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The influence of inhomogeneities on the large-scale expansion of the universe

The evolution of an inhomogeneous universe composed entirely of matter is followed from an early, nearly uniform state until the time when the inhomogeneities have begun to grow large. The particular distribution of matter studied in this article is chosen to have a periodic variation in only one of the directions, which is simple enough to allow the behavior of the metric to be solved analytically, well beyond a linear approximation based on the initial smallness of the fluctuation. This example provides an illustration of a universe where the inhomogeneities can affect its average expansion rate; and its simplicity allows a condition to be derived that tells when their presence should begin to become important. Since the averages of the non-uniform parts of the metric and the matter density grow faster than their uniform parts, the average expansion rate accelerates with the advent of the era governed by the inhomogeneities.