CMB 2 pcf的新几何表示
New Geometric Representations of the CMB 2pcf
摘要：
当在CMB中搜索统计各向同性的偏差时，流行的策略是将两点关联函数（2 pcf）写为四个球面角的最一般函数（即，两个单位向量）在天球中。然后，使用双极球谐函数的基础上，统计各向异性将显示，当且仅当任何系数的膨胀与非平凡的双极动量被检测到-虽然这种检测将不会在一般阐明起源的各向异性。在这项工作中，我们表明，存在两组新的四个角度和基函数，完全指定2 pcf，同时，提供了一个更清晰的几何解释的机制产生的信号。由于这些展开式的系数为零，当且仅当各向同性成立，它们作为统计各向同性的简单和几何动机的零测试，其优点是允许宇宙方差以系统的方式控制。我们报告的结果，这些零测试的应用程序的最新温度数据公布的普朗克合作。
英文摘要：
When searching for deviations of statistical isotropy in CMB, a popular strategy is to write the two-point correlation function (2pcf) as the most general function of four spherical angles (i.e., two unit vectors) in the celestial sphere. Then, using a basis of bipolar spherical harmonics, statistical anisotropy will show up if and only if any coefficient of the expansion with non-trivial bipolar momentum is detected -- although this detection will not in general elucidate the origin of the anisotropy. In this work we show that two new sets of four angles and basis functions exist which completely specifies the 2pcf, while, at the same time, offering a clearer geometrical interpretation of the mechanisms generating the signal. Since the coefficients of these expansions are zero if and only if isotropy holds, they act as a simple and geometrically motivated null test of statistical isotropy, with the advantage of allowing cosmic variance to be controlled in a systematic way. We report the results of the application of these null tests to the latest temperature data released by the Planck collaboration.
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