2-FAST: Fast and accurate computation of projected two-point functions

TL;DR

The paper introduces 2-FAST, an algorithm that efficiently computes integrals involving spherical Bessel functions, crucial for projecting galaxy power spectra into different spaces, by combining FFTlog transformation and analytical recursion methods.

Contribution

The paper presents a novel algorithm that significantly speeds up and improves the accuracy of computing spherical Bessel integrals for cosmological applications.

Findings

Achieves faster computation than traditional methods

Maintains high accuracy in projection calculations

Reduces complexity of oscillatory integral evaluations

Abstract

We present the 2-point function from Fast and Accurate Spherical Bessel Transformation (2-FAST) algorithm for a fast and accurate computation of integrals involving one or two spherical Bessel functions. These types of integrals occur when projecting the galaxy power spectrum $P(k)$ onto the configuration space, $\xi_\ell^\nu(r)$, or spherical harmonic space, $C_\ell(\chi,\chi')$. First, we employ the FFTlog transformation of the power spectrum to divide the calculation into $P(k)$-dependent coefficients and $P(k)$-independent integrations of basis functions multiplied by spherical Bessel functions. We find analytical expressions for the latter integrals in terms of special functions, for which recursion provides a fast and accurate evaluation. The algorithm, therefore, circumvents direct integration of highly oscillating spherical Bessel functions.