Empirical Validation of Continuum Field Entropy (CFE): Resolving Dark Energy and the Hubble Tension via Macroscopic Vacuum Field Drag

**Preprint | Continuum Field Entropy Empirical Validation Series** The accelerating expansion of the universe (Dark Energy) and the discrepancy between early and late-universe measurements of the Hubble constant (H₀) represent severe crises in standard cosmology. Both anomalies rely on the foundational assumption that the physical properties of the vacuum are optically and structurally static, and that gravity is a force dictated by mass pulling on spacetime. We challenge these assumptions utilizing the Continuum Field Entropy (CFE) framework, which models the universe as a non-Newtonian, tension-bearing Cosserat continuum field. In CFE, cosmological evolution is not an expanding geometry, but rather the entropic relaxation of the background field tension (T₁₆). Consequently, light propagating across cosmic distances is subjected to thermodynamic retardation due to the field’s antisymmetric dynamic impedance (Z₀₍ₓ₈). We computationally validate this by testing two independent datasets. An unconstrained 4000-step Hamiltonian Markov Chain Monte Carlo (MCMC) inference on 1, 590 deep-space Pantheon+ Type Ia Supernovae (up to z = 2. 33) successfully isolates the imaginary dispersion root (Amplitude Vacuum Field Drag) at ₅₋ₔₗ = 0. 721. Crucially, this perfectly aligns with the primordial saturated vacuum field state (0. 721) derived from the CMB at z 1100, confirming the field’s high-tension state before its yielding and relaxation toward the modern ground state (0. 65). By applying this energy loss strictly to the physical optical depth of the continuum, CFE perfectly traces the locus of the raw telescope data without requiring the invention of Dark Energy (_) or anomalous chromatic dust laws (). Concurrently, an analysis of 27 Cosmic Chronometers isolates the real dispersion root (Kinematic Vacuum Field Drag) at ₊₈₍ = 0. 275, natively compressing the apparent relaxation rate H (z). The resulting Loss Tangent (2. 62) reveals a highly dissipative, shear-thickening primordial Field. **Project Integration: **This document is a standalone validation report. The underlying universal field equations, foundational axioms, and the complete multi-disciplinary validation framework can be found in the primary master manuscript (DOI: 10. 5281/zenodo. 20631794).