Numerical Cosmology

TL;DR

Numerical Cosmology provides a comprehensive, method-focused overview of simulating the Universe's matter distribution from dark matter dynamics to baryonic processes. It articulates the core framework of collisionless N-body methods solving the Vlasov-Poisson system, complemented by halo finding, light-cone construction, and halo-based galaxy painting, as well as post-processing baryonification to capture baryonic effects. The hydrodynamics chapter details Euler-Poisson on grids, radiative cooling, and simple star-formation recipes, while the subgrid chapter develops turbulence, gravo-turbulent star formation, stellar feedback, and SMBH feedback as essential ingredients for realistic galaxy populations. Together, these elements enable robust mock surveys and interpretation of precision cosmology data, while addressing numerical systematics and exploring beyond-LCDM scenarios. The work thus outlines a practical, end-to-end pipeline for generating and analyzing cosmological simulations in the era of large galaxy surveys, with explicit attention to accuracy, scalability, and physical fidelity.

Abstract

In these lecture notes, we describe the current state-of-the-art for numerical simulations of large-scale structure and galaxy formation. Numerical simulations play a central role in the preparation and the exploitation of large-scale galaxy surveys, in which galaxies are the fundamental observational objects. We first describe basic methods for collisionless N-body dynamics that enable us to model dark matter accurately by solving the Vlasov-Poisson equations. We then discuss simple methods to populate dark matter halos with galaxies, such as Halo and Sub-halo Abundance Matching techniques and baryonification techniques for capturing baryonic effects on the matter distribution. We finally describe how to model the gas component by solving the Euler-Poisson equations, focusing on the foundational assumptions behind these equations, namely local thermo-dynamical equilibrium, and the nature of the truncation errors of the numerical scheme, namely numerical diffusion. We show a few examples of simulations of a Milky-Way-like halo without cooling, with cooling and with star formation. We finally describe different subgrid prescriptions recently developed to model star formation, supernovae feedback and active galactic nuclei and how they impact cosmological simulations.

Figures (10)

• Figure 1: Color rendering of the dark matter particle distribution from a N-body simulation of a LCDM model. Dark matter halos are visible as clumps of different sizes. The color coding follows the mass of the halos, with large halos appearing redder and small halos appearing bluer. The characteristic filamentary structure of the Cosmic Web is striking. Simulation credit: RAMSES. Image credit: S. Colombi.
• Figure 2: Halo mass function from 200 Mpc/h N-body simulations with different particle number (from $128^3$ to $1024^3$). We used Poisson error bars in each mass bin. The vertical dashed lines indicate the 100 particles per halo limit below which we cannot trust the simulations. The solid red line is the analytical fit from Tinker (2010). Credit figure: R. Ait Ekioui. Credit simulation: R. Teyssier.
• Figure 3: Density profile of the simulated halo shown in Figure \ref{['fig:dmo_zoom']} (blue circles) compared to the analytical NFW profile with $c=20.5$. The isodensity level $\rho_{\rm min}=60$ is shown as the horizontal green line. The innermost blue point corresponds to twice the resolution of the grid. Credit figure and simulation: R. Teyssier.
• Figure 4: Left panel: Particle positions of a zoom-in N-body simulation of a Milky Way size dark matter halo. Middle panel: Central peak of the dark matter halo (shown as a single large red circle) with particle (shown as blue dots) assigned to the central peak. Right panel: Satellite peaks of the dark matter halo (shown as the many small red circles) with particles (shown as blue dots) bound to each satellite. Credit figure and simulation: R. Teyssier.
• Figure 5: Left panel: Light cone as seen from an observer sitting at the tip of the triangle within a thin slice on the sky and up to redshift $z=0.5$. Right panel: Light cone as seen from the same observer but face-on for a thin slice in redshift around redshift $z=0.25$. Credit figure and simulation: T. Akieda-Codron.