GRP Addendum — CMB Decoupling and Dark Matter Reinterpretation: Exact ER → GR Decoupling at Recombination
Year: 2026
Type: preprint
Abstract: This addendum to the Geometric Relay Programme (GRP) addresses the CMB sector of the programme by showing why the Cosmic Microwave Background can remain effectively identical to the standard GR/ΛCDM description at recombination, while still allowing a geometric reinterpretation of dark matter at lower redshift and galactic scales. The central result is an exact ER → GR decoupling theorem at recombination. In Entangled Relativity, based on the action S = -|C| ∫ L_m^2/R sqrt(-g) d^4x, the matter Lagrangian L_m is physically active and cannot be replaced by a fluid shortcut without care. The addendum resolves the L_m ambiguity for radiation by distinguishing the microscopic electromagnetic Lagrangian from the Hamiltonian energy density. For thermal photons, the electromagnetic Lagrangian satisfies = 0 because of the E ↔ B symmetry of free radiation, while the energy density remains nonzero. Therefore, at z ≈ 1100, baryons and electrons contribute L_m ≈ T ≈ -rho_b, while thermal photons contribute L_m = 0 and T_gamma = 0. This yields L_m = T and activates the Minazzoli decoupling condition: Entangled Relativity reduces exactly to General Relativity at recombination. This result is not treated as a weakness of the GRP but as a structural advantage. It explains why the CMB can measure Ω_m in the standard way, without relay contamination. The Planck value of Ω_m then feeds the GRP closure chain: Ω_m → m_0 = sqrt(Ω_m) H_0 → a_0 = m_0 c / 3 → MOND fixed point. The addendum further proposes that the quantity usually interpreted as cold dark matter, Ω_m - Ω_b ≈ 0.266, corresponds in the GRP to the relay tension R*(z), scaling as (1+z)^3 in the CRT V3 mixed regime. Thus the same geometric relay field behaves as an effective CDM component at the CMB epoch and as a MOND-like non-linear relay at galactic scales. The work introduces no new free parameter. It does not claim a full replacement of the Boltzmann perturbation calculation. The next required step is a quantitative implementation of the relay perturbations in a modified Boltzmann framework such as hi_CLASS or EFTCAMB, with the key failure criterion being whether R* reproduces the observed acoustic peak amplitude ratios, especially D_l3/D_l2, within observational tolerance. In short: the GRP does not modify the CMB at recombination; it explains why the CMB must look standard, then reinterprets the dark component measured by Planck as a geometric relay tension rather than a particle species.
Author: Lane-larquey, Olivier
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7161377182
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