We consider the benefits of measuring cosmic statistical anisotropy from redshift-space correlators of the galaxy number density fluctuation and the peculiar velocity field without adopting the plane-parallel (PP) approximation. Since the correlators are decomposed using the general tripolar spherical harmonic (TripoSH) basis, we can deal with wide-angle contributions untreatable by the PP approximation, and at the same time, target anisotropic signatures can be cleanly extracted. We, for the first time, compute the covariance of the TripoSH decomposition coefficient and the Fisher matrix to forecast the detectability of statistical anisotropy. The resultant expression of the covariance is free from nontrivial mixings between each multipole moment caused by the PP approximation and hence the detectability is fully optimized. Compared with the analysis under the PP approximation, the superiority in detectability is always confirmed, and it is highlighted, especially in the cases that the shot noise level is large and that target statistical anisotropy has a blue-tilted shape in Fourier space. The application of the TripoSH-based analysis to forthcoming all-sky survey data could result in constraints on anisotropy comparable to or tighter than the current cosmic microwave background ones.

我们考虑了在不采用平面平行 (PP) 近似的情况下从星系数密度波动和特殊速度场的红移空间相关器测量宇宙统计各向异性的好处。由于使用一般三极球谐函数 (TripoSH) 基分解相关器，我们可以处理 PP 近似无法处理的广角贡献，同时可以清晰地提取目标各向异性特征。我们首次计算了TripoSH分解系数和Fisher矩阵的协方差来预测统计各向异性的可检测性。协方差的结果表达式没有由 PP 近似引起的每个多极矩之间的非平凡混合，因此可检测性得到充分优化。与PP近似下的分析相比，可探测性的优越性始终得到证实，并且突出，特别是在散粒噪声水平较大且目标统计各向异性在傅里叶空间呈蓝色倾斜形状的情况下。将基于 TripoSH 的分析应用于即将到来的全天空调查数据可能会导致对各向异性的限制与当前宇宙微波背景的限制相当或更严格。