Department of Physics and Astronomy, Johns Hopkins University, Baltimore, Maryland 21218, USA.
Phys Rev Lett. 2014 Jan 31;112(4):041303. doi: 10.1103/PhysRevLett.112.041303. Epub 2014 Jan 28.
When a cosmic microwave background (CMB) photon travels from the surface of last scatter through spacetime metric perturbations, the polarization vector may rotate about its direction of propagation. This gravitational rotation is distinct from, and occurs in addition to, the lensing deflection of the photon trajectory. This rotation can be sourced by linear vector or tensor metric perturbations and is fully coherent with the curl deflection field. Therefore, lensing corrections to the CMB polarization power spectra as well as the temperature-polarization cross correlations due to nonscalar perturbations are modified. The rotation does not affect lensing by linear scalar perturbations, but needs to be included when calculations go to higher orders. We present complete results for weak lensing of the full-sky CMB power spectra by general linear metric perturbations, taking into account both deflection of the photon trajectory and rotation of the polarization. For the case of lensing by gravitational waves, we show that the B modes induced by the rotation largely cancel those induced by the curl component of deflection.
当一个宇宙微波背景（CMB）光子从最后散射面穿过时空度量波动时，偏振矢量可能会在其传播方向上旋转。这种引力旋转与光子轨迹的透镜偏折不同，并且是在其之外发生的。这种旋转可以由线性矢量或张量度量波动引起，并且与卷曲偏转场完全相干。因此，CMB 偏振功率谱中的透镜修正以及由于非标量扰动引起的温度-偏振交叉相关都会发生改变。旋转不会影响线性标量扰动的透镜作用，但在计算进行到更高阶时需要将其包括在内。我们给出了由一般线性度量波动对全天空 CMB 功率谱进行弱透镜的完整结果，同时考虑了光子轨迹的偏折和偏振的旋转。对于引力波透镜的情况，我们表明旋转引起的 B 模式在很大程度上抵消了由偏转的卷曲分量引起的 B 模式。
