Astronomy & Astrophysics

Free access article

A&A 385, 761-767 (2002)
DOI: 10.1051/0004-6361:20020187

Transients from Zel'dovich initial conditions

P. Valageas

Service de Physique Théorique, CEN Saclay, 91191 Gif-sur-Yvette, France

(Received 5 December 2001 / Accepted 29 January 2002 )

Abstract
We investigate the error implied by the use of the Zel'dovich approximation to set up the initial conditions at a finite redshift $z_{\rm i}$ in numerical simulations. Using a steepest-descent method developed in a previous work (Valageas 2002a) we derive the probability distribution ${\cal P}(\delta_{R})$ of the density contrast in the quasi-linear regime. This also provides its dependence on the redshift $z_{\rm i}$ at which the simulation is started. Thus, we find that the discrepancy with the exact pdf (defined by the limit $z_{\rm i}\rightarrow \infty$ ) is negligible after the scale factor has grown by a factor $a/a_{\rm i}\ga 5$ , for scales which were initially within the linear regime with $\sigma_{\rm i} \la 0.1$ . This shows that the use of the Zel'dovich approximation to implement the initial conditions is sufficient for practical purposes since these are not very severe constraints.

Key words: cosmology: theory -- large-scale structure of Universe