发表机构
Graduate School of Science, Nagoya University; Gifu Shotoku Gakuen University; Kobayashi-Maskawa Institute for the Origin of Particles and the Universe, Nagoya University; Institute for Advanced Research, Nagoya University（名古屋大学研究生院; 岐阜圣德学园大学; 名古屋大学小林-益川粒子宇宙起源研究所; 名古屋大学高等研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究CMB B模偏振对宇宙拓扑（立方三维环面）约束的影响，发现即使理想条件下，B模仅带来边际改进，温度、E模和B模的约束能力差异源于传递函数和拓扑诱导的非对角相关性。
AI 中文摘要
宇宙的全局空间结构是宇宙学中的一个基本问题。尽管标准模型通常假设平凡的拓扑结构，但多重连通宇宙可能破坏统计各向同性，并在宇宙微波背景涨落的球谐系数之间产生非对角协方差。在本工作中，我们研究CMB B模偏振是否能够改进对立方三维环面（即$E_1$拓扑）的约束。我们构建了温度、E模和原初B模各向异性的完整谐波空间协方差矩阵，包括不同$(\ell,m)$模之间的相关性，并使用从具有平凡拓扑的统计各向同性$\Lambda$CDM模型生成的随机实现来评估高斯似然。为了隔离每个CMB观测量所携带的内在拓扑信息，我们考虑了理想的宇宙方差极限情况，忽略了仪器噪声和引力透镜效应。我们发现，即使在这些理想条件下，加入原初B模偏振对区分$E_1$拓扑与平凡拓扑的能力仅带来边际改善。温度、E模和B模各向异性的不同约束能力可以通过它们的传递函数响应和拓扑引起的谐波空间非对角相关性的综合效应来理解。
英文摘要
The global spatial structure of the universe is a fundamental question in cosmology. Although the standard model usually assumes a trivial topology, a multiply connected universe can break statistical isotropy and generate off-diagonal covariance between the spherical-harmonic coefficients of cosmic microwave background fluctuations. In this work, we investigate whether CMB B-mode polarization improves constraints on the cubic three-torus, or $E_1$ topology. We construct the full harmonic-space covariance matrices of the temperature, E-mode, and primordial B-mode anisotropies, including correlations between different $(\ell,m)$ modes, and evaluate Gaussian likelihoods using random realizations generated from a statistically isotropic $Λ$CDM model with trivial topology. To isolate the intrinsic topological information carried by each CMB observable, we consider the ideal cosmic-variance-limited case, neglecting instrumental noise and gravitational lensing. We find that adding primordial B-mode polarization yields only a marginal improvement in the ability to distinguish the $E_1$ topology from the trivial topology, even under these ideal conditions. The different constraining powers of the temperature, E-mode, and B-mode anisotropies can be understood through the combined effects of their transfer-function responses and the topology-induced off-diagonal correlations in harmonic space. }
Comments23 pages, 7 figures
