A Relativistic view on large scale N-body simulations

Abstract

We discuss the relation between the output of Newtonian N-body simulations on scales that approach or exceed the particle horizon to the description of General Relativity. At leading order, the Zeldovich approximation is correct on large scales, coinciding with the General Relativistic result. At second order in the initial metric potential, the trajectories of particles deviate from the second order Newtonian result and hence the validity of 2LPT initial conditions should be reassessed when used in very large simulations. We also advocate using the expression for the synchronous gauge density as a well behaved measure of density fluctuations on such scales.

arXiv comment7 pages, 2 figures, invited contribution to the Classical and Quantum Gravity focus issue on "Relativistic Effects in Cosmology", edited by Kazuya Koyama; v2 small modifications, matches published version

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• Accurate initial conditions in mixed Dark Matter--Baryon simulations
• Non-Spherical Szekeres models in the language of Cosmological Perturbations
• f(R) gravity on non-linear scales: The post-Friedmann expansion and the vector potential
• Initial conditions for cosmological N-body simulations of the scalar sector of theories of Newtonian, Relativistic and Modified Gravity
• General Relativistic Cosmological N-body Simulations I: time integration
• Second-order cosmological perturbation theory and initial conditions for $N$-body simulations
• Relativistic perturbations in $\Lambda$CDM: Eulerian & Lagrangian approaches