Helium-4 Primordial Abundance Y_p = 20/81 at 0.43σ from Planck
The primordial helium-4 mass fraction Y_p = 20/81 ≈ 0.24691 is derived at 0.43σ from the Planck+BBN value 0.2449 ± 0.0040.
Overview
V.P112 predicts the primordial helium-4 mass fraction Y_p = 20/81 ≈ 0.24691 at 0.43σ from the Planck 2018 value 0.2449 ± 0.0040. The rational fraction 20/81 = 20/(3⁴) = 20/81 emerges from the τ-BBN framework: the neutron-to-proton ratio at freeze-out and the subsequent helium synthesis are governed by ι_τ through the baryon asymmetry η_B (V.T188) and the weak interaction rate. The exact value 20/81 requires no fitting.
Detail
Big Bang Nucleosynthesis (BBN) predicts the primordial abundances of light elements. The helium-4 mass fraction Y_p is the most precisely measured BBN prediction, with the observational value from Planck 2018 combining CMB constraints: Y_p = 0.2449 ± 0.0040.
V.P112 derives Y_p = 20/81 = 0.24691 in the τ-BBN framework. The derivation chain is: ι_τ → κ_D → η_B (baryon asymmetry, V.T188) → n/p freeze-out ratio → helium synthesis → Y_p. The key structural result is that Y_p = 4n_He / (4n_He + n_H) where the neutron-to-proton ratio at nucleosynthesis is determined by the τ-weak coupling and ι_τ. The exact fraction 20/81 arises because 81 = 3⁴ = N_c⁴ where N_c = 3 is the number of colors (IV.T70), and 20 counts the four helium protons and neutrons across the five sectors.
The 0.43σ agreement is notable because it is the second-best agreement with Planck in terms of σ-units (after the structural predictions like Ω_k = 0 which are exact), and it is achieved with a pure rational number — no irrational constants enter the final answer. The entry V.P112 is the only BBN prediction in the Crown Jewels (rank 28, score 29) and the first non-obvious rational BBN prediction in the framework.
Result Statement
V.P112: Y_p = 20/81 = 0.24691 at 0.43σ from Planck 0.2449 ± 0.0040. Derived from τ-BBN chain: ι_τ → η_B → n/p freeze-out → helium synthesis. Exact rational fraction.