Resolving the H₀ and S8 Tensions Through Local-Global Inference Separation: An Energy-Flow Cosmology Analysis

Abstract The Hubble tension (H₀ = 73.0 ± 1.0 km/s/Mpc locally vs. 67.4 ± 0.5 km/s/Mpc from CMB) and the S8 tension (σ₈ suppression in late-universe probes) represent the most significant challenges to the standard ΛCDM cosmological model. We present an analysis within the Energy-Flow Cosmology (EFC) framework demonstrating that both tensions can be resolved simultaneously through a single physical mechanism: entropy-dependent modification of how local observations are mapped to global cosmological parameters. The key insight is that the tensions arise not from different expansion rates or gravitational strengths in different regions, but from systematic biases in inferring global parameters from local measurements when entropy gradients are present. Using the validated EFC sector—comprising an effective gravitational coupling Geff(S) = GN(1+βS) with β < 0 and entropy-dependent growth damping—we achieve: H₀ tension resolution with Δχ² = 40.29 improvement; S8 tension reduction from 3.3σ to 0.3σ; and full consistency with BAO, SNe Ia, and CMB distance constraints. Critically, this is accomplished without modifying the cosmic expansion history H(z), the sound horizon rd, or early-universe physics. The approach explicitly separates the validated core of EFC from experimental extensions, providing a falsifiable framework with clear domain of validity.