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Matter power spectrum and the challenge of percent accuracy


Schneider, Aurel; Teyssier, Romain; Potter, Doug; Stadel, Joachim; Onions, Julian; Reed, Darren S; Smith, Robert E; Springel, Volker; Pearce, Frazer R; Scoccimarro, Roman (2016). Matter power spectrum and the challenge of percent accuracy. Journal of Cosmology and Astroparticle Physics, 2016(04):047.

Abstract

Future galaxy surveys require one percent precision in the theoretical knowledge of the power spectrum over a large range including very nonlinear scales. While this level of accuracy is easily obtained in the linear regime with perturbation theory, it represents a serious challenge for small scales where numerical simulations are required. In this paper we quantify the precision of present-day N-body methods, identifying main potential error sources from the set-up of initial conditions to the measurement of the final power spectrum. We directly compare three widely used N-body codes, Ramses, Pkdgrav3, and Gadget3 which represent three main discretisation techniques: the particle-mesh method, the tree method, and a hybrid combination of the two. For standard run parameters, the codes agree to within one percent at k<=1 h Mpc-1 and to within three percent at k<=10 h Mpc-1. We also consider the bispectrum and show that the reduced bispectra agree at the sub-percent level for k<= 2 h Mpc-1. In a second step, we quantify potential errors due to initial conditions, box size, and resolution using an extended suite of simulations performed with our fastest code Pkdgrav3. We demonstrate that the simulation box size should not be smaller than L=0.5 h-1Gpc to avoid systematic finite-volume effects (while much larger boxes are required to beat down the statistical sample variance). Furthermore, a maximum particle mass of Mp=109 h-1Msolar is required to conservatively obtain one percent precision of the matter power spectrum. As a consequence, numerical simulations covering large survey volumes of upcoming missions such as DES, LSST, and Euclid will need more than a trillion particles to reproduce clustering properties at the targeted accuracy.

Abstract

Future galaxy surveys require one percent precision in the theoretical knowledge of the power spectrum over a large range including very nonlinear scales. While this level of accuracy is easily obtained in the linear regime with perturbation theory, it represents a serious challenge for small scales where numerical simulations are required. In this paper we quantify the precision of present-day N-body methods, identifying main potential error sources from the set-up of initial conditions to the measurement of the final power spectrum. We directly compare three widely used N-body codes, Ramses, Pkdgrav3, and Gadget3 which represent three main discretisation techniques: the particle-mesh method, the tree method, and a hybrid combination of the two. For standard run parameters, the codes agree to within one percent at k<=1 h Mpc-1 and to within three percent at k<=10 h Mpc-1. We also consider the bispectrum and show that the reduced bispectra agree at the sub-percent level for k<= 2 h Mpc-1. In a second step, we quantify potential errors due to initial conditions, box size, and resolution using an extended suite of simulations performed with our fastest code Pkdgrav3. We demonstrate that the simulation box size should not be smaller than L=0.5 h-1Gpc to avoid systematic finite-volume effects (while much larger boxes are required to beat down the statistical sample variance). Furthermore, a maximum particle mass of Mp=109 h-1Msolar is required to conservatively obtain one percent precision of the matter power spectrum. As a consequence, numerical simulations covering large survey volumes of upcoming missions such as DES, LSST, and Euclid will need more than a trillion particles to reproduce clustering properties at the targeted accuracy.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute for Computational Science
Dewey Decimal Classification:530 Physics
Language:English
Date:2016
Deposited On:04 Jan 2017 09:20
Last Modified:02 Feb 2018 11:13
Publisher:IOP Publishing
ISSN:1475-7516
OA Status:Green
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1088/1475-7516/2016/04/047

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