Davis,
The only way I could imagine that the universe is “done”; would be (and some scientists do have interesting arguments to back this up); if another big bang was to occur. But this would be more of a reset; than a state of completion in this case.
I’m curious to know however; what you are defining as “completion”. What exactly makes the universe complete? I think that like biological beings; the universe itself evolves, changes and adapts in its own way.
