Rotation Field of the Cosmic Microwave Background — Universe-model evaluation and intrinsic Δℓ structure (v2.2)

Summary Version 2.2 examines what kind of universe naturally produces the observed intrinsic harmonic in the CMB polarization rotation field α(n̂). Prior versions (v2.0–v2.1) established a fixed periodicity Δℓ ≈ 109 ± 3 and a corresponding angular correlation scale θ₀ ≈ 3.3° ± 0.3°. This version translates those empirical facts into theoretical evaluation, comparing possible cosmological model classes. Fixed priors inherited from v2.1 - Locked residual: alpha_residual_used_v20DETFOUND_20251110_235343.npy (SHA-256 b84ee7ed…) - Multipole range: 100 ≤ ℓ ≤ 1500 - Δℓ = 109 ± 3 → θ₀ = 3.3° ± 0.3° - Duality relation: θ₀ ≈ 360° / Δℓ (valid within 1 σ) - No re-estimation or recomputation of residuals Methods and tests **Mathematical framework** The Δℓ–θ₀ duality was verified through direct projection of the Cℓ(αα) residual into ξ(θ) via the Gauss–Legendre transform, confirmed by the Bessel-limit relation θ ≈ 360° / Δℓ. Both domains were cross-checked for internal consistency and unit integrity (degrees, not radians). **Model discrimination approach** Six universe models were identified as candidates and represented by an analytical damping form applied to the residual spectrum. Two were scored at the time of this release: - M₀ (ΛCDM baseline): constant or white residual, no intrinsic structure. - M₁ (Axion / scalar-field birefringence): exponentially damped cosine term. - M₂ (Anisotropic dark-energy / multi-field inflation): Gaussian-damped cosine. - M₃ (Domain / topological universe): bounded oscillation with phase-locking across ℓ-space. - M₄ (Holographic / boundary-condition universe): standing-wave boundary periodicity. - M₅ (Simulation / computational periodicity): synthetic Δℓ repetition from discretized spacetime. The ΛCDM baseline and domain/topological models were scored using AICc/BIC-style likelihood comparison on the locked residual spectrum, with Δℓ and θ₀ treated as fixed observational priors. Scores for all six models were computed subsequently and are reported in v2.33. **Validation diagnostics** - Cross-validation between ℓ-space and θ-space projections. - Confirmed phase coherence under band-detrending and smoothing. - Independent sanity check via ξ(θ) peaks (θ₀ = 2.9–3.3° range). - No numerical instability, sign inversion, or coordinate-basis drift detected. Findings The comparative scorecard favored the domain / topological framework (compatibility ≈ 0.9) as the universe type most consistent with a rotation field α(n̂) that possesses an intrinsic angular correlation scale. The ΛCDM baseline cannot reproduce a persistent Δℓ–θ duality without additional structure. Interpretively, this suggests a universe containing large-scale domain coherence or topological phase segmentation within which the CMB polarization rotation field retains a preferred harmonic scale. Deliverables - Locked-input manifest (no overwrites) - Model-scorecard CSV (scored + provenance) - Δℓ↔θ duality figure (clean version) - Residual-spectrum figure with Δℓ guides - Export bundle ZIP (archival integrity verified) - Full SHA-256 manifest for data reproducibility Instructions for reproducibility All computations performed in Colab (Python 3.12) using numpy, matplotlib, astropy, and healpy. Workflow follows strict no-overwrite policy; every artifact carries a timestamp and SHA-256 hash. Reproducibility verified through pointer locks and manifest checks. Update (June 2026): Additional models were subsequently evaluated in a full computed comparison published as v2.33, which determined the Anisotropic Dark Energy/Gaussian-damped model is preferred. Both predict spatially organized rotation fields with a preferred coherence scale, differing only in generating mechanism. The domain/topological finding of this release is preserved and contextualised by those results; see v2.33 for the complete quantitative assessment. This release is part of an iterative research series in which analysis methods, masks, and calibration procedures were progressively refined. Later releases establish the physical calibration of the α(n̂) field. PUBLICATION RECORD PREDECESSOR PUBLICATION (Separate Record) Sep 20, 2025 (v1.0) — Harmonic Phase Alignments in Planck 2018 CMB — DOI:10.5281/zenodo.17167268 MAIN RESEARCH SERIES Concept DOI:10.5281/zenodo.17317397 Oct 10, 2025 (v1.0) — Scale-Dependent Anisotropic Birefringence: Initial Detection — DOI:10.5281/zenodo.17317398 Oct 20, 2025 (v1.1) — Scale-Dependent Anisotropic Birefringence: Validation Dataset — DOI:10.5281/zenodo.17396428 Oct 21, 2025 (v1.2) — Two-Harmonic Extension — DOI:10.5281/zenodo.17410764 Oct 28, 2025 (v1.3) — Two-Harmonic Dipole Verification — DOI:10.5281/zenodo.17468988 Nov 1, 2025 (v1.4) — MASTER-Calibrated Dipole — DOI:10.5281/zenodo.17500791 Nov 1, 2025 (v1.41) — Extended MASTER Calibration and Robustness — DOI:10.5281/zenodo.17508908 Nov 7, 2025 (v1.42) — Dependence-Aware Joint Validation — DOI:10.5281/zenodo.17553829 Nov 8, 2025 (v1.43) — Phase Model Validation — DOI:10.5281/zenodo.17561313 Nov 8, 2025 (v1.44) — Axis + Frequency + Half-Mission Validation — DOI:10.5281/zenodo.17561768 Nov 9, 2025 (v1.5) — Multipole Structure and Model Selection — DOI:10.5281/zenodo.17562965 Nov 9, 2025 (v1.6) — Phenomenology and Physical Interpretation — DOI:10.5281/zenodo.17566197 Nov 9, 2025 (v1.7) — Prediction and Experiment Overlays — DOI:10.5281/zenodo.17566870 Nov 9, 2025 (v1.8) — Model Rejection and Δℓ Persistence — DOI:10.5281/zenodo.17567241 Nov 10, 2025 (v2.0) — Intrinsic Periodicity in ℓ-Space — DOI:10.5281/zenodo.17574048 Nov 10, 2025 (v2.1) — Physical Origin of Δℓ Modulation — DOI:10.5281/zenodo.17577086 Nov 11, 2025 (v2.2) — Universe-Model Evaluation — DOI:10.5281/zenodo.17585419 Nov 12, 2025 (v2.3) — Domain Geometry and Topological Inference — DOI:10.5281/zenodo.17594157 Nov 13, 2025 (v2.4) — Real-Space Correlation of the Birefringence Field — DOI:10.5281/zenodo.17597537 Nov 13, 2025 (v2.5) — Spectral Surgery on the Δℓ ≈ 109 Harmonic — DOI:10.5281/zenodo.17604982 Nov 14, 2025 (v2.6) — Angular Locality of the Δℓ = 109 Standing Wave — DOI:10.5281/zenodo.17613348 Nov 15, 2025 (v2.7) — Sky-Local Origin of the Δℓ ≈ 109 Standing Wave — DOI:10.5281/zenodo.17620029 Nov 15, 2025 (v2.8) — Domain Topology of the Δℓ ≈ 109 Standing Wave — DOI:10.5281/zenodo.17620605 Nov 16, 2025 (v2.9) — Dual-Domain Coherence and Boundary Geometry — DOI:10.5281/zenodo.17621871 Nov 17, 2025 (v2.10) — Boundary Sequence Structure on the Dual-Domain Loop — DOI:10.5281/zenodo.17635811 Nov 19, 2025 (v2.11) — Boundary Standing-Wave and Phase-Structure Analysis — DOI:10.5281/zenodo.17648033 Nov 21, 2025 (v2.12) — Boundary Universality and Standing-Wave Fingerprints — DOI:10.5281/zenodo.17676377 Nov 23, 2025 (v2.13) — Interior Propagation and Boundary-Driven Structure — DOI:10.5281/zenodo.17693540 Jun 18, 2026 (v2.29) — Rotation Field of the Cosmic Microwave Background — Interior Propagation Audit & Harmonic Normalization — DOI:10.5281/zenodo.20753037 Jun 19, 2026 (v2.30) — Calibrated Interior Propagation Validation — DOI: 10.5281/zenodo.20755330 Jun 20, 2026 (v2.31) — Rotation Field of the Cosmic Microwave Background — Physical Origin of Boundary-to-Interior Propagation — DOI: 10.5281/zenodo.20777435 Jun 21, 2026 (v2.32) — Rotation Field of the Cosmic Microwave Background — Antipodal Specificity, Boundary Ordering, and Cross-Scale Spectral Organization — DOI: 10.5281/zenodo.20787307 22 Blue - The Heartbeat of the Universe