Matter power spectrum and the challenge of percent accuracy

By A. Schneider, Romain Teyssier, D. Potter, Joachim Stadel, Julian Onions, Darren S. Reed, Rowan J. Smith, Volker Springel, Frazer R. Pearce, R. Scoccimarro. 2015

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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−1M⊙ 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.

Subfields: Astronomy and Astrophysics, Instrumentation

View Paper: https://www.semanticscholar.org/paper/b384ab0d5e567c44abf8c71f46529722da3a2b06

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Citations in the corpus

The Effective Field Theorist's Approach to Gravitational Dynamics (2016, background): “atter are currently challenging. Secondly, simultaneously scanning over a large space of parameters, and a wide range of scales, becomes computationally expensive the more precision is targeted. (See [329] for a recent critical assessment of their ultimate feasibility and level of accuracy.) Perhaps”
A new method to quantify the effects of baryons on the matter power spectrum (2015, methodology): “This has been shown to be sufficient for power spectrum measurements [15, 35].”
FastPM: a new scheme for fast simulations of dark matter and haloes (2016, methodology): “In contrast, full N-body codes often do not match each other at very low k (Heitmann et al. 2008; Schneider et al. 2016), with constant offsets between them, likely due to inaccuracies in the linear growth.”
Biased Tracers in Redshift Space in the EFT of Large-Scale Structure (2016, background): “However, keeping pace with the data to achieve the required accuracy over the full range of parameter space needed will be challenging [1].”
gevolution: a cosmological N-body code based on General Relativity (2016, background): “In other words, the difference is roughly what one expects for two different integration methods (see also [44]).”