The Chern-Simons term, through which the cosmic Axion-like field couples to the electromagnetic field, has the effect to rotate CMB polarization directions and to break the CPT symmetry. This rotation will change the CMB power spectra, no matter isotropic or anisotropic the rotation angle is. In this paper we revisit this issue by further considering the correlations between the (anisotropic) rotation angle $\alpha$ and the CMB temperature and (unrotated) $E$ polarization fields. These correlations could be generated in the Axion-like models with nonzero potential under the adiabatic initial condition. We first investigate how these correlations contribute further modifications to the CMB power spectra, then calculate the CMB bispectra for the temperature and rotated polarization fields. These bispectra would vanish if the $T\alpha$ and $E\alpha$ correlations are absent. So, they are useful in searching for CPT violation and the $T\alpha$ and $E\alpha$ correlations arisen in the Axion-like models.

中文翻译：

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偏振旋转对CMB功率谱和双谱的影响及其与温度和E偏振的相关性

Chern-Simons 项，通过该项将类宇宙轴子场耦合到电磁场，具有旋转 CMB 极化方向和破坏 CPT 对称性的效果。无论旋转角度是各向同性还是各向异性，这种旋转都会改变 CMB 功率谱。在本文中，我们通过进一步考虑（各向异性）旋转角 $\alpha$ 与 CMB 温度和（未旋转的）$E$ 极化场之间的相关性来重新讨论这个问题。这些相关性可以在绝热初始条件下具有非零电位的类轴子模型中生成。我们首先研究这些相关性如何进一步修改 CMB 功率谱，然后计算温度和旋转偏振场的 CMB 双谱。如果不存在 $T\alpha$ 和 $E\alpha$ 相关性，这些双谱将消失。因此，它们可用于搜索 CPT 违规以及类似 Axion 模型中出现的 $T\alpha$ 和 $E\alpha$ 相关性。