The Decoupling Mechanism as a Boundary Condition: A Geometric Resolution to the Cosmological Constant and Hubble Tensions

Are the “Crisis in Cosmology” and the “Vacuum Catastrophe” simply geometric artifacts of how we parametrize Λ and H₀? This data note and accompanying Python script demonstrate that two of the largest anomalies in physics—the Hubble tension and the cosmological constant problem—can be numerically reproduced as simple geometric boundary conditions, without introducing new dynamical physics or free parameters. Key findings Hubble tension via sphere packing We show that the discrepancy between global (CMB) and local (SH0ES) measurements of H₀ corresponds to the geometric difference between a continuous fluid and a discrete packed structure. Applying the 3D kissing‑number packing factor (1 + 1/12) to the Planck 2018 value H₀ᴄᴍʙ = 67.4 km/s/Mpc predicts a local value of 73.02 km/s/Mpc, matching the SH0ES measurement (73.04 ± 1.04) at the level of about 0.02 standard deviations. Cosmological constant as a horizon invariant We show that the apparent 10¹²² “fine‑tuning” of Λ disappears when Λ is treated as a boundary curvature term. The dimensionless product of Λ and the Hubble‑horizon area A_H reduces to an algebraic identity of order unity (~25.8), consistent with the geometric phase‑space factor 4π(π³/15) ≈ 25.98 to within about 0.7%. Content PDF note: concise derivation and statement of the geometric constraints on Λ and H₀. Python script (`cosmic_geometry_test_suite.py`): a reproducible, zero‑parameter test suite that evaluates these geometric identities against Planck 2018 and SH0ES inputs and reports explicit PASS/FAIL criteria.“宇宙学危机”与“真空灾变”是否仅是我们对Λ（宇宙学常数）与H₀（哈勃常数）进行参数化时所产生的几何伪影？ 本数据说明文档与配套Python脚本证明，物理学中两大最突出的反常现象——哈勃张力（Hubble tension）与宇宙学常数问题（cosmological constant problem），可借助简单几何边界条件实现数值复现，无需引入新的动力学物理机制或自由参数。 ### 核心发现 #### 基于球堆积（sphere packing）的哈勃张力解释 我们证明，H₀的全局（宇宙微波背景（Cosmic Microwave Background，CMB））与局域（SH0ES）测量结果之间的偏差，对应于连续流体与离散堆积结构之间的几何差异。将三维接吻数堆积因子（kissing-number packing factor）(1 + 1/12)应用于普朗克2018（Planck 2018）给出的H₀^CMB=67.4 km/s/Mpc值，可以预测局域H₀值为73.02 km/s/Mpc，与SH0ES测量结果(73.04 ± 1.04)的吻合度约为0.02个标准差。 #### 作为视界不变量的宇宙学常数 我们证明，当将Λ视为边界曲率项时，Λ看似10¹²²量级的“精细调谐”问题将不复存在。Λ与哈勃视界面积A_H的无量纲乘积可简化为一个量级约为1的代数恒等式（~25.8），与几何相空间因子4π(π³/15)≈25.98的偏差仅约0.7%。 ### 内容说明 1. PDF说明文档：对Λ与H₀的几何约束条件的简洁推导与阐述。 2. Python脚本（`cosmic_geometry_test_suite.py`）：一个可复现的无参数测试套件，可基于普朗克2018与SH0ES的输入数据对上述几何恒等式进行验证，并输出明确的通过/不通过判定标准。