Papers · William Alexander Aldred

One Density, Two Tables: The Baryon Closure Between Nucleosynthesis and the Microwave Background, Priced on Published Values

by William Alexander Aldred — Independent Researcher

Published October 31, 2026 · Zenodo · 7 pp · DOI: 10.5281/zenodo.23851500

Abstract

One number has to pay two tables. The baryon density ω_b = Ω_b h² sets how much deuterium survives the first minutes (the abundance table), and it sets the sound of the photon-baryon fluid at recombination, about 380,000 years later (the acoustic table). The standard model holds the comoving baryon density fixed between those two epochs, so the model makes a hard prediction: the density read off primordial deuterium and the density read off the microwave background are the same number. This paper writes that prediction as a single closure condition, ω_b(BBN) = ω_b(CMB), and executes it on published values, with the defect printed in two units: the separation in combined sigmas, and the separation in dex. The deuterium input is the corrected figure, (2.527 ± 0.030) × 10⁻⁵ (Cooke, Pettini & Steidel 2018). The primary BBN inference is the deuterium-only, LUNA-era value ω_b = 0.02233 ± 0.00036 (Mossa et al. 2020, PArthENoPE network, LUNA d(p,γ)³He rate; graded fitted/imported, not derived here). The CMB inference is ω_b = 0.02237 ± 0.00015 (Planck Collaboration 2020, CMB alone). The primary defect is +0.10 combined sigmas, +0.0008 dex. One density pays both tables at current precision. The paper then prices the step the verdict rides on. Run through a second network (PRIMAT, same LUNA rate), the BBN inference moves to 0.02195 ± 0.00022 and the defect grows to +1.58 sigmas against the CMB alone. Read in abundance space, with that network's yield spent at the CMB+BAO density, the same pairing stands at +1.85 sigmas. The two networks disagree with each other by 0.90 combined sigmas, a central gap of 0.00038 that is wider than the CMB error bar itself. Every pairing tested still lands inside the registered 2-sigma closure band, so the verdict is closure. But the honest headline is the pair of numbers together: the tables close, and the width of the closure is set by nuclear-rate bookkeeping, not by the sky. The BBN leg carries 85% of the primary test's error variance. Sharper rates, not sharper telescopes, are what would move this number next.

The result, in plain language

One baryon density has to pay for the universe twice: once at minute three, where it sets how much deuterium survives, and once at recombination, where it sets the sound of the microwave background. Stated as one closure condition and run on the published numbers, the defect is +0.10 sigma. The tables close.

Then the paper prices what the closure rides on. Two LUNA-era reaction networks disagree with each other by 0.00038 in the density — wider than Planck’s own error bar, 2.5× over. The sky agrees. The rate book is the width.

Program note

Cube Campaign Batch 1, target C-09 — the Closure Identity’s method carried to a second pair of tables: the baryon density as read by big-bang nucleosynthesis and by the microwave background. Its grades are printed on its face: the closure test is executed on published values, every input verified against its source, the registered exclusion rule fired only on the registered exclusions; the BBN leg is graded fitted/imported throughout. This paper makes no re-grade of the house TOE-TO-TOE board; it prices one closure, at current precision, and prints the width of the price.

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