宇宙学中零均值假设的检验
A Test for the Zero Mean Hypothesis in Cosmology
摘要：
分析宇宙学数据的一个工作假设是零系综平均假设，它与宇宙学扰动的统计均匀性有关。然而，这个假设应该在当今精密宇宙学时代的观测数据中得到检验。在这里，我们测试的假设，通过分析最近，前景减少宇宙微波背景（CMB）的地图，结合球谐系数的掩蔽CMB温度各向异性的方式，组合的变量可以被视为统计独立的样本。我们发现证据反对零均值假设在两个特定范围的多极，与显著水平的$2.5 σ$和$3.1 σ$的多极范围的$\ell \approx 61$ - $86$和$213$ - $256$，分别为普朗克和威尔金森微波各向异性探测地图。后者的信号是一致的，我们以前的结果发现，通过使用蛮力蒙特卡罗模拟。然而，在本文中所采用的方法，我们得出结论，零均值假设是一致的，与目前的CMB数据的基础上，斯托弗的加权Z统计，其中考虑到多重检验。
英文摘要：
One working hypothesis on which analyses of cosmological data are based is the zero ensemble mean hypothesis, which is related to the statistical homogeneity of cosmological perturbations. This hypothesis, however, should be tested by observational data in the current era of precision cosmology. Herein, we test the hypothesis by analyzing recent, foreground-reduced cosmic microwave background (CMB) maps, combining the spherical harmonic coefficients of the masked CMB temperature anisotropies in such a way that the combined variables can be treated as statistically independent samples. We find evidence against the zero mean hypothesis in two particular ranges of multipoles, with significance levels of $2.5 σ$ and $3.1 σ$ in the multipole ranges of $\ell \approx 61$-$86$ and $213$-$256$, respectively, for both the Planck and Wilkinson Microwave Anisotropy Probe maps. The latter signal is consistent with our previous result found by using brute-force Monte-Carlo simulations. However, within the method employed in this paper we conclude that the zero mean hypothesis is consistent with the current CMB data on the basis of Stouffer's weighted Z statistics, which takes multiple testing into account.
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