NEWTONIAN COSMOLOGY IN LAGRANGIAN FORMULATION - FOUNDATIONS AND PERTURBATION-THEORY

The ''Newtonian'' theory of spatially unbounded, self-gravitating, pre ssureless continua in Lagrangian form is reconsidered. Following a rev iew of the pertinent kinematics, we present alternative formulations o f the Lagrangian evolution equations and establish conditions for the equivalence of the Lagrangian and Eulerian representations. We then di stinguish open models based on Euclidean space R-3 from closed models based (without loss of generality) on a flat torus T-3. Using a simple averaging method we show that the spatially averaged variables of an inhomogeneous toroidal model form a spatially homogeneous ''background '' model and that the averages of open models, if they exist at all, i n general do not obey the dynamical laws of homogeneous models. We the n specialize to those inhomogeneous toroidal models whose (unique) bac kgrounds have a Hubble flow, and derive Lagrangian evolution equations which govern the (conformally rescaled) displacement of the inhomogen eous flow with respect to its homogeneous background. Finally, we set up an iteration scheme and prove that the resulting equations have uni que solutions at any order for given initial data, while for open mode ls there exist infinitely many different solutions for given data.