  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.

Astrophysics