Transients from Zel’dovich initial conditions

Abstract. We investigate the error implied by the use of the Zel’dovich approximation to set up the initial conditions at a finite redshift zi in numerical simulations. Using a steepest-descent method developed in a previous work (Valageas (2002a)) we derive the probability distribution P(δR) of the density contrast in the quasi-linear regime. This also provides its dependence on the redshift zi at which the simulation is started. Thus, we find that the discrepancy with the exact pdf (defined by the limit zi → ∞) is negligible after the scale factor has grown by a factor a/ai >∼ 5, for scales which were initially within the linear regime with σi <∼ 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.