Bridging perturbation theory and simulations: initial conditions and fast integrators for cosmological simulations

arXiv:2608.03400 · astro-ph.CO · Submitted 2026-08-04 · Read on arXiv

Oliver Hahn

astro-ph.CO

Submitted: 2026-08-04

Comments: Lecture given at the Les Houches Summer School: 'The Dark Universe' (7 Jul - 1 Aug 2025). 16 pages, 3 figures. Accepted for publication in SciPost Physics Lecture Notes. For associated notebook, see https://github.com/ohahn/LesHouches2025

Code: https://github.com/ohahn/LesHouches2025

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Initial Data — 11× in this paper · explained in 2 episodes
• N-body simulations — 7× in this paper · explained in 2 episodes
• Matter Power Spectrum — 3× in this paper · explained in 2 episodes
• Accuracy — 1× in this paper · explained in 1 episode
• Clustering — 1× in this paper · explained in 2 episodes
• Consistency — 1× in this paper · explained in 3 episodes
• Fast Fourier Transform — 1× in this paper

Sources

• Cosmological Vlasov-Poisson equations for dark matter: Recent developments and connections to selected plasma problems
• Perturbative Lagrangian Approach to Gravitational Instability
• The recursion relation in Lagrangian perturbation theory
• Time-analyticity of Lagrangian particle trajectories in ideal fluid flow
• Recursive Solutions of Lagrangian Perturbation Theory
• Shell-crossing in a $\Lambda$CDM Universe
• Accurate initial conditions for cosmological N-body simulations: Minimizing truncation and discreteness errors
• General relativity and cosmic structure formation
• Time stepping N-body simulations
• Perturbation-theory informed integrators for cosmological simulations
• FastPM: a new scheme for fast simulations of dark matter and halos
• BullFrog: Multi-step perturbation theory as a time integrator for cosmological simulations
• Improving Initial Conditions for Cosmological $N$-Body Simulations

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