Department of Astronomy, University of Florida, 211 Bryant Space Science Center, Gainesville, FL 32611-2055, USA, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA 94720, USA
ABSTRACT Perturbation theory (PT) is often used to model statistical observables capturing the translation and rotation-invariant information in cosmological density fields. PT produces higher order corrections by integration over linear statistics of the density fields weighted by kernels resulting from recursive solution of the fluid equations. These integrals quickly become high dimensional and naively require increasing computational resources the higher the order of the corrections. Here, we show how to decouple the integrands that often produce this issue, enabling PT corrections to be computed as a sum of products of independent 1D integrals. Our approach is related to a commonly used method for calculating multiloop Feynman integrals in quantum field theory, the Gegenbauer Polynomial x-Space Technique. We explicitly reduce the three terms entering the 2-loop power spectrum, formally requiring 9D integrations, to sums over successive 1D radial integrals. These 1D integrals can further be performed as convolutions, rendering the scaling of this method Nglog Ng with Ng the number of grid points used for each fast Fourier transform. This method should be highly enabling for upcoming large-scale structure redshift surveys where model predictions at an enormous number of cosmological parameter combinations will be required by Monte Carlo Markov Chain searches for the best-fitting values.
Slepian, Zachary. "On decoupling the integrals of cosmological perturbation theory." Monthly Notices of the Royal Astronomical Society, vol. 507, no. 1, Jun. 2020. https://doi.org/10.1093/mnras/staa1789
Slepian, Zachary (2020). On decoupling the integrals of cosmological perturbation theory. Monthly Notices of the Royal Astronomical Society, 507(1). https://doi.org/10.1093/mnras/staa1789
Slepian, Zachary, "On decoupling the integrals of cosmological perturbation theory," Monthly Notices of the Royal Astronomical Society 507, no. 1 (2020), https://doi.org/10.1093/mnras/staa1789
@article{osti_1814875,
author = {Slepian, Zachary},
title = {On decoupling the integrals of cosmological perturbation theory},
annote = {ABSTRACT Perturbation theory (PT) is often used to model statistical observables capturing the translation and rotation-invariant information in cosmological density fields. PT produces higher order corrections by integration over linear statistics of the density fields weighted by kernels resulting from recursive solution of the fluid equations. These integrals quickly become high dimensional and naively require increasing computational resources the higher the order of the corrections. Here, we show how to decouple the integrands that often produce this issue, enabling PT corrections to be computed as a sum of products of independent 1D integrals. Our approach is related to a commonly used method for calculating multiloop Feynman integrals in quantum field theory, the Gegenbauer Polynomial x-Space Technique. We explicitly reduce the three terms entering the 2-loop power spectrum, formally requiring 9D integrations, to sums over successive 1D radial integrals. These 1D integrals can further be performed as convolutions, rendering the scaling of this method Nglog Ng with Ng the number of grid points used for each fast Fourier transform. This method should be highly enabling for upcoming large-scale structure redshift surveys where model predictions at an enormous number of cosmological parameter combinations will be required by Monte Carlo Markov Chain searches for the best-fitting values.},
doi = {10.1093/mnras/staa1789},
url = {https://www.osti.gov/biblio/1814875},
journal = {Monthly Notices of the Royal Astronomical Society},
issn = {ISSN 0035-8711},
number = {1},
volume = {507},
place = {United Kingdom},
publisher = {Oxford University Press},
year = {2020},
month = {06}}
Monthly Notices of the Royal Astronomical Society, Journal Name: Monthly Notices of the Royal Astronomical Society Vol. 507 Journal Issue: 1; ISSN 0035-8711