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Title: Fast large scale structure perturbation theory using one-dimensional fast Fourier transforms

The usual fluid equations describing the large-scale evolution of mass density in the universe can be written as local in the density, velocity divergence, and velocity potential fields. As a result, the perturbative expansion in small density fluctuations, usually written in terms of convolutions in Fourier space, can be written as a series of products of these fields evaluated at the same location in configuration space. Based on this, we establish a new method to numerically evaluate the 1-loop power spectrum (i.e., Fourier transform of the 2-point correlation function) with one-dimensional fast Fourier transforms. This is exact and a few orders of magnitude faster than previously used numerical approaches. Numerical results of the new method are in excellent agreement with the standard quadrature integration method. This fast model evaluation can in principle be extended to higher loop order where existing codes become painfully slow. Our approach follows by writing higher order corrections to the 2-point correlation function as, e.g., the correlation between two second-order fields or the correlation between a linear and a third-order field. These are then decomposed into products of correlations of linear fields and derivatives of linear fields. In conclusion, the method can also be viewed asmore » evaluating three-dimensional Fourier space convolutions using products in configuration space, which may also be useful in other contexts where similar integrals appear.« less
Authors:
 [1] ;  [2] ;  [3]
  1. Univ. of California, Berkeley, CA (United States). Berkeley Center for Cosmological Physics, Dept. of Physics; Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
  2. Stanford Univ., CA (United States). Stanford Inst. for Theoretical Physics and Dept. of Physics; SLAC National Accelerator Lab., Menlo Park, CA (United States). Kavli Inst. for Particle Astrophysics and Cosmology
  3. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Publication Date:
Grant/Contract Number:
AC02-05CH11231; AC02-76SF00515
Type:
Accepted Manuscript
Journal Name:
Physical Review D
Additional Journal Information:
Journal Volume: 93; Journal Issue: 10; Journal ID: ISSN 2470-0010
Publisher:
American Physical Society (APS)
Research Org:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org:
USDOE Office of Science (SC)
Country of Publication:
United States
Language:
English
Subject:
79 ASTRONOMY AND ASTROPHYSICS
OSTI Identifier:
1430671
Alternate Identifier(s):
OSTI ID: 1254214

Schmittfull, Marcel, Vlah, Zvonimir, and McDonald, Patrick. Fast large scale structure perturbation theory using one-dimensional fast Fourier transforms. United States: N. p., Web. doi:10.1103/PhysRevD.93.103528.
Schmittfull, Marcel, Vlah, Zvonimir, & McDonald, Patrick. Fast large scale structure perturbation theory using one-dimensional fast Fourier transforms. United States. doi:10.1103/PhysRevD.93.103528.
Schmittfull, Marcel, Vlah, Zvonimir, and McDonald, Patrick. 2016. "Fast large scale structure perturbation theory using one-dimensional fast Fourier transforms". United States. doi:10.1103/PhysRevD.93.103528. https://www.osti.gov/servlets/purl/1430671.
@article{osti_1430671,
title = {Fast large scale structure perturbation theory using one-dimensional fast Fourier transforms},
author = {Schmittfull, Marcel and Vlah, Zvonimir and McDonald, Patrick},
abstractNote = {The usual fluid equations describing the large-scale evolution of mass density in the universe can be written as local in the density, velocity divergence, and velocity potential fields. As a result, the perturbative expansion in small density fluctuations, usually written in terms of convolutions in Fourier space, can be written as a series of products of these fields evaluated at the same location in configuration space. Based on this, we establish a new method to numerically evaluate the 1-loop power spectrum (i.e., Fourier transform of the 2-point correlation function) with one-dimensional fast Fourier transforms. This is exact and a few orders of magnitude faster than previously used numerical approaches. Numerical results of the new method are in excellent agreement with the standard quadrature integration method. This fast model evaluation can in principle be extended to higher loop order where existing codes become painfully slow. Our approach follows by writing higher order corrections to the 2-point correlation function as, e.g., the correlation between two second-order fields or the correlation between a linear and a third-order field. These are then decomposed into products of correlations of linear fields and derivatives of linear fields. In conclusion, the method can also be viewed as evaluating three-dimensional Fourier space convolutions using products in configuration space, which may also be useful in other contexts where similar integrals appear.},
doi = {10.1103/PhysRevD.93.103528},
journal = {Physical Review D},
number = 10,
volume = 93,
place = {United States},
year = {2016},
month = {5}
}