Optimal computation of anisotropic galaxy three point correlation function multipoles using 2DFFTLOG formalism

Abstract

We study two key issues militating against the use of the anisotropic three-point correlation function (3PCF) for cosmological parameter inference: difficulties with its computational estimation and high-dimensionality. We show how high-dimensionality may be reduced significantly by multipole decompositions of all angular dependence. This allows deriving the full expression for the multipole moments of the anisotropic 3PCF and its covariance matrix in a basis where the dimensionality reduces from nine to two at each multipole in the plane-parallel limit. We use 2D FFTLog formalism to show how the multipole moments with double momentum integrals over the product of bispectrum and two highly oscillating spherical Bessel functions and its covariance with double momentum integrals over the product of three galaxy power spectra and a combination of four highly oscillating spherical Bessel functions may be computed optimally.

27 pages, 7 figures, A comparison figure added. Accepted for publication by JCAP

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• The halo 3-point correlation function: a methodological analysis
• The effect of finite halo size on the clustering of neutral hydrogen
• Galaxy and halo angular clustering in LCDM and Modified Gravity cosmologies
• The imprints of massive neutrinos on the three-point correlation function of large-scale structures
• Modeling and measuring the anisotropic halo 3-point correlation function: a coordinated study
• Accelerating BAO Scale Fitting Using Taylor Series
• Delensing CMB B-modes using galaxy surveys: the effect of galaxy bias and matter clustering non-linearities
• Euclid preparation. Full-shape modelling of 2-point and 3-point correlation functions in real space