Abstract
We explore the development of galaxy clustering after an extremely long time in a flat Einstein–de Sitter universe. The time-scale for growth of clustering in this universe is shorter than the global expansion time-scale. This eventually leads to a single cluster of arbitrary large size, which dominates each expanding particle horizon. Since the particle horizons expand faster than the metric, one cluster may ultimately dominate the universe. Assuming that the distribution of galaxies in such a static, bound cluster becomes approximately isothermal, we show how it can be represented by a general relativistic metric embedded in an expanding Einstein–de Sitter universe. The embedding is achieved by means of a ‘Schwarzschild membrane’. Pressure is important, unlike in previous Tolman–Bondi models of inhomogeneities. These new hybrid models generalize previous descriptions of growing clusters and show how a changing equation of state for the matter may alter the large-scale symmetry of space–time over growing regions in the universe.
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