Lagrangian theory of gravitational instability of Friedman-Lematre cosmologies and the 'Zel'dovich approximation'

Abstract

The aim of this paper is to clarify the connection between the so-called Zel'dovich approximation and perturbative solutions of the Euler-Poisson system for the motion of a self-gravitating dust continuum, evaluated in the Lagrangian picture of fluid dynamics. Solutions of the Lagrangian equations, linearized at an isotropically expanding background, are derived. This approximation is investigated; it contains the Zel'dovich approximation as well as a generalized form of it as subclasses, and allowed treatment of the non-linear evolution of vortical perturbations consistently within the framework of self-gravitating motions. In contrast to the prediction of the standard linear approximation, vorticity is coupled to the density enhancement and is amplified in the present approximation