Big Bang Nucleosynthesis Simulator: Primordial Element Abundances

simulator advanced ~12 min
Loading simulation...
Yp ≈ 0.247 — 24.7% helium by mass

With standard parameters (η = 6.1×10⁻¹⁰, τn = 879s, Nν = 3), BBN predicts Yp ≈ 0.247, D/H ≈ 2.5×10⁻⁵, and ⁷Li/H ≈ 5×10⁻¹⁰ — matching observations for H, He, and D but overpredicting lithium by a factor of ~3.

Formula

Yp ≈ 2(n/p)_f / (1 + (n/p)_f) with (n/p)_f ≈ exp(−Δm/T_f)
D/H ∝ η^(−1.6) (approximate scaling)
T(t) ≈ 10¹⁰ K × (t/1s)^(−1/2)

The First Three Minutes

Within minutes of the Big Bang, the universe was a hot, dense plasma of protons, neutrons, electrons, and photons. As temperature dropped below ~10⁹ K, nuclear reactions began fusing these particles into the lightest elements. This epoch of Big Bang nucleosynthesis (BBN) lasted roughly 20 minutes and determined the primordial chemical composition of the cosmos — about 75% hydrogen, 25% helium-4, with trace amounts of deuterium, helium-3, and lithium-7.

The Deuterium Bottleneck

Nucleosynthesis cannot proceed until deuterium (the first stepping stone to heavier nuclei) survives photodisintegration. Despite deuterium's low binding energy (2.22 MeV), the enormous photon-to-baryon ratio (~10¹⁰) means that even at temperatures well below this threshold, the high-energy tail of the photon distribution destroys deuterium efficiently. Only when T drops to ~0.8×10⁹ K does deuterium accumulate — this 'bottleneck' delays nucleosynthesis and allows more neutrons to decay, reducing the final helium yield.

Abundance Predictions

BBN predictions depend on a single free parameter: the baryon-to-photon ratio η, now precisely measured from the CMB. With η = 6.1×10⁻¹⁰, the theory predicts Yp ≈ 0.247, D/H ≈ 2.5×10⁻⁵, and ³He/H ≈ 10⁻⁵. These predictions match observations beautifully for hydrogen, helium, and deuterium — but lithium-7 is overpredicted by a persistent factor of ~3, a discrepancy known as the cosmological lithium problem.

A Window into Particle Physics

BBN's sensitivity to the expansion rate makes it a powerful particle-physics probe. Extra light species (like a fourth neutrino) would speed expansion, increasing the freeze-out neutron fraction and overproducing helium. The agreement between predicted and observed abundances constrains the effective number of neutrino species to Neff = 2.99 ± 0.17, confirming three light neutrino flavors and placing stringent limits on exotic particles and forces in the early universe.

FAQ

What is Big Bang nucleosynthesis?

Big Bang nucleosynthesis (BBN) is the process by which light elements — hydrogen, deuterium, helium-3, helium-4, and lithium-7 — were formed in the first 1–20 minutes after the Big Bang. The abundances depend sensitively on the baryon-to-photon ratio, the neutron lifetime, and the number of light neutrino species, making BBN a powerful probe of both particle physics and cosmology.

Why is helium-4 abundance ~25%?

Neutrons freeze out of weak equilibrium with protons at T ≈ 10¹⁰ K with a ratio n/p ≈ 1/6. After accounting for neutron decay before nucleosynthesis begins, n/p ≈ 1/7. Nearly all neutrons end up in He-4 (the most tightly bound light nucleus), giving Yp ≈ 2×(1/7)/(1+1/7) ≈ 0.25.

What is the cosmological lithium problem?

BBN with Planck-measured baryon density predicts ⁷Li/H ≈ 5×10⁻¹⁰, but observations of metal-poor halo stars consistently find ~1.6×10⁻¹⁰ — a factor of ~3 discrepancy. Despite decades of effort, no stellar, nuclear, or cosmological solution has been universally accepted.

How does BBN constrain new physics?

The remarkable agreement between predicted and observed D/H and He-4 abundances constrains the number of light particle species (Neff ≈ 3), limits variations in fundamental constants, and rules out many beyond-Standard-Model scenarios that would alter the expansion rate or weak reaction rates during the first minutes.

Sources

Embed

<iframe src="https://homo-deus.com/lab/cosmology/big-bang-nucleosynthesis/embed" width="100%" height="400" frameborder="0"></iframe>
View source on GitHub