DOI: 10.5281/zenodo.17553829
title: Rotation Field of the Cosmic Microwave Background — Dependence-Aware Joint Validation of Anisotropic Cosmic Birefringence (v1.42)

description: Rotation Field α(ℓ) — Version 1.42

Dependence-Aware Joint Validation of Anisotropic Cosmic Birefringence

 

This dataset presents evidence that the Universe rotates the polarization of the Cosmic Microwave Background (CMB) in a directional and structured way — a phenomenon known as anisotropic cosmic birefringence.

 

Using Planck 2018 SMICA and NILC EB cross-spectra, the birefringence rotation field α(ℓ) is reconstructed over multipoles ℓ = 500–1500 and decomposed into spherical-harmonic modes (αₗₘ, L ≤ 10). The resulting α-map shows large-scale anisotropic rotation in the sky.

 

The key result is that the Universe does not rotate polarization uniformly. After applying the Minami–Komatsu isotropic EB calibration, the constant (global) rotation component becomes consistent with zero. What remains is directional: a structured, anisotropic rotation field.

 

Observed features of α(ℓ):

 

• A broad rotation dipole near Galactic coordinates (ℓ, b) ≈ (278°, 18°)

• A repeating multi-harmonic pattern with Δℓ ≈ 180 and 360

• Consistency across SMICA/NILC, masks, half-mission splits, Δℓ sweeps, and LOOCV

 

These features are consistent with a slowly varying pseudoscalar (axion-like) field coupled to photons, producing large-scale parity violation.

 

Version 1.42 (this release) introduces a dependence-aware empirical joint significance test to determine whether the observed anisotropy could arise from noise or from mode selection. Two statistically independent signatures of α(ℓ) are evaluated simultaneously on the same null ensemble:

 



Low-L even/odd parity asymmetry of the αₗₘ map (dipole removed; L = 2–10)

High-ℓ multi-harmonic structure in α(ℓ) using k = {3, 4, 7} over ℓ = 500–1500


 

 

A total of 165,000 dependence-aware null realizations were generated. Each realization is passed through identical mask coupling, window transfer, ℓ-binning, and harmonic modeling, and both statistics (parity and harmonic power) are computed for each null.

 

No null realization exceeded the observed joint statistic.

 

Results:

 

• parity statistic: p ≈ 6.1 × 10⁻⁶  (≈ 4.4σ one-sided)

• harmonic structure: p ≈ 6.1 × 10⁻⁶  (≈ 4.4σ one-sided)

• joint dependence-aware significance: p ≈ 6.1 × 10⁻⁶  (≈ 4.4σ one-sided)

 

No Fisher/Stouffer independence assumption was used. The significance is purely empirical.

 

This rules out the possibility that both signals arise from the same noise fluctuation or from trial-factor bias. The anisotropy of α(ℓ) is stable under Δℓ bin sweeps, leave-one-out cross-validation, high-k controls, and half-mission splits.

 

Relation to the “22 Blue” Research Series:

 

The “22 Blue” project documents the full progression from initial discovery to joint validation:

 

• Publication (Sep 20 2025): Evidence for Harmonic Phase Alignments in Planck 2018 CMB Polarization Data — independent first publication, identifying multi-harmonic structure in polarization (Δℓ ≈ 320)

• v1.0 (Oct 10 2025): First quantitative detection of anisotropic birefringence

• v1.1–v1.3: Validation, TB/EB diagnostics, simulation and calibration checks

• v1.4: MASTER-calibrated anisotropic rotation field

• v1.41: Extended calibration and robustness testing

• v1.42 (this release): Dependence-aware empirical joint significance

 

Together, these releases constitute the full archival record of the discovery known as:

“22 Blue — The Heartbeat of the Universe.”

 

Contents (v1.42):

 

• α(ℓ) rotation series and αₗₘ map (L ≤ 10)

• Harmonic fits (k = 3, 4, 7), LOOCV stability, Δℓ sweeps, high-k controls

• Dependence-aware joint null ensemble (165,000 simulations)

• Replication notebook (run-all) and JSON proof artifacts

 

Created by Amy Condit (22 Blue) — independent cosmology research into parity violation and anisotropic cosmic birefringence in Planck 2018 polarization data.