Reducing the twoloop largescale structure power spectrum to lowdimensional, radial integrals
Modeling the largescale 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 highdimensional loop integrals that are cumbersome to evaluate. Here, trying to simplify this, we show how twoloop (nexttonexttoleading order) corrections to the density power spectrum can be reduced to lowdimensional, radial integrals. Many of those can be evaluated with a onedimensional fast Fourier transform, which is significantly faster than the fivedimensional MonteCarlo 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.
 Authors:

^{[1]};
^{[2]}
 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)
 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)
 Publication Date:
 Grant/Contract Number:
 AC0276SF00515
 Type:
 Accepted Manuscript
 Journal Name:
 Physical Review D
 Additional Journal Information:
 Journal Volume: 94; Journal Issue: 10; Journal ID: ISSN 24700010
 Publisher:
 American Physical Society (APS)
 Research Org:
 SLAC National Accelerator Lab., Menlo Park, CA (United States)
 Sponsoring Org:
 USDOE
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
 OSTI Identifier:
 1360171
 Alternate Identifier(s):
 OSTI ID: 1333589
Schmittfull, Marcel, and Vlah, Zvonimir. Reducing the twoloop largescale structure power spectrum to lowdimensional, radial integrals. United States: N. p.,
Web. doi:10.1103/PhysRevD.94.103530.
Schmittfull, Marcel, & Vlah, Zvonimir. Reducing the twoloop largescale structure power spectrum to lowdimensional, radial integrals. United States. doi:10.1103/PhysRevD.94.103530.
Schmittfull, Marcel, and Vlah, Zvonimir. 2016.
"Reducing the twoloop largescale structure power spectrum to lowdimensional, radial integrals". United States.
doi:10.1103/PhysRevD.94.103530. https://www.osti.gov/servlets/purl/1360171.
@article{osti_1360171,
title = {Reducing the twoloop largescale structure power spectrum to lowdimensional, radial integrals},
author = {Schmittfull, Marcel and Vlah, Zvonimir},
abstractNote = {Modeling the largescale 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 highdimensional loop integrals that are cumbersome to evaluate. Here, trying to simplify this, we show how twoloop (nexttonexttoleading order) corrections to the density power spectrum can be reduced to lowdimensional, radial integrals. Many of those can be evaluated with a onedimensional fast Fourier transform, which is significantly faster than the fivedimensional MonteCarlo 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.},
doi = {10.1103/PhysRevD.94.103530},
journal = {Physical Review D},
number = 10,
volume = 94,
place = {United States},
year = {2016},
month = {11}
}