Beyond the traditional Line-of-Sight approach of cosmological angular statistics

TL;DR

This paper introduces an improved FFTlog-based method for calculating cosmological angular power spectra efficiently, significantly reducing computation time while maintaining high precision, applicable to various large-scale structure observables.

Contribution

The paper develops a new FFTlog-based algorithm with better convergence for computing exact angular power spectra, implemented in CLASS, and achieves a 400-fold speed-up.

Findings

Speeds up $C_0$ calculations by a factor of 400.

Maintains 0.1% precision without the Limber approximation.

Applicable to number counts, weak lensing, and relativistic corrections.

Abstract

We present a new efficient method to compute the angular power spectra of large-scale structure observables that circumvents the numerical integration over Bessel functions, expanding on a recently proposed algorithm based on FFTlog. This new approach has better convergence properties. The method is explicitly implemented in the CLASS code for the case of number count $C_\ell$'s (including redshift-space distortions, weak lensing, and all other relativistic corrections) and cosmic shear $C_\ell$'s. In both cases our approach speeds up the calculation of the exact $C_\ell$'s (without the Limber approximation) by a factor of order 400 at a fixed precision target of 0.1%.