First-Principles Derivation of Cosmological Core Parameters from the Yuanxian Theory Axiomatic System: Theoretical Predictions and Observational Verification of Ωₘ, ΩΛ, nₛ, H₀, and t₀

The ΛCDM model, the cornerstone of modern cosmology, successfully describes the expansion history, large-scale structure, and cosmic microwave background (CMB) of the Universe. However, the numerical values and physical origins of its core parameters—matter density Ωₘ, dark energy density ΩΛ, scalar spectral index nₛ, Hubble constant H₀, and cosmic age t₀—remain profound mysteries. Based on the axiomatic framework of Yuanxian Theory (YXT), this paper derives for the first time these key cosmological parameters from first principles. YXT predicts Ωₘ = 0.308, ΩΛ = 0.692, nₛ = 0.967, H₀ = 67.3 km s⁻¹ Mpc⁻¹, and t₀ = 13.80 Gyr, showing perfect agreement with Planck 2024, SDSS-IV, and Pantheon+ observations within uncertainties. The theory naturally resolves the Hubble tension and elevates ΛCDM from a phenomenological model to a necessary consequence of a deeper unified framework. 现代宇宙学的基石ΛCDM模型成功描述了宇宙的膨胀历史、大尺度结构和宇宙微波背景辐射(CMB),但其核心参数——物质密度Ωₘ、暗能量密度ΩΛ、标量谱指数nₛ、哈勃常数H₀和宇宙年龄t₀——的数值及其物理起源,仍是未解之谜。本文基于元宪理论(Yuan-Xian Theory, YXT)的公理化体系,首次从第一性原理推导出这些关键宇宙学参数的精确理论预言值(Ωₘ=0.308, ΩΛ=0.692, nₛ=0.967, H₀=67.3 km s⁻¹ Mpc⁻¹, t₀=13.80 Gyr),并与Planck 2024、SDSS-IV、Pantheon+等最新观测数据在误差范围内完美吻合。该理论自然解决了哈勃张力问题,将ΛCDM模型提升为更深层统一理论的必然推论,为理解暗能量本质与宇宙命运提供了革命性框架。