In Papers I and II 1, 2, we introduced Inflationary Domain Theory (IDT) as a minimal extension of ΛCDM in which epoch-localized energy density contributions modify the expansion history and structure growth at specific cosmological epochs, achieving ∆AIC =−8.1 with hand-chosen domain widths and perturbative dephasing (η0 =−0.05). In this paper, we present three advances. First, we introduce the MS phase quantum formalism, an effective description in which each domain resonance accumulates a constant cosmological phase ∆ = (1+w) dN, providing a data-supported relation that determines domain widths σln from a single parameter. Second, we perform full parameter liberation with converged posteriors from adaptive Metropolis–Hastings sampling (four ˆ independent chains, all Gelman–Rubin R < 1.1, 32,000 post-burn-in samples). Third, we identify the combination g= fdom ×(1 + η0) as a conserved observable governing the net dephasing effect: the posterior is bimodal in (fdom,η0) space but unimodal in g, with gearly = 0.035 ±0.016. With six parameters beyond ΛCDM (all free, data-determined), the model achieves ∆AIC =−24 under the compressed Planck likelihood with P(k) constraints (AIC penalty of 12). The S8 tension is reduced from approximately 3σ to 0.2σ, and the CMB acoustic scale la is reproduced to 0.0σ. The dephasing parameter η0 =−0.57 (−0.70 to−0.40) produces behavior analogous to a gravitational Lagrange point, where competing influences from neighboring domains lead to partial cancellation of the effective gravitational coupling. The bimodal posterior represents a physical degeneracy between neighbor configurations that produce identical net dephasing, analogous to the emergence of Ωmh2 as the primary CMB-constrained quantity rather than Ωm and h separately. H0 = 68.1 ± 0.5 km s−1 Mpc−1 is consistent with the CMB-inferred global expansion rate; the discrepancy with local distance-ladder measurements may reflect a local void effect rather than requiring additional modifications to early-universe physics.
Jose Ramon Gonzalez (Tue,) studied this question.