Cosmic birefringence is the in-vacuo, frequency independent rotation of the polarization plane of linearly polarized radiation, induced by a parity-violating term in the electromagnetic Lagrangian. We implement a harmonic estimator for the birefringence field that only relies on the CMB E to B mode cross-correlation, thus suppressing the effect of cosmic variance from the temperature field. We derive constraints from Planck public releases 3 and 4, revealing a cosmic birefringence power spectrum consistent with zero at about 2σ up to multipole L = 1500. Moreover, we find that the cross-correlations of cosmic birefringence with the CMB T-, E- and B-fields are also well compatible with null. The latter two cross-correlations are provided here for the first time up to L = 1500.

中文翻译：

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宇宙双折射的普朗克约束及其与 CMB 的互相关

宇宙双折射是线性偏振辐射的偏振面在真空中、与频率无关的旋转，由电磁拉格朗日中的宇称破坏项引起。我们实现了一种双折射场谐波估计器，仅依赖于 CMB E 到 B 模式互相关，从而抑制了温度场的宇宙方差的影响。我们得出约束条件普朗克公开版本 3 和 4，揭示了宇宙双折射功率谱在大约 2 处与零一致σ最多多极L= 1500。此外，我们发现宇宙双折射与CMB T场、E场和B场的互相关性也与零值很好地兼容。后两个互相关在这里首次提供L= 1500。