星系巡天统计各向异性的最小方差估计
Minimum variance estimation of statistical anisotropy via galaxy survey
摘要：
我们考虑的好处，测量宇宙统计各向异性的星系数密度波动和奇特的速度场的红移空间的放大器，而不采用平面平行（PP）近似。由于相关器是使用一般三极球谐（TripoSH）基分解的，因此我们可以处理PP近似无法处理的广角贡献，同时可以干净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。由此产生的协方差表达式是免费的非平凡的混合之间的每个多极矩所造成的PP近似，因此，检测能力是完全优化的。与PP近似下的分析相比，在可检测性方面的优越性总是被确认的，并且特别是在散粒噪声水平大并且目标统计各向异性在傅立叶空间中具有蓝倾斜形状的情况下，其被突出。将TripoSH分析应用于即将进行的全天巡天数据，可能导致对各向异性的限制与目前的宇宙微波背景限制相当或更严格。
英文摘要：
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.
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