Large-scale dark matter simulations
  We review the field of collisionless numerical simulations for the
large-scale structure of the Universe. We start by providing the main set of
equations solved by these simulations and their connection with General
Relativity. We then recap the relevant numerical approaches: discretization of
the phase-space distribution (focusing on N-body but including alternatives,
e.g., Lagrangian submanifold and Schr\"odinger-Poisson) and the respective
techniques for their time evolution and force calculation (Direct summation,
mesh techniques, and hierarchical tree methods). We pay attention to the
creation of initial conditions and the connection with Lagrangian Perturbation
Theory. We then discuss the possible alternatives in terms of the
micro-physical properties of dark matter (e.g., neutralinos, warm dark matter,
QCD axions, Bose-Einstein condensates, and primordial black holes), and
extensions to account for multiple fluids (baryons and neutrinos), primordial
non-Gaussianity and modified gravity. We continue by discussing challenges
involved in achieving highly accurate predictions. A key aspect of cosmological
simulations is the connection to cosmological observables, we discuss various
techniques in this regard: structure finding, galaxy formation and baryonic
modelling, the creation of emulators and light-cones, and the role of machine
learning. We finalise with a recount of state-of-the-art large-scale
simulations and conclude with an outlook for the next decade.
