BICEP/Keck XXI: Constraints on Early-Universe Parity Violation from Multipole-Dependent Birefringence

Abstract

We present the first constraints on multipole-dependent cosmic birefringence using CMB polarization data from the BK18 dataset, which combines observations from BICEP2, Keck Array, and BICEP3 at frequencies of 95, 150, and 220 GHz. Photon coupling to an axion-like field leads to the rotation of CMB polarization, inducing non-zero EB cross-correlations. We show that a multipole-dependent rotation beta(l) imprints a distinct signature in the polarization spectra that can be constrained. Specifically, we consider an Early Dark Energy (EDE) scenario in which a pseudoscalar field couples to photons through a Chern-Simons interaction, generating a polarization rotation with multipole dependence. We introduce a phenomenological beta(l) as a step function, obtaining constraints on the step function size consistent with zero, with uncertainties less than 0.15 degrees (68% CL). In addition, using multi-frequency EE, BB, and EB cross-spectra, along with robust BICEP/Keck foreground treatment and likelihood framework, we derive constraints on the axion-photon coupling amplitude g for several choices of EDE parameters. For the baseline best-fit value f_EDE = 0.087 from the Planck 2018 analysis, we obtain g = 0.11 +/- 0.37 (68% CL), consistent with previous limits.

Figures (9)

• Figure 1: Multipole dependence in Early Dark Energy. (Left) $EB$ and $EE$ spectra generated by Early Dark Energy models with different values of $f_{\mathrm{EDE}}$. As $f_{\mathrm{EDE}}$ increases, the $EB$ spectrum (blue) becomes more pronounced and deviates further from a constant rotation model, while the $EE$ spectrum (orange) stays roughly the same. $f_{\mathrm{EDE}}$ is the primary driver of these shifts Karwal2016Hill2022Herold2022, but other parameters (both EDE and standard cosmological parameters) also vary according to best fit values in Table \ref{['tab:ede_bestfits_reordered']}. Note that $EE$ spectra and $EB$ spectra are on different scales for visual comparison. (Right) Effective rotation angle (red) approximated by $\beta(\ell) = \frac{1}{4}\arcsin(2D_\ell^{EB} / D_\ell^{EE})$, where $EB$ (blue) is derived from an EDE model with $f_{\text{EDE}}=0.07$, and $EE$ (orange) is the best fit curve from Planck 2013. Constant-angle models are insufficient for fitting to $\beta(\ell)$.
• Figure 2: Comparison of simulated CMB spectra under isotropic vs. multipole-dependent rotation. (Left) Standard $\Lambda$CDM spectra rotated by different constant angles, $\beta_{\mathrm{cmb}}$ (isotropic birefringence only, $g=0$). (Right) Spectra including an Early Dark Energy contribution ($g=1$) rotated by different $\beta_{\mathrm{cmb}}$. The EDE signal introduces distinct features in the $EB$ spectrum that differ significantly from the isotropic case.
• Figure 3: Distributions of the jackknife $\chi^2$ and $\chi$ PTE values for the Keck Array 2016, 2017, and 2018 220 GHz data. This figure is analogous to Fig. 12 of BKXIII BICEPKeck2021b, but with an additional rightmost column showing the extended multipole range (bandpowers 1--14), explicitly checking that the higher multipole bandpowers also satisfy the jackknife consistency criteria.
• Figure 4: Step Function Constraints. Best-fit $\beta(\ell)$ step function for five values of the $\ell_b$ breakpoints with 1$\sigma$ uncertainty. All values are consistent with $\Delta\beta_{\ell_b}=0$.
• Figure 5: EDE Constraints. Posterior distribution on the axion-photon coupling $g$ from BK18 (this work), overlaid with the constraint from Planck EB analysis by Eskilt et al.Eskilt2023 with the EDE parameters from their baseline result.