Part 35: A Direct Comparison Between Dual–H4 Geometry and ΛCDM Distinct Predictions from Topological Expansion and Void-Driven Cosmology

Overview The ΛCDM model remains the most successful phenomenological framework for modern cosmology. It accurately organizes a wide range of observations, including the expansion history of the Universe, the cosmic microwave background, baryon acoustic oscillations, large-scale structure, gravitational clustering, and the statistical distribution of matter on cosmological scales [8–12]. Nevertheless, ΛCDM contains effective components whose microscopic origin remains unresolved, most notably cold dark matter and the cosmological constant. Origin Geometry proposes a different microscopic interpretation. In the Dual–H4 branch of OG, the dark sector is not treated primarily as a passive cold particle component. Instead, it is modeled as a geometric sector whose topological relaxation, stress redistribution, bulk collective modes, and realized network growth may contribute to effective cosmological evolution [1–7]. In this view, cosmic expansion is not fundamentally introduced as metric stretching at the microscopic level, but emerges as a coarse-grained consequence of activated topological network degrees of freedom. Comparison and Central Distinction The present Part provides a direct comparison between ΛCDM and Dual–H4 Origin Geometry. The goal is not to reject ΛCDM, replace General Relativity, or claim that OG has already achieved precision cosmology. Rather, the goal is to identify where the two frameworks agree at the large-scale phenomenological level, where they differ at the microscopic and dynamical level, and what observational discriminants may eventually distinguish them. The central distinction can be summarized as follows. In ΛCDM, cosmic expansion is described by a scale factor a(t) governed by the Friedmann equations and an effective dark-energy sector. In OG, the effective scale factor is related to the realized topological network count: a_eff(t) = [ ⟨n(t)⟩ / ⟨n(t₀)⟩ ]^(1/3) so that: H_eff(t) ~ (1/3) (∂t⟨n⟩ / ⟨n⟩) Expectations and Discriminant Tests This difference leads to distinct qualitative and semi-quantitative expectations. OG predicts that effective expansion may depend on environment, that void regions may act as preferred relaxation channels, that expansion residuals may correlate with large-scale structure, and that ultra-high-frequency bulk stress backgrounds may exist if the microscopic relaxation mechanism is physically realized [4, 37–40]. These are not claims of confirmed observation. They are proposed discriminant tests. If future data show no environment-dependent expansion residuals, no topology-correlated structure effects, no viable bulk-mode channel, and no consistent mapping from topological growth to observed distance relations, then the OG cosmological branch would be strongly constrained. Conversely, robust detection of void-correlated expansion behavior, topology-sensitive residuals, or high-frequency bulk signatures would motivate further development of the Dual–H4 framework.