The Fate of our Three Different Universes
A Flat Universe has sufficient mass to slow the expansion down, and bring it nearly to a stop.. but not quite! It can't stop exactly, or it would collapse. Such a universe is always expanding, but it does so almost imperceptively after some time. Such a universe has zero curvature
In a Closed Universe, there is a lot of matter. The gravitational force of all that matter will inevitably slow the expansion down. In this universe, the radius (size) of the universe will reach a maximum at some point, and then the universe will begin to shrink back down until it crashes back into an infinitely small point. Such a universe has positive curvature. Its possible that such a universe might be ``re-born'', bouncing back to make a new big bang. This is called the oscillating universe theory.
It should be apparent to the astute student, that the issue of Dark Matter is vital if we are to answer the question of the eventual fate of our Universe!