DOI: 10.5281/zenodo.17562965
title: Rotation Field of the Cosmic Microwave Background — Multipole Structure & Model Selection (v1.5)

description: Summary

Version v1.5 performs model selection and multipole structure analysis on the same locked α(n̂) rotation field used in v1.43 and v1.44.No α reconstruction is performed and no calibration or preprocessing changes occur.The purpose of v1.5 is to determine what spatial structure best explains the rotation field.

All models use: • the same locked α(n̂) map (alpha_lowL_combined_v141.fits), • the same apodized polarization mask (NSIDE=512, f_sky≈0.467), • the same low-ℓ band (2–10).

The anisotropy detection from v1.43 (4.38σ empirical exceedance over 165,000 null simulations) remains unchanged.

Models tested:

Model    FormA — Dipole                        α(n̂) = a₀ + d · n̂B — Dipole + traceless quadrupole α(n̂) = a₀ + d · n̂ + Q : (n̂n̂)C — Harmonic in multipole space   α(ℓ) = A sin(kℓ + φ) + C + G/ℓ

Results

 • Dipole-only is decisively rejected. Model selection strongly prefers a dipole + quadrupole structure:       ΔAIC ≈ +2.16×10⁵, ΔBIC ≈ +2.16×10⁵.

 • The rotation spectrum α(ℓ) contains a harmonic periodicity.

Note on Δℓ:

Earlier unconstrained harmonic fits (v1.2) favored Δℓ ≈ 360.

In v1.5, the harmonic frequency scan was intentionally restricted for model-selection stability (AIC/BIC).

The bootstrap distribution saturated the upper bound of that allowed range, giving Δℓ ≈ 454.

Both fits are consistent with periodic structure in α(ℓ); the difference arises from modeling constraints, not a change in the data.

       Best-fit periodicity: Δℓ = 454.7       68% confidence interval (bootstrap): 433.07 – 454.72 – 454.72       (median and upper bound coincide because the bootstrap distribution        is truncated by the allowed k-scan range.)

 • Δℓ is stable under:       – different bin widths (Δℓ_bin = 12, 15, 20)       – mask apodization changes (+0.5°, +1.5°)       – posterior predictive checks (best-fit model reproduces the amplitude envelope)

 • Cross-validated prediction error decreases from Model A → Model B → Model C.

v1.5 does not modify the detection established in v1.43/v1.44; it characterizes the structure of α(n̂).

Archive contents(All files are timestamped; no file is ever overwritten.)

 • dipole_fit_modelA.json/png • quadrupole_fit_modelB.json • harmonic_modelC_fit_*.json/png • harmonic_modelC_series_*.csv • v1_5_metrics_table_*.json/txt (AIC/BIC/logL/CV-RMSE/residual ratios) • v1_5_robustness_summary_*.json (bootstrap, binning, mask-apod tests) • v1_5_numbers_table_*.txt (human-readable summary) • v1_5_README_paragraph_*.txt (text for manuscripts / papers) • v1_5_bundle_manifest_*.json (SHA-256 for every file)

Reproducibility

 • Same α(n̂) FITS map and same mask from v1.43/v1.44 • No α computation — this version analyzes structure only • Results reproduced with a single notebook: run_v15_model_selection.ipynb

Conservative statement

The CMB rotation field is not well described by a dipole-only pattern.The data require a dipole + quadrupole component and show harmonic periodicity in multipole space.

——————————————————————————Version history (22 Blue dataset series)

Separate publication — Sep 20, 2025 • Evidence for Harmonic Phase Alignments in Planck 2018 CMB Polarization Data   Identifies coherent multi-harmonic structure (Δℓ ≈ 320).

v1.0 — Oct 10, 2025 • First quantitative detection of scale-dependent, anisotropic cosmic birefringence   (8.5σ isotropic + 4–5σ directional).

v1.1 — Oct 20, 2025 • Adds full statistical validation and reproducibility materials   (TB/EB diagnostics, covariance checks).

v1.2 — Oct 21, 2025 • Introduces two-harmonic extension (Δℓ ≈ 180 and 360).

v1.3 — Oct 28, 2025 • Completes verification and robustness tests   (calibration, simulation, injection/recovery).

Harvard Dataverse Mirror — Oct 29, 2025 • Dataset mirrored on Harvard Dataverse v2   DOI: 10.7910/DVN/PTDG20

v1.4 — Nov 1, 2025 • MASTER-calibrated rotation field α(ℓ); low-ℓ transfer verified.

v1.41 — Nov 1, 2025 • Extended calibration and robustness evaluation   (SMICA/NILC, half-mission splits).

v1.42 — Nov 7, 2025 • Dependence-aware empirical joint significance (parity + high-ℓ harmonics)   165,000 null realizations; add-one p ≈ 6.06×10⁻⁶ (≈4.38σ).

v1.43 — Nov 8, 2025 • Phase model validation — calibration-invariant parity result.   MASTER coupling reproduces parity to ≤ 0.26%; null exceedances 0 / 165,000.

v1.44 — Nov 8, 2025 • Axis + frequency + half-mission validation using the same locked α(n̂).   The anisotropic rotation field remains stable under component separation,   frequency choice, and detector splits.

v1.5 — Nov 9, 2025 (this release) • Multipole structure analysis and model selection using the same locked α(n̂). • Dipole-only model is decisively rejected (ΔAIC ≈ +2.16×10⁵, ΔBIC ≈ +2.16×10⁵). • α(ℓ) exhibits harmonic periodicity: Δℓ = 454.7 (68% CI: 433.07 – 454.72 – 454.72). • Δℓ stable under binning, mask variation, and posterior predictive checks.

——————————————————————————Part of the “22 Blue — The Heartbeat of the Universe” research archive.