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

Naonori S. Sugiyama*, Shun Saito, Florian Beutler, Hee Jong Seo

*Corresponding author for this work

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To fully extract cosmological information from non-linear 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 newdecomposition formalism for computing the anisotropic bispectrum in redshift space and formeasuring 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-Paczyński (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 to measure the bispectrum and (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 14σ detection of the anisotropic bispectrum in the L = 2 mode.

Original languageEnglish
Pages (from-to)364-384
Number of pages21
JournalMonthly Notices of the Royal Astronomical Society
Issue number1
Early online date30 Nov 2018
Publication statusPublished - 1 Mar 2019


  • Cosmology: observations
  • Cosmology: theory
  • Dark matter
  • Large-scale structure of Universe


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