Angular cosmological correlators are infamously difficult to compute due to the highly oscillatory nature of the projection integrals. Motivated by recent development on analytic approaches to cosmological perturbation theory, in this paper we present an efficient method for computing cosmological four-point correlations in angular space, generalizing previous works on lower-point functions. This builds on the FFTLog algorithm that approximates the matter power spectrum as a sum over power-law functions, which makes certain momentum integrals analytically solvable. The computational complexity is drastically reduced for correlators in a "separable" form---we define a suitable notion of separability for cosmological trispectra, and derive formulas for angular correlators of different separability classes. As an application of our formalism, we compute the angular galaxy trispectrum at tree level, with and without primordial non-Gaussianity. This includes effects of redshift space distortion and bias parameters up to cubic order. We also compute the non-Gaussian covariance of the angular matter power spectrum due to the connected four-point function, beyond the Limber approximation. We demonstrate that, in contrast to the standard lore, the Limber approximation can fail for the non-Gaussian covariance computation even for large multipoles.

中文翻译：

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宇宙角三谱和非高斯协方差

由于投影积分的高度振荡性质，角宇宙学相关器是出了名的难以计算。受宇宙学微扰理论分析方法的最新发展的启发，在本文中，我们提出了一种计算角空间中宇宙学四点相关性的有效方法，概括了以前关于低点函数的工作。这建立在 FFTLog 算法的基础上，该算法将物质功率谱近似为幂律函数的总和，这使得某些动量积分可以解析求解。对于“可分离”形式的相关器，计算复杂度大大降低——我们为宇宙学三谱定义了一个合适的可分离性概念，并推导出不同可分离性类别的角相关器的公式。作为我们形式主义的应用，我们在树级别计算角星系三谱，有和没有原始非高斯性。这包括红移空间失真和高达三次方的偏置参数的影响。由于连接的四点函数，我们还计算了角物质功率谱的非高斯协方差，超出了 Limber 近似。我们证明，与标准知识相反，即使对于大的多极点，Limber 近似也可能无法用于非高斯协方差计算。超越 Limber 近似。我们证明，与标准知识相反，即使对于大的多极点，Limber 近似也可能无法用于非高斯协方差计算。超越 Limber 近似。我们证明，与标准知识相反，即使对于大的多极点，Limber 近似也可能无法用于非高斯协方差计算。