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arXiv 2411.08087astro-ph.COgr-qc

Fréchet向量作为CMB异常盲检验的敏感工具

Fréchet Vectors as sensitive tools for blind tests of CMB anomalies

Ricardo G. Rodrigues, Thiago S. Pereira, Miguel Quartin

备注：
28 pages, 13 figures. Matches published version
发表信息：
JCAP 06 (2025) 039
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AI总结：

本文提出利用Fréchet向量作为盲检验工具，通过模拟和Planck数据证明其能灵敏检测CMB异常，并在小尺度上以高显著性拒绝标准假设。

摘要：

在球面上收集的宇宙学数据，如CMB各向异性，通常由球谐系数表示，记为$a_{\ell m}$。角功率谱，即$C_\ell$，是该数据方差的基本估计量。或者，球面数据及其方差也可以用多极向量（MVs）和Fréchet方差来表征。最小化该方差的向量，称为Fréchet向量（FVs），定义了紧致空间上点的质心，并且是不同多极之间统计相关性的极佳指标。我们通过模拟和真实数据来证明这一点。通过模拟，我们表明FVs能够盲检测并重建在原本各向同性的天空中引入的模拟冷斑异常的位置。将这些工具应用于2018年Planck地图，我们在先前对高斯性和统计各向同性的零假设检验中实施了若干改进，直至弧分级尺度。当应用共同掩膜时，Planck的MVs在尺度$2 \leq\ell \leq 1500$上与这些假设一致，而使用FVs的相同检验则以5.3至8.2$\sigma$的显著性拒绝它们。包含各向异性噪声模拟使得FVs在同一尺度上与零假设勉强一致（$\geq 2\sigma$），但当我们考虑$\ell>1500$以上的尺度（信噪比很小）时，仍以3.5-3.7$\sigma$的显著性拒绝它们。噪声和/或前景建模的局限性可能解释这些与零假设的偏差。

英文摘要：

Cosmological data collected on a sphere, such as CMB anisotropies, are typically represented by the spherical harmonic coefficients, denoted as $a_{\ell m}$. The angular power spectrum, or $C_\ell$, serves as the fundamental estimator of the variance in this data. Alternatively, spherical data and their variance can also be characterized using Multipole Vectors (MVs) and the Fréchet variance. The vectors that minimize this variance, known as Fréchet Vectors (FVs), define the center of mass of points on a compact space, and are excellent indicators of statistical correlations between different multipoles. We demonstrate this using both simulations and real data. Through simulations, we show that FVs enable a blind detection and reconstruction of the location associated with a mock Cold Spot anomaly introduced in an otherwise isotropic sky. Applying these tools to the 2018 Planck maps, we implement several improvements on previous null tests of Gaussianity and statistical isotropy, down to arc-minute scales. Planck's MVs appear consistent with these hypotheses at scales $2 \leq\ell \leq 1500$ when the common mask is applied, whereas the same test using the FVs rejects them with significances between 5.3 and 8.2$σ$. The inclusion of anisotropic noise simulations render the FVs marginally consistent ($\geq 2σ$) with the null hypotheses at the same scales, but still rejects them at $3.5-3.7σ$ when we consider scales above $\ell=1500$, where the signal-to-noise is small. Limitations of the noise and/or foregrounds modeling may account for these deviations from the null hypothesis.

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