Cosmological simulations

Numerical simulations using the N-body method are the primary instrument used to probe the non-linear regime of structure formation in cosmology and provide the basis for all theoretical predictions for the distribution of dark matter at the corresponding physical scales. Over the last few decades, such simulations have gained in refinement and complexity and have allowed the exploration of an ever larger range of scales. Nevertheless, the understanding of their precision and their convergence toward the continuum limit remains, at very least, incomplete, in particular for smaller scales.
Indeed, numerical simulations of structure formation in the universe in cosmology use the N body method in which the continuum density field of dark matter is represented by a finite number of discrete particles interacting by a smoothed Newtonian two body potential. It is evidently of importance to control as much as possible for their precision and reliability. Specifically, beyond issues of numerical convergence, it is important to understand the limits imposed on the accuracy of results by the use of a finite number of particles to represent the theoretical continuum density field, and the associated introduction of a smoothing scale (or equivalent) in the gravitational force.