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

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...

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Published inJournal of cosmology and astroparticle physics Vol. 2016; no. 9; p. 15
Main Authors McEwen, Joseph E., Fang, Xiao, Hirata, Christopher M., Blazek, Jonathan A.
Format Journal Article
LanguageEnglish
Published United States 12.09.2016
Subjects
ALGORITHMS
ASTROPHYSICS, COSMOLOGY AND ASTRONOMY
COMPUTERIZED SIMULATION
CORRECTIONS
COSMOLOGICAL MODELS
COUPLING
DISTURBANCES
FOURIER TRANSFORMATION
MARKOV PROCESS
MONTE CARLO METHOD
NONLINEAR PROBLEMS
NONLUMINOUS MATTER
PERTURBATION THEORY
RENORMALIZATION
SCALE INVARIANCE
SPECTRA
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ISSN1475-7516
1475-7516
DOI10.1088/1475-7516/2016/09/015

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Summary: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. The code, along with a user manual and example implementations, is available at https://github.com/JoeMcEwen/FAST-PT.
ISSN:1475-7516
1475-7516
DOI:10.1088/1475-7516/2016/09/015