Will the universe stop expanding?
Not likely, but not impossible either.
As we sit now, every constellation in the universe is moving away from every other constellation and their speed is, at least at present, accelerating.
The reason behind the acceleration is unknown, but speculation is that is has to do with dark energy.
For the universe to start contracting, there would need to be a force, gravity, strong enough to slow down the rate of acceleration until it is reverse but at present there does not appear to be enough gravity in the universe to do that.
But the wild card is dark matter. Dark matter/energy makes up about 95% of the known universe. If there is gravity associated with dark matter, that would be enough to reverse the expansion.
The physics of astronomy and quantum physics are really in their infancy and we have much to learn. The answer to all this may lie in the unified field theory which would bring astro-physics and quantum physics together.