Correlation of Newtonian and relativistic cosmologies

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Abstract
Comoving metrics of relativistic dust universes are interpreted locally in terms of conventional Newtonian cosmology. Quasi-classical equations for these universes show how anistropies in the motion and the spatial curvature affect the dynamics. Though generally indeterminate, the equations have heuristic and possibly predictive value, especially as regards matter singularities and indefinite expansion, for which they offer simple classifications. Examples are provided by homogeneous world models, including some with an apparently new kind of singularity behavior.

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