Bridging perturbation theory and simulations: initial conditions and fast integrators for cosmological simulations
Abstract
These lecture notes provide an introduction to the generation of initial conditions for cosmological N-body simulations. Starting from the definition and properties of Gaussian random fields, we discuss their role in cosmology and the efficient generation of such fields using Fourier methods. The Vlasov-Poisson system is introduced as the governing framework for cold collisionless matter, and its solution via characteristics and Lagrangian perturbation theory (LPT) is detailed. We discuss the use of LPT for initializing N-body simulations, emphasizing the importance of high-order LPT and late-time starts to minimize truncation and discreteness errors. Finally, we discuss time integration schemes, including PT-informed integrators, and their role in accurately evolving the system. These notes aim to bridge the gap between theoretical perturbation methods and practical simulation techniques.
Versions
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BibTeX
@misc{hahn2026bridging,
title = {{Bridging perturbation theory and simulations: initial conditions and fast integrators for cosmological simulations}},
author = {Oliver Hahn},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.03400},
eprint = {2608.03400},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.03400},
}
RIS
TY - UNPB
TI - Bridging perturbation theory and simulations: initial conditions and fast integrators for cosmological simulations
AU - Oliver Hahn
PY - 2026
DA - 2026/08/04
PB - arXiv
DO - 10.48550/arxiv.2608.03400
UR - https://arxiv.org/abs/2608.03400
AB - These lecture notes provide an introduction to the generation of initial conditions for cosmological N-body simulations. Starting from the definition and properties of Gaussian random fields, we discuss their role in cosmology and the efficient generation of such fields using Fourier methods. The Vlasov-Poisson system is introduced as the governing framework for cold collisionless matter, and its solution via characteristics and Lagrangian perturbation theory (LPT) is detailed. We discuss the use of LPT for initializing N-body simulations, emphasizing the importance of high-order LPT and late-time starts to minimize truncation and discreteness errors. Finally, we discuss time integration schemes, including PT-informed integrators, and their role in accurately evolving the system. These notes aim to bridge the gap between theoretical perturbation methods and practical simulation techniques.
ER -