A Geometric Origin of the Cosmic Baryon-to-Matter Ratio: 0.15634133

Abstract

Abstract :In the standard ΛCDM model, the baryon density Ω_b and the total matter density Ω_m are treated as independent free parameters, fitted directly to Cosmic Microwave Background (CMB) and large-scale structure observations. In this brief report, we propose a geometric derivation for their exact ratio. Based on the premise that the minimal stable redundancy for a closed measurement network is three nodes, the geometry of an equilateral triangle and its inscribed circle yields a fundamental area ratio a = π/(3√3). From this, the unmeasured fraction u_0 = 1-a gives the predicted ratio Ω_b/Ω_m = u_0^2 = 0.15634133. We compare this zero-parameter geometric prediction with the latest Planck 2018, BBN+Planck, and BOSS EFT data. The prediction lies well within 1σ of all observational datasets. This geometric structure not only eliminates the fine-tuning problem of density parameters but also provides a purely mathematical constraint for early-universe cosmology. 摘要 :在标准 ΛCDM 模型中,重子密度 Ω_b 和总物质密度 Ω_m 被视为独立的自由参数,直接拟合于宇宙微波背景(CMB)和大尺度结构观测。在这份简报中,我们提出了一种关于它们精确比值的几何推导。基于“闭合测量网络的最小稳定冗余为三节点”这一前提,等边三角形及其内切圆的几何结构给出了一个基本面积比 a = π/(3√3)。由此,未被测量的份额 u_0 = 1-a 给出了预测比值 Ω_b/Ω_m = u_0^2 = 0.15634133。我们将这一零参数几何预言与最新的 Planck 2018、BBN+Planck 以及 BOSS EFT 数据进行了比较。该预言完美落在所有观测数据集的 1σ 置信区间内。这种几何结构不仅消除了密度参数的微调问题,也为早期宇宙学提供了一个纯数学的约束。