利用普朗克温度角功率谱的非参数估计揭示CMB的声学物理
Unveiling acoustic physics of the CMB using nonparametric estimation of the temperature angular power spectrum for Planck
摘要：
角功率谱估计是宇宙微波背景（CMB）数据分析的重要步骤之一。在这里，我们提出了普朗克2013年CMB数据的温度角功率谱的非参数估计。在这项工作中实现的方法是模型独立的，并允许数据，而不是模型，来决定适合。由于我们分析的主要目标之一是测试$Λ$ CDM模型与普朗克2013年数据的一致性，因此我们使用与最佳拟合$Λ$ CDM角功率谱相关的干扰参数来消除多极$\ell \geq50$数据的前景贡献。因此，我们得到一个组合的角功率谱数据集连同完整的协方差矩阵，适当加权频率通道。我们随后的非参数分析解决了温度角功率谱中的六个峰（和五个谷）直到$\ell \sim1850$。我们在$95\%$置信水平下给出了峰/谷位置和高度的不确定性。我们进一步展示了这些如何反映声峰的谐波，并可用于声学尺度估计。基于这种非参数形式主义，我们发现最佳拟合的$Λ$ CDM模型与非参数置信集中心的置信距离为$36\%$--这远大于先前从WMAP 7年数据的类似分析中得出的置信距离（$9\%$）。我们分析的另一个有趣的结果是，在低多极，普朗克数据并没有表明任何上升，相反的期望基于集成的萨克斯-沃尔夫贡献的最佳拟合$Λ$ CDM宇宙学。
英文摘要：
Estimation of the angular power spectrum is one of the important steps in Cosmic Microwave Background (CMB) data analysis. Here, we present a nonparametric estimate of the temperature angular power spectrum for the Planck 2013 CMB data. The method implemented in this work is model-independent, and allows the data, rather than the model, to dictate the fit. Since one of the main targets of our analysis is to test the consistency of the $Λ$CDM model with Planck 2013 data, we use the nuisance parameters associated with the best-fit $Λ$CDM angular power spectrum to remove foreground contributions from the data at multipoles $\ell \geq50$. We thus obtain a combined angular power spectrum data set together with the full covariance matrix, appropriately weighted over frequency channels. Our subsequent nonparametric analysis resolves six peaks (and five dips) up to $\ell \sim1850$ in the temperature angular power spectrum. We present uncertainties in the peak/dip locations and heights at the $95\%$ confidence level. We further show how these reflect the harmonicity of acoustic peaks, and can be used for acoustic scale estimation. Based on this nonparametric formalism, we found the best-fit $Λ$CDM model to be at $36\%$ confidence distance from the center of the nonparametric confidence set -- this is considerably larger than the confidence distance ($9\%$) derived earlier from a similar analysis of the WMAP 7-year data. Another interesting result of our analysis is that at low multipoles, the Planck data do not suggest any upturn, contrary to the expectation based on the integrated Sachs-Wolfe contribution in the best-fit $Λ$CDM cosmology.
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