It's interesting to ponder the end of the universe. For a long time, the big question was whether there was enough matter in the universe to make it recollapse, or whether it would expand forever. A cosmological constant with the right sign makes the energy density of the vacuum positive, but makes its pressure negative - and 3 times as big. This makes the universe tend to expand.
Normal matter makes the universe tend to recollapse.
Let's suppose this happens. First let me set the stage. First, galaxies will keep colliding. These collisions seem to destroy spiral galaxies - they fuse into bigger elliptical galaxies. We can already see this happening here and there, and our own Milky Way may collide with Andromeda in only 3 billion years or so.