Non-linear structure formation in scale free cosmological models

Calculation of the clustering of matter in the universe in different cosmological models, even in the approximation that all but gravitational forces are neglected, relies essentially on numerical simulations which use the N body method. The physics of non-linear clustering remains poorly understood, and there are open questions about the resolution/precision of simulations.

After a brief overview of these issues, I will discuss them in the framework of a particularly simple class of “scale-free” cosmological models which have the interest of providing a very simple diagnostic for determining spatial resolution, and also some simple analytical predictions for non-linear clustering.

We explore two questions which turn out to be intimately linked to the issue of numerical resolution: the relevance of the so-called stable clustering approximation in the strongly non-linear regime, and the dependence of halo profiles on cosmology and initial conditions.