Untitled

Cosmological Parameters from Galaxy Clusters: An Introduction

“…The filter function corresponding to a top-hat in real space is oscillating due to the sharp edges (see Kolb & Turner 1990, Kaiser 2002). Since every mode grows independently from each other in the linear regime, we expect that δ is proportional to the linear growth factor D(t).…”

“…If we assume that the radius of the virialized halo is about half of the radius of maximum expansion, the reader should be able to derive the actual average density contrast within the virialized halo with respect to the ambient density, as well as the linear value of the density contrast at the time of collapse. This can be left as a useful exercise, in the simple case of an EdS universe (see Kaiser 2002 for the solution and much more on cosmic stucture formation). It turns out that the linear threshold for collapse in an EdS universe is δ c0 = 1.686, while the actual density contrast of a virialized halo is ∆ vir = 178.…”