CTD Self-Consistent Cosmology: Physicalization of C and Parameter Validation under Cross-Probe Constraints

中文摘要 第一篇论文[1]建立了CTD框架,在七个分支中验证了其有效性。但宇宙学分支仍依赖于ΛCDM的H(z),未实现自治。本文将C物理化为暗能量驱动的宇宙膨胀路径,从公理出发自洽生成H(z)=ηH₀exp(βz/(1+z)),不再借用任何外部宇宙学参数。 使用Pantheon+数据和完整协方差矩阵进行MCMC采样(16链5000步),得到CTD模型参数H₀=71.50⁺⁴·⁸⁶₋₆.₁₅ km/s/Mpc,β=1.3283±0.0074,η=0.1124⁺⁰·⁰¹²⁵₋₀.₀₀₃₉。对应的局部哈勃常数(即z=0处的哈勃参数值)为H(0)=ηH₀≈8 km/s/Mpc。 ΔT(z)在z≈1.07处呈现清晰的谷状结构(谷值-37.31 Gyr),这是ΛCDM无法产生的非线性偏差。宇宙计时器数据独立验证了H(z)随红移递增的方向。本文证明:CTD框架在宇宙学分支上可完全自治,不依赖任何外部模型,且提供可检验预言。联合BAO+CMB拟合修正版(含路径曲率因子κ₀)将在后续补充。 English Abstract The first paper[1] established the CTD framework and verified its validity in seven branches. However, the cosmological branch still relied on the H(z) of ΛCDM and was not self-consistent. In this paper, we physicalize C as the dark-energy-driven cosmic expansion path and self-consistently derive H(z)=ηH₀exp(βz/(1+z)) from the axioms, without borrowing any external cosmological parameters. Using the Pantheon+ dataset with the full covariance matrix and MCMC sampling (16 chains, 5000 steps), we obtain the CTD model parameter H₀=71.50⁺⁴·⁸⁶₋₆.₁₅ km/s/Mpc, β=1.3283±0.0074, and η=0.1124⁺⁰·⁰¹²⁵₋₀.₀₀₃₉. The corresponding local Hubble constant (i.e., the Hubble parameter at z=0) is H(0)=ηH₀≈8 km/s/Mpc. ΔT(z) exhibits a clear valley structure at z≈1.07 (depth −37.31 Gyr), a nonlinear deviation that ΛCDM cannot produce. Cosmic chronometer data independently confirm the increasing trend of H(z) with redshift. We demonstrate that the CTD framework is fully self-consistent in the cosmological branch, independent of any external model, and provides testable predictions. The joint BAO+CMB fit with the path-curvature correction factor κ₀ will be presented in a future update. 中文免责声明 本文为初步预印本版本(v1.0-preliminary),提交至Zenodo以锁定优先权。作者已发现参数η(见第2.3节)属于不必要的冗余参数(过度参数化)。简化参数化模型H(z)=H₀exp(βz/(1+z))(取消η)的MCMC验证正在进行中。本文中的所有数值结果(包括H₀、β、ΔT(z)等)在验证完成后可能发生变化。建议读者以最新的修正版为准。 English Disclaimer This is a preliminary preprint version (v1.0-preliminary) submitted to Zenodo for priority registration. The author has identified that Parameter η (see Section 2.3) is an unnecessary redundant parameter (over-parameterization). A revised version with the simplified parameterization H(z)=H₀exp(βz/(1+z)) (with η removed) is currently undergoing MCMC verification. All numerical results (including H₀, β, and ΔT(z)) in this document are subject to change upon completion of the verification process. Readers are advised to refer to the latest revised version for final conclusions.