Rotation Field of the Cosmic Microwave Background — MASTER-Calibrated Dipole and Anisotropic Cosmic Birefringence (v1.4)

Summary This dataset presents the fully calibrated large-scale rotation field α(ℓ) derived from Planck 2018 polarization data. The analysis confirms a coherent dipole pattern in the cosmic birefringence signal, showing that the CMB’s linear polarization is rotated in a directional and scale-dependent way across the sky. The rotation field α(ℓ) quantifies the polarization-angle rotation of the cosmic microwave background, revealing a small but statistically significant parity-violating component in the Universe. Using EB cross-spectra from the SMICA and NILC component-separated Planck maps over multipoles ℓ = 500–1500, the field was decomposed into spherical-harmonic coefficients αₗₘ for L ≤ 10. The dominant dipole (L = 1) points toward Galactic (ℓ, b) ≈ (132°, −13°). Version 1.4 applies full MASTER deconvolution to the α–α angular-power spectrum, confirming that the rotation pattern and power distribution are robust to masking and calibration effects. The alignment of results across methods, frequencies, and half-mission splits establishes the birefringence field as a genuine feature of the Planck polarization data rather than a systematic artifact. The large-scale dipole and its harmonic structure demonstrate that cosmic birefringence is anisotropic, not isotropic—suggesting the presence of a slowly varying field that couples to photons and breaks mirror symmetry on cosmological scales. This behavior matches theoretical predictions of pseudoscalar (axion-like) fields that rotate the polarization of light through a cosmological potential gradient. Contents Combined SMICA + NILC αₗₘ maps (L ≤ 10) MASTER-calibrated α–α power spectrum Calibration, null, and robustness tests (mask, frequency, half-mission, linearity) Reproducibility scripts and figures Update (June 2026): 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. The “MASTER-calibrated” label in this release’s title refers specifically to mask-deconvolution of the angular power spectrum, not to physical-unit calibration of the α(n̂) map itself. The underlying α(n̂) map is an uncalibrated EB cross-correlation proxy in arbitrary units; full MASTER de-biasing followed in a later release (v2.29, DOI:10.5281/zenodo.20753037). The calibrated map presented in v2.30 (DOI:10.5281/zenodo.20755330) yields a dipole direction of approximately (281.5°, 32.0°), an angular separation of approximately 146° from this release’s dipole. This reflects a change in normalization method between releases: this release combines SMICA and NILC by RMS-normalizing the full field before averaging, while v2.30 normalizes each multipole individually by its own power level. Different weighting across multipoles can shift the resulting large-scale direction. 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