When will the universe stop expanding?
Based on the most recent empirical evidence the universe will never stop expanding.
Presently scientific observations indicate that the universe is expanding and increasing its rate of expansion. If these observations are correct there is not enough mass to reverse the process of expansion.
If the expansion of the universe does not reverse the universe will continue to expand until the density of the universe is similar to what is presently called empty space. This is also called the heat death of universe. The law of entropy says that disorder will continue to increase until there is no useable matter or energy left in the universe.
The implication of an ever expanding universe is that the universe is not eternal it will have an ending and had a beginning.