If the universe stopped expanding, when would we realize it? Suppose in this moment the universe stopped expanding, how long would if take and how would we register the change?
Since the bodies are still and it is space that is expanding in between, we wouldn't notice the change even if the expansion would completely stop in a short time?
 A: A few million to about 30 million years from now. I.e., we'd be able to measure a change in the previously observed redshifts for galaxies a few to about 10 Mega parsecs away. A parsec is a little more than 3 light years. 
The reason is that closer in galaxies are in our local group or cluster, and we are to a great extent gravitationally bounded to them. Our relative velocities then depend more on each other than the cosmological expansion. If we go further then the cosmological expansion starts becoming the dominant effect. We would have to see more than one Galaxy doing that, but it certainly would be deemed as totally unexpected to see even one radically having changed its velocity.
Of course, since it might have happened a few to 30 million years ago, we could start seeing that tomorrow. 
Now, something huge cosmologically had to happen for the expansion to stop. Maybe some huge increase in the matter density. If so, we might see some of that in more local galaxies, maybe even ours, as we would see the local gravitational effects. So we actually then would discover it pretty quickly, say a year or two for astronomers to realize they are seeing something and not simply errors in everything they calculate from more local observations. If not an increase in mass or energy density, then some strange field would have settled to some value other than its current one, and again it could affect things everywhere. If it happened 30 million light years away we'd wait the same time as in my first answer. 
But none of that makes much sense.  
