When is the universe expected to cease expanding?

After the General Relativity of Einstein we thought that we had a model to describe the universe. The assumption was that the only force on a large scale was the gravity and the theory of Einstein was an excelent description of the gravity. So it was "enough" to establish the distribution of the masses in the universe to have a fair prediction of the expansion.

Today we know that the original assumption of gravity as the sole force on a large scale is wrong. The reason is simple: gravity, in Einstein theory, is purely attractive, while we observed that the objects in the universe are repelling each other. The expansion of the universe is accelerating, so there is something pushing away the bodies.

We call this "something" Dark Energy, but we have no clue of what it could be. The consequence is that we no longer have a good model of the forces acting on the large scale of the universe, so we cannot make a realistic prediction about the expansion until we figure out what Dark Energy is and how it works,

As of right now, there is no evidence or widely accepted theory that suggests the expansion of the universe will stop, and it is assumed that it will continue to expand indefinitely.