Cosmological simulations of galaxy formation

Over recent decades, cosmological simulations of galaxy formation have been instrumental in advancing our understanding of structure and galaxy formation in the Universe. These simulations follow the nonlinear evolution of galaxies, modelling a variety of physical processes over an enormous range of time and length scales. A better understanding of the relevant physical processes, improved numerical methods and increased computing power have led to simulations that can reproduce a large number of the observed galaxy properties. Modern simulations model dark matter, dark energy and ordinary matter in an expanding space-time starting from well-defined initial conditions. The modelling of ordinary matter is most challenging due to the large array of physical processes affecting this component. Cosmological simulations have also proven useful to study alternative cosmological models and their impact on the galaxy population. This Technical Review presents a concise overview of the methodology of cosmological simulations of galaxy formation and their different applications. Cosmological computer simulations of galaxy formation emerged as the primary tool to study structure formation in the Universe. This Technical Review describes the main techniques and ingredients of such simulations and their application to develop and constrain galaxy formation theories. Key pointsThe formation of structures and galaxies in the Universe, which consists of ordinary matter, dark energy and dark matter, involves various physical processes such as gravity, gas cooling, star formation, supernova feedback, supermassive black hole feedback, stellar evolution, radiation, magnetic fields, cosmic rays and more.Cosmological simulations allow detailed studies of the formation and evolution of structures and galaxies in the cosmos, starting from smooth initial conditions constrained through observations of the cosmic microwave background, yielding detailed predictions of the galaxy population at different epochs of the Universe.The dark matter component is typically numerically modelled through the -body approach. Here, the dark matter phase-space distribution is sampled by an ensemble of phase-space sampling points, resulting in a Monte Carlo scheme, to follow its dynamics, which are governed by the collisionless Boltzmann equation.NThe gas content of the baryonic matter component is, in its simplest form, described through the Euler equations, discretized with Eulerian, Lagrangian or arbitrary Lagrangian-Eulerian schemes, coupled to other physical processes such as gravity, cooling processes, feedback processes and star formation.Alternative forms of dark matter, dark energy and gravity can also be explored through suitable modified simulation methods to test and constrain such theories in the context of structure and galaxy formation, by comparing to observational data such as galaxy surveys, leading to important insights into the overall cosmological framework of structure formation and cosmological parameters.