Vacuum Folding Dynamics: Cosmological Signatures of Holographic Vacuum Screening

Previous papers in the VFD series established the Vacuum Folding Dynamics framework, deriving twelve standard-model observables from the vacuum micro-state density σ_f, constructing electromagnetic coupling channels, and designing a laboratory detection strategy. One key question remained open: the dynamical evolution of σ_f through cosmological history and its observable imprints. In the present paper we address this question in three stages. First, we derive the cosmological field equation for σ_f in a Friedmann–Lemaître–Robertson–Walker background, showing that the chameleon mass m_eff(ρ) tracks the cosmic mean density through radiation domination, matter domination, and Λ-domination. Second, we integrate this equation numerically from z = 10¹⁰ (post-BBN) to z = 0, demonstrating that σ_f remains deeply frozen (m_eff >> H) throughout the entire cosmological history: the ratio m_eff/H grows monotonically from ~10¹³ at BBN to ~10³⁰ today. The chameleon contribution to m_eff becomes sub-dominant below z ~ 3×10⁹, after which m_eff ≈ m₀; the transition from radiation- to matter-dominated expansion at z_eq ≈ 3400 leaves m_eff essentially unchanged. Third, we compute the perturbative imprints of σ_f on the cosmic microwave background (CMB) and matter power spectrum, finding: (a) a scale-dependent modification of the ISW effect at ℓ ≤ 30 with amplitude ΔC_ℓ/C_ℓ ~ 10⁻¹⁰⁸, (b) an oscillatory feature in the matter transfer function at the Compton scale k_σ ~ 10²⁶ Mpc⁻¹, utterly inaccessible to cosmological probes, and (c) a characteristic oscillation frequency f_σ ~ 2.4×10¹¹ Hz today (redshifted to ~7×10⁷ Hz when sourced at matter–radiation equality). All three signatures are astronomically below current observational sensitivity, confirming that VFD is cosmologically inert. The numerical cosmology confirms that the ρ → 0 analytic limit used in the foundational papers is an excellent approximation (relative deviation < 10⁻³²) in the late-universe vacuum, validating the foundational derivations.