Cosmic Birefringence in Cosmology

• Cosmic birefringence is the rotation of the plane of electromagnetic polarization over cosmological distances, signaling potential parity-violating phenomena.
• Observational strategies using radio galaxy emissions, UV polarization, and CMB data employ precise calibration and statistical techniques to detect subtle rotation angles.
• Empirical constraints on cosmic birefringence provide critical limits on axion-like particles, dark energy models, and extensions to the Standard Model.

Cosmic birefringence is defined as a rotation of the plane of linear polarization of electromagnetic radiation as it traverses cosmological distances, predicted to occur in models where new, parity-violating physics augments the standard electromagnetic Lagrangian. This parity violation can stem from extensions of the Standard Model, such as Chern–Simons-type couplings to axion-like fields, early dark energy, or Lorentz-violating terms. In observational cosmology, cosmic birefringence is probed through the polarized flux from distant radio galaxies, ultraviolet (UV) polarization from active galactic nuclei, and, most stringently, by the cosmic microwave background (CMB) polarization measurements, where its signature is a frequency-independent, global (isotropic) or spatially varying (anisotropic) rotation angle that mixes E and B polarization modes. Constraints on this effect place direct limits on new physics scenarios and may inform the nature of dark energy, dark matter, and early-universe dynamics.

1. Physical Principles and Theoretical Motivation

Cosmic birefringence arises generically when parity is not a symmetry of the photon propagation Hamiltonian over cosmological distances. The most widely considered scenario involves an additional Chern–Simons term in the Lagrangian,

$$\mathcal{L}_{\text{CS}} \sim \frac{\phi}{M} F_{\mu\nu} \tilde{F}^{\mu\nu},$$

where $F_{\mu\nu}$ is the electromagnetic field strength, $\tilde{F}^{\mu\nu}$ its dual, $\phi$ a pseudo-scalar (typically an axion-like field), and $M$ a high mass scale (Contreras et al., 2017, Alighieri, 2010). As photons traverse cosmological distances in this background, the left and right circularly polarized states accumulate different phase velocities, resulting in a rotation of linear polarization by an angle

$$\alpha = \frac{g_{\phi\gamma}}{2} \left[\phi(t_0) - \phi(t_{\text{LSS}})\right],$$

where $g_{\phi\gamma}$ is the coupling constant. Extensions include models with multiple pseudo-scalars (“Axiverse”) (Gasparotto et al., 2023), scalar-tensor quintessence, Lorentz/CPT violation, and scenarios coupling axion fields to dark photons (Lee et al., 2023).

The rotation angle may possess both a uniform (monopole/isotropic) component $\alpha_0$ and an anisotropic component $\delta\alpha(\hat{\mathbf{n}})$ arising from spatial fluctuations in the field (Greco et al., 2022). The isotropic (all-sky) rotation directly signals parity violation and, if detected, would be evidence for low-mass, weakly-coupled fields beyond the Standard Model (Nakai et al., 2023, Luo et al., 2023).

2. Observational Strategies and Measurement Techniques

Astrophysical tests for cosmic birefringence employ three primary methodologies (Alighieri, 2010):

1. Radio polarization of distant radio galaxies and quasars: By comparing the observed polarization angle with known or inferred emission geometry (typically the radio axis), after correcting for Faraday rotation, deviations from perpendicularity or parallelism are attributed to birefringence. Early limits excluded rotations $|\Delta\theta| \gtrsim 6^\circ$ (95% CL) for $0.4 < z < 1.5$, with more recent, high-resolution samples showing null results at the level of $\theta = -0.6 \pm 1.5^\circ$. The main challenge is uncertainty in intrinsic polarization orientation and complex source structures.
2. Ultraviolet polarization from AGN: In radio-loud AGN, the scattering geometry is well-constrained and predicts the polarization to be strictly perpendicular to extended UV structures. Measurements for 3C 265 (z = 0.811) yield $\theta = -1.4 \pm 1.1^\circ$, with sample-averaged results at $z \sim 2.8$ giving $\theta = -0.8 \pm 2.2^\circ$. UV measurements are robust against Faraday rotation but limited by source faintness.
3. CMB polarization: CMB photons, last-scattered at $z \sim 1100$, carry a predictable polarization pattern set by Thomson scattering and acoustic oscillations. Birefringence generates parity-violating correlations, most notably nonzero $TB$ and $EB$ angular power spectra, which are otherwise forbidden in the standard $\Lambda$CDM model. Modern experiments (e.g., Planck, ACT, POLARBEAR, BICEP, LiteBIRD) employ harmonic-space estimators and map-space methods to search for isotropic ($\beta$) and anisotropic ($\delta\alpha(\hat{\mathbf{n}})$) rotation.

A representative formalism is

$$C_\ell^{EB,\,\mathrm{obs}} = \frac{1}{2} \sin(4\beta) \left[ C_\ell^{EE} - C_\ell^{BB} \right],$$

or, with polarization angle miscalibration $\alpha$,

$$C_\ell^{EB,\,\mathrm{obs}} = \frac{1}{2} \sin 4(\beta+\alpha) \left[ C_\ell^{EE} - C_\ell^{BB} \right],$$

necessitating joint estimation techniques or foreground cross-calibration to break degeneracies (Diego-Palazuelos et al., 2022, Diego-Palazuelos et al., 2022).

For the anisotropic component, quadratic estimators constructed from $EB$ and $TB$ cross-spectra or map-space peak stacking are optimal, as they minimize cosmic variance and instrumental noise (Yadav et al., 2012). Bispectrum analyses provide additional consistency checks, exploiting the unique parity structure of three-point functions (Greco et al., 2022).

3. Principal Results and Empirical Constraints

The most stringent bounds and most debated results arise from CMB polarization analyses. Key empirical findings include:

• Planck and WMAP data: Indicate isotropic birefringence angles in the range $\beta \simeq 0.30 \pm 0.05^\circ$ (not including systematic uncertainties), with specific measurements such as $\beta = 0.30 \pm 0.11^\circ$ (Diego-Palazuelos et al., 2022, Diego-Palazuelos et al., 2022, Ballardini et al., 22 Jul 2025) and, with map-space analysis, $$\beta = 0.46^\circ \pm 0.04^\circ_\text{stat} \pm 0.28^\circ_\text{syst}$$ (Sullivan et al., 11 Feb 2025). The statistical significance typically ranges from $2.4$ to $3.6\sigma$, but instrumental systematics—primarily the absolute miscalibration of polarization angles—dominate the total error budget.
• ACT DR6: Reports $\beta = 0.215^\circ \pm 0.074^\circ$ (68% CL), a $2.9\sigma$ deviation from zero, consistent in sign and magnitude with Planck/WMAP (Diego-Palazuelos et al., 17 Sep 2025). Bayesian techniques are employed with priors on instrument miscalibrations.
• Upper limits on anisotropic birefringence: Recent Planck analyses provide 95% CL upper limits on scale-invariant rotation field amplitude of $\sim 0.07~\mathrm{deg}^2$, with dipolar and quadrupolar components measured at $\lesssim 0.2^\circ$ and $\lesssim 0.1^\circ$ respectively (Contreras et al., 2017). No robust evidence exists for large-scale direction-dependent birefringence.
• Power spectrum and scale dependence: There is no significant evidence for harmonic scale dependence of $\beta_{\ell}$ up to $L \sim 1500$; Bayesian reconstructions and power-law fits robustly favor an isotropic, constant signal within current measurement precision (Ballardini et al., 22 Jul 2025).

4. Mitigation of Instrumental and Foreground Systematics

Extraction of the true cosmic birefringence signal is fundamentally limited by systematic errors:

• Instrumental miscalibration: An unknown uniform rotation of the polarimeter’s calibration angle ($\alpha$) is perfectly degenerate with any isotropic CB signal. This is partially broken by exploiting the fact that the polarized Galactic foreground emission, being local, is unaffected by CB. By modeling the observed $EB$ and $TB$ spectra as the sum of cosmic and instrumental rotations and by using foreground polarization as a calibrator, analyses can independently constrain $\beta$ and $\alpha$ (Diego-Palazuelos et al., 2022, Diego-Palazuelos et al., 2022).
• Foreground $EB$ contamination: Galactic dust and synchrotron emission can introduce spurious $EB$ correlations due to imperfect alignment of magnetic fields and filamentary structures. Two modeling approaches—the "filament model" (using dust geometry and TB/TE ratios) and Commander-based foreground templates—are utilized to correct for this bias, restoring the measured $\beta$ to consistency across sky masks (Diego-Palazuelos et al., 2022, Diego-Palazuelos et al., 2022).
• Residual leakage and spatial variation: End-to-end instrument simulations and map-space analyses are employed to monitor spatially varying systematics and potential anisotropies, finding no significant evidence for direction-dependent CB but indicating small mask- or region-dependent fluctuations, possibly due to foreground residuals or spatially varying calibration (Sullivan et al., 11 Feb 2025).
• Simulation pipelines and future calibration: Simulations with complex, spatially variable foregrounds and random instrumental miscalibration demonstrate the robustness of component-separation and parameter estimation pipelines for future missions (e.g., LiteBIRD), which project achievable uncertainties on $\beta$ down to $\sim 0.02^\circ$ (Hoz et al., 28 Mar 2025).

5. Implications for Fundamental Physics

A robust detection of cosmic birefringence would provide direct evidence for parity-violating new physics. Scenarios constrained or explored by current measurements include:

• Axion-like particles and the Axiverse: The magnitude and isotropy of $\beta$ set direct constraints on axion-photon coupling, initial misalignment, and mass distributions within multi-field (Axiverse) models, with implications for dark matter abundance and the possible tomographic reconstruction of axion properties (Gasparotto et al., 2023, Luo et al., 2023).
• Early dark energy and the Hubble tension: Early dark energy models based on pseudo-Nambu–Goldstone bosons predict anisotropic CB linked to the EDE field’s dynamics. The detection of both the birefringence power spectrum $C_L^{\alpha\alpha}$ and its cross-correlation with CMB temperature would provide evidence in favor of these solutions and potentially discriminate between mechanisms addressing the Hubble tension (Capparelli et al., 2019).
• Limits of Standard Model effective field theory (SMEFT): Systematic studies demonstrate that within SMEFT (and in LEFT at CMB energies), no operator—whether involving dimension-2, -3, or -4 Standard Model combinations—produces a sufficiently large, frequency-independent CB angle. Even neutrino-photon parity-violating interactions yield rotation effects orders of magnitude below observed values. A plausible implication is that any confirmed detection of cosmic birefringence would require a new, light (sub-electroweak) field with extremely weak interactions, such as an ALP (Nakai et al., 2023).
• Constraints on ultralight ALP dark matter: For conventional ALP masses ($10^{-25}$–$10^{-23}$ eV), nonlinear clustering cannot explain the observed static birefringence due to the washout effect during CMB decoupling, placing stringent upper limits on the allowable photon-ALP coupling (Zhang et al., 15 Aug 2024).
• Domain wall and dark photon models: If ALP domain walls formed during inflation, they could produce “kilobyte cosmic birefringence,” encoding discrete information in the rotation pattern, while kinetic mixing with birefringent dark photons could induce both isotropic and anisotropic CB, as well as CMB spectral distortions and circular polarization – all signatures of nonstandard parity-violating physics (Takahashi et al., 2020, Lee et al., 2023).

6. Future Prospects and Experimental Sensitivity

Anticipated advances in experimental sensitivity and systematic control are poised to significantly tighten constraints, as forecasted in both Planck and future mission analyses:

• LiteBIRD, Simons Observatory, and CMB Stage-4 are projected to reduce current uncertainties on $\beta$ by factors of 5–7, reaching a statistical error of $0.01^\circ$–$0.02^\circ$ for an isotropic rotation (Hoz et al., 28 Mar 2025, Ballardini et al., 22 Jul 2025). Simulations demonstrate that the combined power of multi-band polarization data and robust analysis frameworks will enable detection of CB down to $\sim0.02^\circ$ with $5$–$13\sigma$ significance if the signal persists.
• Large-scale anisotropy and bispectrum analysis: Future missions will systematically search for spatial variation in CB at high significance, exploiting map-space and harmonic estimators and cross-correlations (Bortolami et al., 2022, Greco et al., 2022).
• Mitigation of systematics: Improved hardware calibration (e.g., using in-flight polarized sources), sophisticated component separation, and refined foreground modeling are essential for breaking the degeneracy between cosmological signal and instrumental/foreground systematics.
• Interpretational robustness: Combined analyses across independent CMB experiments (Planck, ACT, SPT, LiteBIRD, etc.), radio/UV galaxy polarimetry, and tomographic studies of CB at different cosmological epochs will be necessary to confirm or refute a cosmological origin and to distinguish among possible new-physics scenarios (Diego-Palazuelos et al., 17 Sep 2025).

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Cosmic birefringence remains a highly active research topic at the intersection of observational cosmology and high-energy physics. While no compelling detection is yet claimed, current analyses suggest intriguing hints of an isotropic rotation of the CMB polarization, compatible with parity-violating extensions of the Standard Model. Significant advances are anticipated in coming years, with the potential for a discovery that would directly constrain or reveal new fundamental fields and interactions on cosmological scales.