A complete FFT-based decomposition formalism for the redshift-space bispectrum

TL;DR

This paper introduces a new FFT-based formalism for decomposing the redshift-space bispectrum, enabling efficient measurement and separation of anisotropic signals caused by redshift-space distortions and the Alcock-Paczyński effect.

Contribution

It presents a novel tri-polar spherical harmonic decomposition formalism that preserves key cosmological symmetries and simplifies the analysis of the anisotropic bispectrum in redshift space.

Findings

First detection of the anisotropic bispectrum in the L=2 mode with 14σ significance.

Demonstrated the formalism on BOSS DR12 data, showing practical applicability.

Reduced computational complexity using FFTs and provided a method to correct survey geometry effects.

Abstract

To fully extract cosmological information from nonlinear galaxy distribution in redshift space, it is essential to include higher-order statistics beyond the two-point correlation function. In this paper, we propose a new decomposition formalism for computing the anisotropic bispectrum in redshift space and for measuring it from galaxy samples. Our formalism uses tri-polar spherical harmonic decomposition with zero total angular momentum to compress the 3D modes distribution in the redshift-space bispectrum. This approach preserves three fundamental properties of the Universe: statistical homogeneity, isotropy, and parity-symmetry, allowing us to efficiently separate the anisotropic signal induced by redshift-space distortions (RSDs) and the Alcock-Paczy\'{n}ski (AP) effect from the isotropic bispectrum. The relevant expansion coefficients in terms of the anisotropic signal are reduced to one multipole index $L$, and the $L> 0$ modes are induced only by the RSD or AP effects. Our formalism has two advantages: (1) we can make use of Fast Fourier Transforms (FFTs) to measure the bispectrum; (2) it gives a simple expression to correct for the survey geometry, i.e., the survey window function. As a demonstration, we measure the decomposed bispectrum from the Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 12, and, for the first time, present a $14\sigma$ detection of the anisotropic bispectrum in the $L=2$ mode.