Elastic-Time Cosmology (ETC): Foam-Tension Dynamics and Contextual Entropy Flow

The Elastic-Time Cosmology (ETC) model redefines dark energy as temporal elasticity emerging from quantum-foam dynamics. Instead of a constant Λ, cosmic acceleration arises from an open-system formulation∇_μ T^{μν} = ξ u^ν, where ξ = εₜ ρ_foam ≥ 0,consistent with the second law of thermodynamics. The model introduces two measurable parameters—contextual deviation (ΔQ) and temporal elasticity (εₜ)—linking microscopic foam tension to macroscopic expansion. Bayesian analysis of 1.2×10⁵ MCMC samples yields H₀ = 71.4 ± 1.6 km s⁻¹ Mpc⁻¹ and w = −1.04 ± 0.03, resolving H₀, S₈, and JWST tensions without invoking exotic matter. The ETC framework remains GR-compatible in the zero-context limit, interprets energy leakage as entropic flow, and predicts empirically testable ΔQ variations observable via DESI and Euclid surveys. Supplementary Fig. S1 (TT-spectrum residuals ±0.3%) confirms consistency with Planck 2018 data.