紧致拓扑下的跨频率随机引力波背景各向异性：CMB B模式协方差作为转移探针
Cross-frequency SGWB anisotropy from compact topology: CMB B-mode covariance as a transfer probe
- National Space Science Center, Chinese Academy of Sciences（中国科学院国家空间科学中心）
- Center for Gravitational Wave Experiment, National Microgravity Laboratory, Institute of Mechanics, Chinese Academy of Sciences（中国科学院力学研究所微重力国家实验室引力波实验中心）
- Key Laboratory of Gravitational Wave Precision Measurement of Zhejiang Province, Hangzhou Institute for Advanced Study, UCAS（浙江省引力波精密测量重点实验室，杭州高等研究院，中国科学院大学）
- Taiji Laboratory for Gravitational Wave Universe (Beijing/Hangzhou), University of Chinese Academy of Sciences (UCAS)（太极引力波宇宙实验室（北京/杭州），中国科学院大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究以CMB B模式协方差为转移探针，分析紧致拓扑下原初SGWB的跨频率各向异性，对比张量与标量通道，确定了相关信噪比转变阈值并分离出原初SGWB贡献。
AI中文摘要：
紧致空间拓扑会限制原初张量扰动的本征模式，由此产生的离散性可使原初随机引力波背景（SGWB）呈现各向异性。本文将CMB张量B模式协方差视为该超低频各向异性经转移滤波后的测量量。将归一化角张量功率度量表示为$F(k,\hat k)=1+Q(k,\hat k)$，其非单极矩表示为$q_{LM}(k)$，我们得到一个显式核函数，可将$q_{LM}(k)$映射到非对角协方差$\delta C^{BB}_{\ell m,\ell' m'}$。该核函数可分解为张量转移函数和自旋加权Gaunt系数，满足宇称规则：对于BB项，$L+\ell+\ell'$为偶数；对于TB/EB项，$L+\ell+\ell'$为奇数。它是完整紧致协方差的精确源-响应表示，而非额外可观测量。对于立方三维环面，该几何结构确定了跨频率带的公共立方角子空间和取向，尽管允许的多极矩振幅仍依赖于径向壳层和源谱。因此，同一拓扑限制模板既可以通过CMB B模式核函数读出，也可以通过PTA/LISA/Taiji/TianQin探测的各向异性响应读出。利用CAMB转移函数和不变各向异性模板统计量，我们对比了该张量通道与标量T/E协方差。独立的直接角壳层求和和$q_{LM}$-Gaunt收缩在$L_q^{\max}=2\ell_{\max}$下吻合，相对Frobenius残差为$1.4\times10^{-14}$至$3.0\times10^{-14}$。标量部分包含了大部分实用的CMB拓扑信息；固定模板扫描给出全天空联合信噪比（S/N）=1的转变位于$L/\chi_*=2.34$至$2.36$之间，而B模式通道仍处于阈值以下，但可分离出原初SGWB的贡献。
英文摘要：
Compact spatial topology restricts the eigenmodes of primordial tensor perturbations, and the resulting discreteness can render the primordial stochastic gravitational-wave background (SGWB) anisotropic. Here we treat the CMB tensor $B$-mode covariance as a transfer-filtered measurement of that ultra-low-frequency anisotropy. Writing the normalized angular tensor-power measure as $F(k,\hat k)=1+Q(k,\hat k)$ and its nonmonopole moments as $q_{LM}(k)$, we obtain an explicit kernel that maps $q_{LM}(k)$ onto the off-diagonal covariance $δC^{BB}_{\ell m,\ell' m'}$. The kernel factorizes into tensor transfer functions and a spin-weighted Gaunt coefficient and obeys the parity rule $L+\ell+\ell'$ even for $BB$ and odd for $TB/EB$. It is an exact source--response representation of the full compact covariance rather than an additional observable. For a cubic three-torus the geometry pins down a common cubic angular subspace and orientation across frequency bands, although the amplitudes of the allowed multipoles still depend on the radial shell and source spectrum. The same topology-restricted template can therefore be read out either through the CMB $B$-mode kernel or through the anisotropy response of PTA/LISA/Taiji/TianQin searches. Using CAMB transfer functions and an invariant anisotropic-template statistic, we contrast this tensor channel with the scalar $T/E$ covariance. Independent direct angular-shell sums and $q_{LM}$--Gaunt contractions agree at $L_q^{\max}=2\ell_{\max}$ to relative Frobenius residuals of $1.4\times10^{-14}$--$3.0\times10^{-14}$. The scalar sector holds most of the practical CMB topology information; a fixed-template scan places the combined full-sky $S/N=1$ transition between $L/χ_*=2.34$ and $2.36$, while the $B$-mode channel remains subthreshold but isolates the primordial SGWB contribution.
