SciPost Submission Page
Bridging perturbation theory and simulations: initial conditions and fast integrators for cosmological simulations
by Oliver Hahn
Submission summary
| Authors (as registered SciPost users): | Oliver Hahn |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202507_00057v1 (pdf) |
| Date submitted: | July 22, 2025, 2:10 p.m. |
| Submitted by: | Oliver Hahn |
| Submitted to: | SciPost Physics Lecture Notes |
| for consideration in Collection: |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
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.