Why is most helium already set by BBN?

Once deuterium forms past the bottleneck, nearly all available neutrons are quickly assembled into ⁴He. That yields Y_p ≈ 0.25 with only weak dependence on later stellar processing for the primordial floor. Stars make more metals and some helium, but the bulk cosmic ⁴He fraction is a Big Bang relic.

What does increasing η₁₀ do to deuterium?

Higher baryon density means more efficient burning of D into heavier nuclei, so residual deuterium falls steeply with η₁₀. Helium Y_p rises only mildly. That is why measured primordial D/H is a sharp baryometer. A misconception is that all light elements scale the same way with η — they do not.

How does N_eff change the curves?

Extra radiation speeds early expansion, freezing a higher n/p ratio and typically raising Y_p while shifting freeze-out timing. The simulator’s N_eff slider shows that expansion-rate lever next to η₁₀. Full neutrino decoupling physics is simplified; treat the curves as standard pedagogical BBN trends with observed values marked for comparison.

Big Bang Nucleosynthesis (BBN)

Light-element abundance curves H, ⁴He, D, ³He, ⁷Li vs cosmic time / temperature. Weak freeze-out, neutron decay gap, deuterium bottleneck → Y_p ≈ 0.245. Slide η₁₀ and N_eff over the classic BBN curves; observed values overlaid.

About this model

Light-element Big Bang nucleosynthesis (BBN) curves track mass fractions of H, ⁴He, D, ³He, and ⁷Li versus cosmic time and temperature. Weak freeze-out sets the n/p ratio; a neutron-decay gap follows; then the deuterium bottleneck delays fusion until T is low enough for D to survive photodissociation, after which ⁴He locks most neutrons into Y_p ≈ 0.245. Sliders η₁₀ (baryon-to-photon ratio ×10¹⁰) and N_eff (effective neutrino species) shift the classic abundance curves, with observed bands overlaid. The network is pedagogical: incomplete reaction rates, no full nuclear Monte Carlo, and no stellar astration modeling. Vary η₁₀ and N_eff to see how helium and deuterium respond — the classic probe of early-universe expansion and baryon density.

Who it's for: Cosmology and nuclear astrophysics courses covering BBN abundances and early-universe parameters.

Key terms

Big Bang nucleosynthesis
helium mass fraction
deuterium bottleneck
baryon-to-photon ratio
N_eff
weak freeze-out

How it works

Big-Bang nucleosynthesis (BBN) — within the first ~3 minutes the universe forged the bulk of its primordial light elements. Watch the n/p ratio drop from equilibrium toward freeze-out at T_F ≈ 0.8 MeV, decay slowly through neutron β-decay, and then suddenly lock into He-4 when the deuterium bottleneck breaks at T ≈ 0.07 MeV. Trace amounts of D, ³He and ⁷Li survive. The asymptotic abundances depend almost only on the baryon-to-photon ratio η₁₀ (and a little on the effective neutrino number N_eff) — moving the slider walks you across the famous BBN curves and explains why measuring just D/H in distant quasars or Y_p in HII regions pins down Ω_b h² independently of the CMB. Right-edge ticks mark the observationally inferred values; note the long-standing ⁷Li discrepancy.

Key equations

T(t) = (1.32 s·MeV²)^{1/2} / √t (radiation era)

(n/p)_eq = exp(−Q/T), Q = m_n − m_p = 1.293 MeV

Y_p ≈ 2(n/p) / (1 + n/p) at BBN onset

D/H ∝ η₁₀^{−1.6}, ³He/H ∝ η₁₀^{−0.6}, ⁷Li/H : U-shape vs η

Frequently asked questions

Why is most helium already set by BBN?: Once deuterium forms past the bottleneck, nearly all available neutrons are quickly assembled into ⁴He. That yields Y_p ≈ 0.25 with only weak dependence on later stellar processing for the primordial floor. Stars make more metals and some helium, but the bulk cosmic ⁴He fraction is a Big Bang relic.
What does increasing η₁₀ do to deuterium?: Higher baryon density means more efficient burning of D into heavier nuclei, so residual deuterium falls steeply with η₁₀. Helium Y_p rises only mildly. That is why measured primordial D/H is a sharp baryometer. A misconception is that all light elements scale the same way with η — they do not.
How does N_eff change the curves?: Extra radiation speeds early expansion, freezing a higher n/p ratio and typically raising Y_p while shifting freeze-out timing. The simulator’s N_eff slider shows that expansion-rate lever next to η₁₀. Full neutrino decoupling physics is simplified; treat the curves as standard pedagogical BBN trends with observed values marked for comparison.

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