Cosmological simulations of structure formation and the Vlasov equation

TL;DR

This paper discusses the role of cosmological simulations in understanding structure formation, focusing on the Vlasov equation and the impact of discreteness errors in N-body simulations of cold dark matter.

Contribution

It provides a detailed explanation of the simulations and theoretical models, and presents recent progress in quantitatively addressing discreteness errors.

Findings

Simulations aim to produce the Vlasov limit for cold dark matter.

Discreteness errors in N-body simulations are only qualitatively understood.

Recent progress offers quantitative insights into discreteness effects.

Abstract

In cosmology numerical simulations of structure formation are now of central importance, as they are the sole instrument for providing detailed predictions of current cosmological models for a whole class of important constraining observations. These simulations are essentially molecular dynamics simulations of N (>> 1), now up to of order several billion) particles interacting through their self-gravity. While their aim is to produce the Vlasov limit, which describes the underlying (``cold dark matter'') models, the degree to which they actually do produce this limit is currently understood, at best, only very qualitatively, and there is an acknowledged need for ``a theory of discreteness errors''. In this talk I will describe, for non-cosmologists, both the simulations and the underlying theoretical models, and will then focus on the issue of discreteness, describing some recent progress in addressing this question quantitatively.