FAST-PT II: an algorithm to calculate convolution integrals of general tensor quantities in cosmological perturbation theory

TL;DR

This paper introduces an efficient algorithm for calculating 1-loop power spectra of tensor quantities in cosmological perturbation theory, significantly reducing computational time for complex mode-coupling integrals.

Contribution

It generalizes the FAST-PT framework to tensor quantities and provides a fast, versatile method applicable to various cosmological phenomena.

Findings

Reduces computational time for 1-loop integrals

Successfully applied to galaxy alignments and CMB effects

Provides publicly available code for broad use

Abstract

Cosmological perturbation theory is a powerful tool to predict the statistics of large-scale structure in the weakly non-linear regime, but even at 1-loop order it results in computationally expensive mode-coupling integrals. Here we present a fast algorithm for computing 1-loop power spectra of quantities that depend on the observer's orientation, thereby generalizing the FAST-PT framework (McEwen et al., 2016) that was originally developed for scalars such as the matter density. This algorithm works for an arbitrary input power spectrum and substantially reduces the time required for numerical evaluation. We apply the algorithm to four examples: intrinsic alignments of galaxies in the tidal torque model; the Ostriker-Vishniac effect; the secondary CMB polarization due to baryon flows; and the 1-loop matter power spectrum in redshift space. Code implementing this algorithm and these applications is publicly available at https://github.com/JoeMcEwen/FAST-PT .