A spherically symmetric self-similar universe

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Abstract
A spherically symmetric self-similar dust-filled universe is considered as a simple model of a hierarchical universe. Observable differences between the model in parabolic expansion and the corresponding homogeneous Einstein–de Sitter model are considered in detail. It is found that an observer at the centre of the distribution has a maximum observable redshift and can in principle see arbitrarily large blueshifts. It is found to yield an observed density–distance law different from that suggested by the observations of de Vaucouleurs. The use of these solutions as central objects for Swiss-cheese vacuoles is discussed.

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