Cosmic Birefringence from the Atacama Cosmology Telescope Data Release 6

1. Problem Statement

The paper addresses the search for cosmic birefringence, a phenomenon where the plane of linear polarization of Cosmic Microwave Background (CMB) photons rotates uniformly across the sky by an angle $\beta$. This rotation violates parity symmetry and could indicate new physics involving interactions between photons and dark matter or dark energy fields.

The Core Challenge:
The observed rotation angle is a sum of the cosmological signal ($\beta$) and instrumental miscalibration angles ($\alpha_i$). Distinguishing between the two is difficult because they produce identical signatures in the CMB power spectra (specifically the parity-odd $EB$ and $TB$ correlations).

• Previous analyses (e.g., by the ACT team in DR6) relied on frequentist methods to estimate a global rotation angle but did not explicitly separate $\beta$ from $\alpha_i$ using Bayesian priors.
• There are unresolved systematic discrepancies in the ACT data, specifically between different frequency bands within the same detector array (e.g., PA5 90 GHz vs. 150 GHz), raising questions about the validity of the instrumental models.

2. Methodology

The authors employ a Bayesian analysis framework to jointly estimate the cosmological rotation angle ($\beta$) and the instrumental miscalibration angles ($\alpha_i$) for five specific array-bands in the ACT DR6 dataset.

Key Methodological Components:

• Data Source: ACT Data Release 6 (DR6), covering 19,000 deg² with a median depth of 10 $\mu$K arcmin. The analysis uses cross-array-band power spectra ($EB$ and $TB$) from frequencies 90, 150, and 220 GHz.
• Joint Estimation: Unlike previous works that treated $\alpha_i$ as fixed or derived them separately, this study treats $\beta$ and all $\alpha_i$ as free parameters in a single likelihood function.
• Priors on Instrumental Systematics: The analysis incorporates Gaussian priors for $\alpha_i$ derived from a detailed optical model of the ACT telescope (Ref. [26]). Three prior configurations are tested to assess robustness:
  1. Independent ($\Pi_{ind}$): $\alpha_i$ are uncorrelated.
  2. Correlated within PA ($\Pi_{PA}$): 90% correlation between bands in the same physical array (baseline).
  3. Correlated per Frequency ($\Pi_{\nu}$): 90% correlation between bands observing at the same frequency across different arrays.
• Leakage Marginalization: The model is extended to include a residual intensity-to-polarization ($I \to P$) leakage parameter ($\gamma_i$) to ensure that spurious correlations from imperfect beam characterization do not bias the $\beta$ measurement.
• Formalism: The posterior distribution is calculated using an iterative semi-analytical formalism in the small-angle approximation ($|\alpha_i|, |\beta| \ll 1$), utilizing the full covariance matrix including off-diagonal bin correlations.

3. Key Contributions

• Explicit Separation of $\beta$ and $\alpha_i$: This is the first analysis of ACT DR6 to explicitly disentangle the cosmological rotation from instrumental miscalibration using Bayesian priors derived from the telescope's optical model.
• Inclusion of TB Correlations: The study incorporates $TB$ power spectra (previously excluded or underutilized in similar contexts) alongside $EB$ spectra to constrain the parameters, although $EB$ remains the dominant signal.
• Robustness Testing: The paper rigorously tests the impact of different prior assumptions regarding the correlation of instrumental errors and the inclusion of residual $I \to P$ leakage, demonstrating that the results are stable across these variations.
• Addressing Systematic Discrepancies: The analysis provides a Bayesian interpretation for the previously noted discrepancy between the 90 GHz and 150 GHz channels in the PA5 array, showing that the data is consistent with a single cosmological signal even if the instrumental angles differ slightly.

4. Results

The analysis yields the following primary results:

• Cosmic Birefringence Measurement:
  • $\beta = 0.215^\circ \pm 0.074^\circ$ (68% Confidence Level).
  • This measurement excludes the null hypothesis ($\beta = 0$) with a statistical significance of 2.9$\sigma$.
• Instrumental Miscalibration ($\alpha_i$):
  • The joint analysis tightens constraints on the instrumental angles for the PA5 and PA6 arrays by 20–37% compared to using prior knowledge alone.
  • The discrepancy between PA5 90 GHz and 150 GHz angles, which was significant in a frequentist analysis, is reduced to 1.1$\sigma$–1.9$\sigma$ when using the correlated priors ($\Pi_{PA}$), suggesting the discrepancy may be within statistical fluctuations or model uncertainties.
• Systematics Check:
  • Marginalizing over residual $I \to P$ leakage ($\gamma_i$) resulted in negligible shifts ($\le 0.07\sigma$) in the $\beta$ posterior, confirming that leakage is not the source of the signal.
  • The inclusion of the 220 GHz band (PA4), despite being noisier, did not significantly alter the central value of $\beta$, indicating robustness against dust contamination.
• Comparison with Other Missions:
  • The result ($\beta \approx 0.2^\circ$) is consistent with previous independent measurements from WMAP and Planck (e.g., $\beta = 0.342^\circ$ from Planck/WMAP joint analysis).
  • Combining ACT results with WMAP/Planck data (assuming statistical independence) increases the significance to 4.6$\sigma$ (ACT + Planck/WMAP) and 3.9$\sigma$ (ACT + Cosmoglobe reanalysis).

5. Significance

• Consistency Across Methodologies: The most significant finding is that independent datasets (ACT vs. Planck/WMAP) and different analysis methodologies (Bayesian vs. Frequentist, different priors) yield the same sign and comparable magnitude for $\beta$. This convergence strengthens the case that the signal is cosmological rather than an artifact of a specific instrument or analysis pipeline.
• Implications for New Physics: While the significance is not yet at the $5\sigma$ discovery threshold, a persistent $\beta \approx 0.2^\circ - 0.3^\circ$ suggests a violation of parity symmetry in the early universe. This would imply physics beyond the Standard Model, potentially involving axion-like particles or other dark sector fields interacting with photons.
• Future Directions: The paper emphasizes that reaching $5\sigma$ significance requires controlling systematics further. It calls for independent confirmation using experiments with artificial polarization sources (e.g., BICEP3, CLASS, Simons Observatory) that do not rely on Galactic polarization or optical models for calibration.

In conclusion, this paper provides a robust, model-dependent confirmation of a non-zero cosmic birefringence signal in ACT DR6 data, aligning with global trends in CMB research and pointing toward potential new fundamental physics.