FAST-PT: a novel algorithm to calculate convolution integrals in cosmological perturbation theory

TL;DR

FAST-PT is a new algorithm that efficiently computes convolution integrals in cosmological perturbation theory, significantly speeding up nonlinear power spectrum calculations for parameter estimation.

Contribution

The paper introduces FAST-PT, a novel algorithm leveraging properties of gravitational structure formation and FFTs to rapidly evaluate mode-coupling integrals in cosmology.

Findings

Enables fast computation of nonlinear corrections to the matter power spectrum.

Demonstrates application to one-loop perturbation theory and renormalization group methods.

Provides a publicly available Python code implementation.

Abstract

We present a novel algorithm, FAST-PT, for performing convolution or mode-coupling integrals that appear in nonlinear cosmological perturbation theory. The algorithm uses several properties of gravitational structure formation -- the locality of the dark matter equations and the scale invariance of the problem -- as well as Fast Fourier Transforms to describe the input power spectrum as a superposition of power laws. This yields extremely fast performance, enabling mode-coupling integral computations fast enough to embed in Monte Carlo Markov Chain parameter estimation. We describe the algorithm and demonstrate its application to calculating nonlinear corrections to the matter power spectrum, including one-loop standard perturbation theory and the renormalization group approach. We also describe our public code (in Python) to implement this algorithm, including the applications described here.