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

Journal Article · · Physical Review D
 [1];  [2]
  1. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Berkeley Center for Cosmological Physics, Dept. of Physics; Inst. for Advanced Study, Princeton, NJ (United States)
  2. Stanford Univ., CA (United States). Stanford Inst. for Theoretical Physics and Dept. of Physics; Stanford Univ., CA (United States). Kavli Inst. for Particle Astrophysics and Cosmology; SLAC National Accelerator Lab., Menlo Park, CA (United States)
+ Show Author Affiliations

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. Here, 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 fast fourier transform perturbation theory 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.

Research Organization:
SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)
Sponsoring Organization:
USDOE
Grant/Contract Number:
AC02-76SF00515
OSTI ID:
1360171
Alternate ID(s):
OSTI ID: 1333589
Journal Information:
Physical Review D, Vol. 94, Issue 10; ISSN 2470-0010
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 29 works
Citation information provided by
Web of Science

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Cited By (9)

FAST-PT II: an algorithm to calculate convolution integrals of general tensor quantities in cosmological perturbation theory journal February 2017
The matter power spectrum in redshift space using effective field theory journal November 2017
Cosmological perturbation theory using the FFTLog: formalism and connection to QFT loop integrals journal April 2018
Measuring neutrino masses with large-scale structure: Euclid forecast with controlled theoretical error journal November 2019
Velocity bias and the nonlinear perturbation theory of peaks journal October 2019
FAST-PT II: an algorithm to calculate convolution integrals of general tensor quantities in cosmological perturbation theory text January 2016
The matter power spectrum in redshift space using effective field theory text January 2017
Cosmological Perturbation Theory Using the FFTLog: Formalism and Connection to QFT Loop Integrals text January 2017
Velocity bias and the nonlinear perturbation theory of peaks text January 2019

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