Growth of structure: beyond linear theory

Abstract

Abstract Going beyond small, linear perturbations, this chapter studies the nonlinear evolution of structure. We describe the perturbation-theory approach, which proceeds by taking moments of the Boltzmann equation as in linear theory. We discuss when this approach breaks down and how gravity-only N-body simulations can help in obtaining a realistic description of structure on fully nonlinear scales. Bound structures, dark matter halos, identified in these simulations can be seen as building blocks of nonlinear structure (halo-model approach). In particular, the most massive, exponentially rare halos host galaxy clusters. We develop a simple theoretical model for the number density (mass function) of dark matter halos, which explains why high-mass halos are so rare and which is useful for obtaining cosmological constraints from galaxy cluster counts. One of the most important aspects of nonlinear large-scale structure is the relation between the clustering of galaxies and that of matter. We show how the linear bias ansatz adopted in the previous chapter is generalized to nonlinear order.