球谐傅里叶-贝塞尔功率谱中的线性相对论修正
Linear Relativistic Corrections in the Spherical Fourier-Bessel Power Spectrum
AI总结：
本研究在球谐傅里叶-贝塞尔基下计算线性阶相对论功率谱并建模相关效应，通过与CLASS对比验证结果，分析其与原初非高斯性的差异，为未来巡天提取透镜效应提供支持。
摘要：
三维星系功率谱是探测原初非高斯性和大尺度上额外广义相对论（GR）效应的有力工具，当前及未来的大尺度结构（LSS）巡天可对其进行约束。本研究在球谐傅里叶-贝塞尔（SFB）基下计算线性阶相对论功率谱，该坐标系保留了弯曲天空的几何特性并充分考虑了广角效应。特别地，我们对离散SFB功率谱中的GR效应进行建模，在存在径向窗的情况下，离散SFB功率谱比连续SFB基更高效且稳定地分解星系密度场。为验证GR计算结果，我们引入角功率谱与SFB功率谱之间的映射关系，并将计算结果与CLASS的输出进行比较。我们讨论了SFB基下GR效应的丰富模式，并将GR效应与局域原初非高斯性（PNG）效应进行对比。在SFB基中，多普勒效应和透镜效应与PNG具有不同的角和傅里叶依赖性，而引力势项与PNG的简并性更强，其信号强度与f_NL∼1相当。我们还讨论了在未来LSS巡天中通过SFB模式提取透镜效应的潜在机会。
英文摘要：
The three-dimensional galaxy power spectrum is a powerful probe of primordial non-Gaussianity and additional general relativistic (GR) effects on large scales, which can be constrained by the current and upcoming large-scale structure surveys. In this work, we calculate the linear-order relativistic power spectrum in the spherical Fourier-Bessel (SFB) basis, a coordinate system that preserves the geometry of the curved sky and fully accounts for the wide-angle effect. In particular, we model the GR effects present in the discrete SFB power spectrum, which is a more efficient and stable decomposition of the galaxy density field compared to the continuous SFB basis in the presence of radial windows. To validate our GR calculations, we introduce a mapping between the angular power spectrum and the SFB power spectrum, and we compare our calculations with outputs from CLASS. We discuss the rich pattern of GR effects in the SFB basis and compare the GR effects to the local primordial non-Gaussianity (PNG) effect. The Doppler and lensing effects have different angular and Fourier dependence compared to the PNG in the SFB basis, while the gravitational potential term is more degenerate with the PNG and comparable to a signal of $f_{\rm NL}\sim 1$. We also discuss the potential opportunities of extracting the lensing effect through SFB modes in upcoming LSS surveys.
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