Construction and some properties of the most general homogeneous Newtonian cosmological models

A general analysis of homogeneous Newtonian cosmological models is given first. This has not been done till now and there is some confusion in the literature on this subject. Homogeneous Newtonian cosmologies are defined in terms of symmetry groups. There are two basic types. The first type possesses a transitive symmetry group on the spacelike hypersurface defined by setting the time equal to a constant. This type has two subclasses; they correspond to the relativistic classification of Bianchi type I and Bianchi type VII, with h = 0. In the second type the spacelike hypersurfaces are not perpendicular to the time axis. It is found that the first seven of the Bianchi types are possible. Velocity fields and equations of motion are discussed. Higher order perturbation theory is discussed also. The simplest possible background model is assumed, namely, the Newtonian model which is homogeneous and isotropic dust and which has the cosmological constant zero and the quantity analogous to the curvature equal to zero. The time dependence of the density and velocity field is found for arbitrary order. The solution for the density in terms of lower order quantities is found explicitly. This is then applied to second order perturbations to understand the interaction of first order perturbations. A Newtonian theory of light propagation due to Trautman is applied to the preceding Newtonian model to first order and the results compared with the relativistic results. Type VII, h = 0, relativistic cosmology is discussed briefly, and comments are made a kinetic theory for the Newtonian analog of this model