Geometric Origin of the Effective Axion Field in MRUV Cosmology: Emergent Chern–Simons Structure, the Coupling Parameter ε, and the Polarimetric Mirage Operator

Recent analyses of cosmic microwave background (CMB) polarization data from the Planck satellite report a non-zero isotropic rotation of the plane of linear polarisation, β = 0.30° ± 0.11°, commonly attributed to an axion-like pseudo-scalar field coupled to electromagnetism through a Chern–Simons interaction LCS ∝ ϕ FµνF̃µν. In this work we propose and develop a geometric alternative within MRUV cosmology, in which the axion-like field appearing in the effective electromagnetic Lagrangian is not an independent particle but an emergent pseudo-scalar mode of the cosmological vacuum structured by the universal deceleration field Φ ≈ 5.571 × 10⁻¹⁰ m s⁻². We show that the effective Chern–Simons pseudo-vector is naturally identified as pµ = ε (Φ/c) uµ, where uµ is the cosmological rest-frame four-velocity and ε is a dimensionless coupling parameter. The resulting birefringence angle Δα = ε Φt0/c coincides with a previous independent derivation from the polarisation transport equation (Prevedello 2026f, zenodo.org/records/18928941), and the constraint from Planck gives ε ≃ 5 × 10⁻³. We discuss the geometric interpretation of ε as a cosmological transport coefficient, its possible relation to the ratio Φ/(cH0), and the conceptual analogy between the birefringence mechanism and the Mirage Operator of MRUV cosmology — both arising from the cumulative interaction between propagating light and the geometric structure of a finite cosmological window. We further show that the dimensionless factor Φt0/c ≈ 1 is a structural identity of MRUV cosmology that can be written equivalently as t0/tmax, ωΦ t0, ct0/λC, or ct0/(2Rmax), simultaneously expressing the ratio of the present cosmic age to the maximum kinematic timescale, the geometric phase accumulated by electromagnetic propagation, and the ratio of the causal propagation distance to the Compton scale λC = 2Rmax associated with the photon mass mγ = ℏΦ/c³ induced by Φ. This unified picture suggests that cosmic birefringence, the Hubble tension, and non-invariant cosmological estimators share a common geometric origin in the universal field Φ.