On the accuracy of N-body simulations at very large scales

Abstract

We examine the deviation of Cold Dark Matter particle trajectories from the Newtonian result as the size of the region under study becomes comparable to or exceeds the particle horizon. To first order in the gravitational potential, the general relativistic result coincides with the Zel'dovich approximation and hence the Newtonian prediction on all scales. At second order, General Relativity predicts corrections which overtake the corresponding second order Newtonian terms above a certain scale of the order of the Hubble radius. However, since second order corrections are very much suppressed on such scales, we conclude that simulations which exceed the particle horizon but use Newtonian equations to evolve the particles, reproduce the correct trajectories very well. The dominant relativistic corrections to the power spectrum on scales close to the horizon are at most of the order of $\sim 10^{-5}$ at $z=49$ and $\sim 10^{-3}$ at $z=0$. The differences in the positions of real space features are affected at a level below $10^{-6}$ at both redshifts. Our analysis also clarifies the relation of N-body results to relativistic considerations.

7 pages, 2 figures; v2: 7 pages, 3 figures, matches version published in MNRAS

References in corpus (2)

• New Perspective on Galaxy Clustering as a Cosmological Probe: General Relativistic Effects
• General Relativistic N-body simulations in the weak field limit

Cited by in corpus (12)

• General relativity and cosmic structure formation
• gevolution: a cosmological N-body code based on General Relativity
• Initial Conditions for Accurate N-Body Simulations of Massive Neutrino Cosmologies
• General Relativistic N-body simulations in the weak field limit
• Relativistic N-body simulations with massive neutrinos
• Horizon Run 4 Simulation: Coupled Evolution of Galaxies and Large-scale Structures of the Universe
• LIGER: mock relativistic light-cones from Newtonian simulations
• The Intrinsic Matter Bispectrum in $\Lambda$CDM
• Cosmology on all scales: a two-parameter perturbation expansion
• Observing relativistic features in large-scale structure surveys -- II: Doppler magnification in an ensemble of relativistic simulations
• General Relativistic Cosmological N-body Simulations I: time integration
• Initial conditions for cosmological N-body simulations of the scalar sector of theories of Newtonian, Relativistic and Modified Gravity