Precision Constraints on Large-Scale Cosmic Structure from CMB Lensing and Galaxy Clustering: An Emergent Substrate Perspective

Abstract

Recent ACT measurements confirm that the gravitational force law adheres strictly to inverse‑square behavior (F ∝ r⁻²) across galaxy clusters separated by hundreds of millions of light‑years. We show that this scaling emerges naturally as the sparse‑regime limit of the emergent correlation metric tensor gμν(x) = ∂μ∂ν[−ln(I/I₀)]|x'→x within the pre‑geometric correlation substrate, without invoking cold dark matter particles or modified gravity. We formulate a Two‑Regime Cosmological Architecture: inside dense virialized halos (R ≤ 1–5 Mpc), correlation‑pressure saturation induces environmental screening that restores Einstein–Newtonian gravity; on large scales (R ≥ 5–10 Mpc), unscreened non‑local correlation fields govern cosmic dynamics and growth suppression. We derive the curvature identity Λ = R/4, eliminating the vacuum energy crisis and fixing the matter density parameter analytically to Ω_m ≈ 0.268. Finally, we construct a screened weak‑lensing shear operator that predicts elongated tangential arcs in cluster outskirts under non‑local correlation curvature. These results establish that cosmic‑scale “dark sector” phenomena are emergent geometric consequences of global correlation closure.