Cosmological Angular Trispectra and Non-Gaussian Covariance

TL;DR

This paper introduces an efficient method for computing angular cosmological four-point correlations, leveraging FFTLog and separability concepts, to better understand non-Gaussian features and covariance in cosmological data.

Contribution

It generalizes previous lower-point function methods to four-point correlations, providing a new formalism for separability and applying it to galaxy trispectrum and covariance calculations.

Findings

Efficient computation of angular galaxy trispectrum including non-Gaussianity.

Demonstration that the Limber approximation can fail for non-Gaussian covariance at large multipoles.

Development of a formalism for separability classes in cosmological trispectra.

Abstract

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.