Vlasov limit and discreteness effects in cosmological N-body simulations

TL;DR

This paper investigates how discreteness effects influence cosmological N-body simulations by developing a perturbative approach for initial conditions and comparing it with fluid theory, aiming to improve understanding of early and non-linear evolution.

Contribution

It introduces a perturbative method to analyze the evolution of perturbed lattices in N-body simulations, enabling precise study of discreteness effects from early to non-linear regimes.

Findings

Perturbative approach accurately describes early evolution of initial lattice conditions.

Comparison with fluid theory highlights discreteness effects in the linear regime.

Ongoing work aims to quantify discreteness impacts in the non-linear regime.

Abstract

We present the problematic of controlling the discreteness effects in cosmological N-body simulations. We describe a perturbative treatment which gives an approximation describing the evolution under self-gravity of a lattice perturbed from its equilibrium, which allows to trace the evolution of the fully discrete distribution until the time when particles approach one another ("shell-crossing"). Perturbed lattices are typical initial conditions for cosmological N-body simulations and thus we can describe precisely the early time evolution of these simulations. A quantitative comparison with fluid Lagrangian theory permits to study discreteness effects in the linear regime of the simulations. We show finally some work in progress about quantifying discreteness effects in the non-perturbative (highly non-linear) regime of cosmological N-body simulations by evolving different discretizations of the same continuous density field.