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

TL;DR

This paper introduces an efficient method for computing anisotropic galaxy three-point correlation function multipoles by reducing dimensionality and employing 2DFFTLOG formalism, facilitating cosmological analyses.

Contribution

It presents a novel approach to compute multipole moments of the anisotropic 3PCF and its covariance efficiently using multipole decomposition and 2DFFTLOG formalism.

Findings

Dimensionality reduced from nine to two at each multipole

Derived full expressions for multipole moments and covariance matrix

Demonstrated optimal computation of complex integrals involving oscillating functions

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.