Weak lensing of the CMB: A harmonic approach
Weak lensing of the CMB: A harmonic approach
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DOI：
10.1103/physrevd.62.043007
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发表时间：
2000-01
影响因子：
5
通讯作者：
Wayne Hu
中科院分区：
文献类型：
--
作者：
Wayne Hu
功率谱和高阶统计量的CMB各向异性和偏振的弱透镜可以直接在谐波空间中处理，而无需求助于实空间相关函数。对于功率谱，这种方法不仅简化了计算，而且通过用球谐函数代替傅里叶谐函数，很容易从通常的平天近似推广到精确的全天形式。与直觉相反的是，由于这种效应的非线性性质，平天近似的误差在较小的尺度上不会改善。它们在声学状态下保持在10%的水平，并且足够大，值得采用全天空形式主义。对于bispectra，宇宙方差有限检测的相关性与二次各向异性有一个数量级更大的信噪比的组合，涉及磁宇称极化比那些涉及单独的温度。然而，即使使用普朗克卫星，对这些双谱的检测也会受到严重的噪声和前景限制，从而为更高灵敏度的实验留下了改进的空间。我们还提供了一个一般性的研究之间的对应关系，平面和所有的天空潜力，偏转角，收敛和剪切的功率谱和双谱。
Weak lensing of CMB anisotropies and polarization for the power spectra and higher order statistics can be handled directly in harmonic-space without recourse to real-space correlation functions. For the power spectra, this approach not only simplifies the calculations but is also readily generalized from the usual flat-sky approximation to the exact all-sky form by replacing Fourier harmonics with spherical harmonics. Counterintuitively, because of the nonlinear nature of the effect, errors in the flat-sky approximation do not improve on smaller scales. They remain at the 10% level through the acoustic regime and are sufficiently large to merit adoption of the all-sky formalism. For the bispectra, a cosmic variance limited detection of the correlation with secondary anisotropies has an order of magnitude greater signal-to-noise for combinations involving magnetic parity polarization than those involving the temperature alone. Detection of these bispectra will, however, be severely noise and foreground limited even with the Planck satellite, leaving room for improvement with higher sensitivity experiments. We also provide a general study of the correspondence between flat and all sky potentials, deflection angles, convergence and shear for the power spectra and bispectra.