AI 中文总结
针对大视场星系巡天中相对论与广角效应显著的问题，本研究基于总角动量形式体系提出新的广角预测参数化方案，开发出可高效计算相对论性角功率谱的PowerFull工具，证实忽略相关效应会导致原初非高斯性参数$f_\text{NL}$的推断偏差。
AI 中文摘要
当前及即将开展的大视场星系巡天（如SPHEREx和Euclid）为探测结构形成的超极大尺度提供了独特机遇，通常以$f_\text{NL}$参数化的原初非高斯性预计会在这些尺度留下最易探测的印记。与此同时，这些巡天不可避免地进入相对论效应和广角效应变得显著的区间，需要精细建模以提取无偏的宇宙学信息。我们通过应用总角动量（TAM）形式体系来描述超出平天近似的红移空间成团性，以应对这些挑战。标准傅里叶模描述通过模与视线之间的角度来表征畸变，在大视场下会变得定义不明确，而TAM基可以自然地分离径向和角向贡献，并纳入相关的相对论效应。在该框架内，我们提出了一种新的广角预测参数化方案，可直接与巡天数据进行比较。随后我们介绍了PowerFull——这是对基于Julia语言的2-FAST程序包的改进版本，能够高效计算完整的相对论性角功率谱。最后，通过基于费希尔信息矩阵的分析，我们表明类似SPHEREx的巡天可达到$σ(f_\text{NL}) \sim 1$的精度，但忽略相对论和广角贡献会使反演得到的$f_\text{NL}$产生与其自身不确定度量级相当的偏移：在这一精度下，除非对成团性进行自洽建模，否则推断值将存在偏差。
英文摘要
Current and forthcoming wide-field galaxy surveys, such as SPHEREx and Euclid, provide a unique opportunity to probe the ultra-large scales of structure formation, where primordial non-Gaussianity, often parameterized by $f_\text{NL}$, is expected to leave its most detectable imprint. At the same time, these surveys inevitably enter regimes where relativistic and wide-angle effects become significant, requiring careful modeling to extract unbiased cosmological information. We address these challenges by applying the total-angular-momentum (TAM) formalism to describe redshift-space clustering beyond the flat-sky approximation. The standard Fourier-mode description, which characterizes distortions by the angle between a mode and a line of sight, becomes ill-defined over wide fields, whereas the TAM basis naturally separates radial and angular contributions and incorporates the relevant relativistic effects. Within this framework, we provide a new parameterization of wide-angle predictions that can be compared directly with survey data. We then introduce PowerFull, a modification of the Julia-based 2-FAST package, which enables efficient computation of the full relativistic angular power spectrum. Finally, using Fisher information matrix-based analyses, we show that a survey like SPHEREx reaches $σ(f_\text{NL}) \sim 1$, but that neglecting the relativistic and wide-angle contributions shifts the recovered $f_\text{NL}$ by an amount of order its own uncertainty: at this precision the inferred value is biased unless the clustering is modeled consistently.
Comments77 pages, 20 figures, 4 tables
