The Geometric Relay as Dark Matter: Exact CMB Decoupling, Identical P(k), and the Reinterpretation of Ωcdm

This paper develops the dark-matter reinterpretation of the Geometric Relay Programme (GRP), built on the Entangled Relativity action of O. Minazzoli, S = -|C| ∫ Lₘ²/R sqrt (-g) d⁴x. The central proposal is that the scalar relay σ of Entangled Relativity reproduces the linear cosmological role usually attributed to cold dark matter, without requiring a new particle component. The paper combines three ingredients. First, the CMB sector is protected by exact decoupling. For thermal radiation, the microscopic electromagnetic Lagrangian satisfies = 0 by E B symmetry. At recombination, the total matter Lagrangian therefore satisfies Lₘ ≈ T, so Entangled Relativity reduces to General Relativity and the standard CMB measurement of Ωₘ remains valid. Second, the relay tension R* (z) scales as (1+z) ³ in the GRP cosmological mixed regime and is identified with Ωₘ - Ωb ≈ 0. 266, the quantity usually interpreted as Ωcdm. In this reading, Planck does not necessarily measure a dark substance; it measures the gravitational effect of a non-baryonic matter-like component, here interpreted as geometric relay tension. Third, the paper argues that the linear background and growth observables H (z), D (z), BAO and P (k) are algebraically identical to ΛCDM at the linear level, while the discriminating departures are expected in the non-linear regime: fσ8 compression, core profiles rather than NFW cusps, lensing, and cluster-scale systems. The manuscript explicitly identifies remaining open tests: full Boltzmann-code implementation, lensing-sector modelling, Bullet Cluster / cluster-subhalo predictions, and non-linear structure formation. A verification script is provided to check the numerical claims using physical constants and Planck 2018 parameters. The claim is not that dark matter particles are disproven, but that the standard linear cosmological observables can be reinterpreted as signatures of a geometric relay sector rather than as direct evidence for a particle substance.