weigh the ordinary matter in the universe.
What is Big Bang nucleosynthesis?
Big Bang nucleosynthesis is the process that forged the universe's lightest nuclei, chiefly hydrogen, helium-4, deuterium, helium-3 and lithium-7, during roughly the first three minutes after the Big Bang. At that time the cosmos was hot and dense enough for nuclear fusion, before expansion cooled it below the threshold for further reactions.
Why is the first three minutes the crucial window?
Fusion needs high temperature and density, both of which fell rapidly as space expanded. Before about one second the universe was too hot for deuterium to survive, and after a few minutes it was too cool and dilute for nuclei to keep reacting. Almost all primordial element production therefore happened in this brief interval.
What does the baryon density control do?
The Ω_b h² slider sets the density of ordinary matter, which the model maps to the baryon-to-photon ratio η via η ≈ 6.1×10⁻¹⁰ × (Ω_b/0.022). A higher baryon density burns deuterium more efficiently into helium, lowering D/H while slightly raising the helium-4 fraction, so the abundances shift across the three views.
The neutron lifetime τ_n (820–920 s) governs how many free neutrons decay before they can be locked into nuclei. A longer lifetime leaves slightly more neutrons available, nudging the helium-4 yield upward. In this model the effect is small, reflecting the modest sensitivity of BBN to the measured neutron lifetime near 880 s.
Around T ≈ 0.8 MeV (about one second), the weak interactions that interconvert neutrons and protons become too slow to keep pace with expansion, so they decouple, or freeze out. This locks the neutron-to-proton ratio near 1/7, which then sets how much helium-4 can ultimately form.
Deuterium is the gateway to building heavier nuclei, but energetic photons photo-dissociate it above about T ≈ 0.07 MeV. Only once the universe cools below this does deuterium accumulate, triggering the chains D+D→³He and ³He+D→⁴He. This delay, the deuterium bottleneck, is why fusion waits until a couple of minutes in.
The model uses Y_p ≈ 2(n/p)/(1+n/p), reflecting that nearly every available neutron pairs with a proton to form ⁴He. With n/p near 1/7 this gives a mass fraction close to 0.25. A small logarithmic correction in baryon density raises Y_p slightly as Ω_b increases.
It is a teaching-grade semi-analytic approximation, not a full reaction-network code. The trends, freeze-out, the deuterium bottleneck, D/H falling with baryon density and Y_p near 0.247, match real BBN, but exact figures from professional codes such as PArthENoPE or AlterBBN will differ in detail. Use it to build intuition rather than for precision research values.
Standard BBN predicts a primordial ⁷Li/H of roughly 5×10⁻¹⁰, yet measurements in old, metal-poor stars sit two to three times lower. This persistent discrepancy, the cosmological lithium problem, is unresolved and may point to stellar depletion, uncertain nuclear rates, or new physics in the early universe.
BBN predicts specific abundances of D, ³He, ⁴He and ⁷Li that all depend on a single parameter, the baryon density. The observed deuterium and helium abundances agree with the same Ω_b h² ≈ 0.022 that the cosmic microwave background independently measures. This concordance is a powerful, quantitative confirmation of hot Big Bang cosmology.