Second-order cosmological perturbation theory and initial conditions for $N$-body simulations

TL;DR

This paper develops a relativistic second-order cosmological perturbation framework to improve initial condition calculations for $N$-body simulations, incorporating relativistic effects beyond Newtonian approximations.

Contribution

It introduces a gauge-invariant, second-order relativistic approach to compute initial displacements for $N$-body simulations, extending beyond traditional Newtonian methods.

Findings

Derived relativistic displacement fields including second-order corrections.

Analyzed the impact of relativistic effects on initial conditions in cosmological simulations.

Provided a framework applicable to Einstein--de Sitter models with both growing and decaying modes.

Abstract

We use gauge-invariant cosmological perturbation theory to calculate the displacement field that sets the initial conditions for $N$-body simulations. Using first and second-order fully relativistic perturbation theory in the synchronous-comoving gauge, allows us to go beyond the Newtonian predictions and to calculate relativistic corrections to it. We use an Einstein--de Sitter model, including both growing and decaying modes in our solutions. The impact of our results should be assessed through the implementation of the featured displacement in cosmological $N$-body simulations.