Primordial Deuterium Abundance D/H

τ-Formula

D/H = τ-native from η_B ≈ 2.52 × 10⁻⁵

Derivation

Using $η_B = (121/270)\,ι_τ^19 ≈ 6.041 × 10^-10$ as the sole input to the standard BBN nuclear network:

in comparison with the observed value $D/H_obs = (2.527 ± 0.030) × 10^-5$ (Cooke et al.\ 2018). The deviation is $+2.7%$ ($+2.3σ$). (Registry: V.T241, $τ$-effective, Wave 25.)

The slight D/H overshoot is physically expected: the $τ$-native $η_B$ is $1.03%$ below the Planck value, meaning fewer baryons per photon, hence less efficient deuterium destruction ($D + D$ and $D + p$ reactions), yielding a slightly higher residual D/H. The BBN sensitivity $d((D/H))/d(η_B) ≈ -1.6$ quantifies this anti-correlation.

Source

This prediction is derived in the Numerical Physics Ledger (Chapter 62 — inflation-cmb-bbn), Books IV–V of Panta Rhei.