Full-sky formulae far weak lensing power spectrum from total angular momentum moethod
Full-sky formulae far weak lensing power spectrum from total angular momentum moethod
复制标题
总角动量法的全天空公式远弱透镜功率谱
DOI：
10.1088/1475-7516/2013/08/051
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发表时间：
2013
影响因子：
6.4
通讯作者：
A. Taruya
中科院分区：
文献类型：
--
作者：
D. Yamauchi;T. Namikawa;A. Taruya
我们从总角动量（TAM）方法中系统地推导出由标量、矢量和张量扰动产生的弱透镜功率谱的全天空公式。基于测地线和测地线偏差方程，我们首先给出偏转角和雅可比图的规范不变表达式，作为CMB透镜和宇宙剪切实验的可观测量。然后，我们应用最初在 CMB 理论研究中开发的 TAM 方法来系统地推导角功率谱。 TAM 表示表征沿视线投影的空间模式的总角度依赖性，可以携带由标量、矢量和张量度量扰动生成的透镜模式的所有信息。这极大地简化了计算，并且我们提出了一套完整的E/B模式宇宙剪切和偏转角梯度/卷曲模式透镜势中角功率谱的全天空公式。基于这些公式，我们给出了在存在矢量和张量扰动的情况下非消失 B 模式宇宙剪切和偏转角旋度模式的说明性示例，并明确计算了功率谱。
We systematically derive full-sky formulae for the weak lensing power spectra generated by scalar, vector and tensor perturbations from the total angular momentum (TAM) method. Based on both the geodesic and geodesic deviation equations, we first give the gauge-invariant expressions for the deflection angle and Jacobi map as observables of the CMB lensing and cosmic shear experiments. We then apply the TAM method, originally developed in the theoretical studies of CMB, to a systematic derivation of the angular power spectra. The TAM representation, which characterizes the total angular dependence of the spatial modes projected along a line-of-sight, can carry all the information of the lensing modes generated by scalar, vector, and tensor metric perturbations. This greatly simplifies the calculation, and we present a complete set of the full-sky formulae for angular power spectra in both the E-/B-mode cosmic shear and gradient-/curl-mode lensing potential of deflection angle. Based on the formulae, we give illustrative examples of non-vanishing B-mode cosmic shear and curl-mode of deflection angle in the presence of the vector and tensor perturbations, and explicitly compute the power spectra.