Cosmological Perturbation Theory from the Clausius-Mossotti Framework: Growth Equation, Observational Tests, and a Falsifiable Prediction

The Clausius-Mossotti (CM) metric ds² = W^(1/3)c²dt² − W^(−1/3)(dr²+r²dΩ²) satisfies g_tt × g_rr = 1 identically and reproduces all six classical tests of GR. This paper derives a CM-specific growth equation for cosmological density perturbations: δ̈ + 2H·W₀^(1/6)·δ̇ = 4πGρ̄δ·W₀^(1/3), where W₀ = Ω_m(z). The modifications arise from the metric's time dilation, not from a change in gravitational coupling. At linear order, CM = GR (from g_tt×g_rr=1). The equation passes six observational tests: matter-era consistency (exact), S₈ vs DES (0.52σ), fσ₈ vs RSD (χ²/N=1.14), H(z) vs chronometers (χ²/N=0.45), BAO vs DESI DR1 (χ²/N=1.51, CM preferred over ΛCDM), and cosmic age (0.48σ). Growth index prediction: γ = 0.607 ± 0.010 (vs GR 0.549), testable by Euclid at 2.9σ. All three tensions (H₀, S₈, Ω_m) traced to one cause: ΛCDM Ω_m = 0.315 too high. CM derives Ω_m = (1−p)² = 0.2784 (p = e^(−3/4), zero fitted parameters), reducing total tension² by 89%. Code: https://github.com/singhmandy25-gif/speed-gap-framework/tree/main/cm-perturbation-theory