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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


Aurel Schneider

Romain Teyssier

Doug Potter

Joachim Stadel

Julian Onions

Darren S. Reed

Robert E. Smith

Volker Springel

Roman Scoccimarro


© 2016 IOP Publishing Ltd and Sissa Medialab srl. 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 k1 h Mpc-1 and to within three percent at k10 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-1Mo 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.


Schneider, A., Teyssier, R., Potter, D., Stadel, J., Onions, J., Reed, D. S., …Scoccimarro, R. (2016). Matter power spectrum and the challenge of percent accuracy. Journal of Cosmology and Astroparticle Physics, 2016(4), 1-21.

Journal Article Type Article
Acceptance Date Apr 12, 2016
Online Publication Date Apr 26, 2016
Publication Date 2016-04
Deposit Date Sep 8, 2016
Publicly Available Date Apr 27, 2017
Journal Journal of Cosmology and Astroparticle Physics
Electronic ISSN 1475-7516
Publisher IOP Publishing
Peer Reviewed Peer Reviewed
Volume 2016
Issue 4
Article Number 047
Pages 1-21
Keywords Cosmological Simulations, Power Spectrum
Public URL
Publisher URL
Additional Information This is an author-created, un-copyedited version of an article accepted for publication in Journal of Cosmology and Astroparticle Physics. The publisher is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at


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