Abstract
Recent experimental results from supernovae Ia observations have been interpreted to show that the rate of expansion of the universe is increasing. Other recent experimental results find strong indications that the universe is ``flat.'' In this paper, I investigate some solutions of Einstein's field equations which go smoothly between Schwarzschild's relativistic gravitational solution near a mass concentration to the Friedmann-Lemaitre expanding universe solution. In particular, the static, curved-space extension of the Lemaitre- Schwarzschild solution in vacuum is given. Uniqueness conditions are discussed. One of these metrics preserves the ``cosmological equation.'' We find that when the rate of expansion of the universe is increasing, space is broken up into domains of attraction. Outside a domain of attraction, the expansion of the universe is strong enough to accelerate a test particle away from the domain boundary. I give a domain-size--mass relationship. This relationship may very well be important to our understanding of the large scale structure of the universe.
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