Transients from Zel'dovich initial conditions

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

Corresponding author: valageas@spht.saclay.cea.fr

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_i in numerical simulations. Using a steepest-descent method developed in a previous work (Valageas [CITE]) we derive the probability distribution of the density contrast in the quasi-linear regime. This also provides its dependence on the redshift z_i at which the simulation is started. Thus, we find that the discrepancy with the exact pdf (defined by the limit ) is negligible after the scale factor has grown by a factor , for scales which were initially within the linear regime with . 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.