FFT-PT: Reducing the two-loop large-scale structure power spectrum to low-dimensional radial integrals

TL;DR

This paper introduces FFT-PT, a method that simplifies two-loop corrections to the large-scale structure power spectrum into low-dimensional radial integrals, enabling faster computations for cosmological modeling.

Contribution

The paper presents a novel approach to reduce complex high-dimensional integrals in large-scale structure modeling to low-dimensional radial integrals using FFT, improving computational efficiency.

Findings

Two-loop corrections can be reduced to radial integrals

Radial integrals can be evaluated with 1D FFTs

Method accommodates features like baryonic oscillations

Abstract

Modeling the large-scale structure of the universe on nonlinear scales has the potential to substantially increase the science return of upcoming surveys by increasing the number of modes available for model comparisons. One way to achieve this is to model nonlinear scales perturbatively. Unfortunately, this involves high-dimensional loop integrals that are cumbersome to evaluate. Trying to simplify this, we show how two-loop (next-to-next-to-leading order) corrections to the density power spectrum can be reduced to low-dimensional, radial integrals. Many of those can be evaluated with a one-dimensional Fast Fourier Transform, which is significantly faster than the five-dimensional Monte-Carlo integrals that are needed otherwise. The general idea of this FFT-PT method is to switch between Fourier and position space to avoid convolutions and integrate over orientations, leaving only radial integrals. This reformulation is independent of the underlying shape of the initial linear density power spectrum and should easily accommodate features such as those from baryonic acoustic oscillations. We also discuss how to account for halo bias and redshift space distortions.