On the Cosmological Equations in a Universe with Small Scale Condensations

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Abstract
The metric describing a Universe containing small scale condensations is divided into two terms. One term represents the large scale, global development of space-time, while the other represents the small scale effects of local condensations. The global term is approximated by an average of the metric over a region containing many condensations. Equations to be satisfied by the individual terms of the metric are then derived from a combination of the Einstein equations and the averaged Einstein equations. The average of the metric is shown to satisfy the usual set of cosmological equations for a ‘smeared out’ metric, to a high degree of approximation; while the difference between the metric and its average satisfies a separate set of equations equivalent to instability equations. The large scale development of such a Universe is therefore shown to be almost independent of the formation of condensations provided the average of the energy–stress tensor is unaffected by the condensations.

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