DOI: 10.5281/zenodo.17585419
title: Rotation Field of the Cosmic Microwave Background — Universe-model evaluation and intrinsic Δℓ structure (v2.2)

description: 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 several possible cosmological model classes.

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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  

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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**  Each universe model was represented by an analytical damping form applied to the residual spectrum:  - 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.

Each was scored using AICc/BIC-style likelihood comparison on the locked residual spectrum, with Δℓ and θ₀ treated as fixed observational priors.  

**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.

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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.  

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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  

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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.  

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Citation  Condit, Amy (2025). *Rotation Field of the Cosmic Microwave Background — Universe-model evaluation and intrinsic Δℓ structure (v2.2).*   22 Blue — The Heartbeat of the Universe.   Zenodo. https://doi.org/10.5281/zenodo.17585419  

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Version History (22 Blue dataset series)  Separate publication — Sep 20 2025 • Evidence for Harmonic Phase Alignments in Planck 2018 CMB polarization data (Δℓ ≈ 320)  v1.0 — Oct 10 2025 • First quantitative detection of anisotropic cosmic birefringence (8.5 σ isotropic + 4–5 σ directional)  v1.1 — Oct 20 2025 • Full statistical validation (TB/EB diagnostics, covariance)  v1.2 — Oct 21 2025 • Two-harmonic extension (Δℓ ≈ 180 and 360)  v1.3 — Oct 28 2025 • Robustness tests (calibration, simulation, injection/recovery)  Harvard Dataverse Mirror — Oct 29 2025 • DOI: 10.7910/DVN/PTDG20  v1.4 — Nov 1 2025 • MASTER-calibrated rotation field α(ℓ)  v1.41 — Nov 1 2025 • SMICA/NILC + half-mission splits  v1.42 — Nov 7 2025 • Joint parity + harmonic significance (165,000 null realizations, ≈ 4.38 σ)  v1.43 — Nov 8 2025 • Parity invariant under MASTER coupling  v1.44 — Nov 8 2025 • Axis + frequency + half-mission validation  v1.5 — Nov 9 2025 • Multipole model selection; dipole-only rejected; Δℓ ≈ 454.7  v1.6 — Nov 9 2025 • Phenomenology & physical interpretation  v1.7 — Nov 9 2025 • Forward prediction (LiteBIRD / SO / CMB-S4 overlays)  v1.8 — Nov 9 2025 • Harmonic persistence & model rejection  v2.0 — Nov 10 2025 • Intrinsic Δℓ discovered (≈ 108) and artifact Δℓ (~454) isolated as low-ℓ leakage  v2.1 — Nov 10 2025 • Physical origin of intrinsic Δℓ ≈ 109 harmonic · ξ(θ) feature at θ ≈ 3.3° ± 0.3° · Legendre→Bessel dual confirmation · Locked/hashes-only workflow  v2.2 — Nov 11 2025 • Universe-model evaluation · Domain/topological framework favored · No reanalysis · Fixed priors Δℓ = 109 ± 3, θ = 3.3° ± 0.3°

 

22 Blue — The Heartbeat of the UniverseTwitter/X: [@Project22Blue]