Sadly, the answer to this might be yes. At least if you believe a theoretical model produced in the early 1980's by Japanese physicists.
From purely mathematical considerations, they proposed that as the universe continues to expand indefinitely, space-time becomes unstable to a topological fluctuation which pinches off part of our space-time to form an independent 'baby' universe. This is all speculative physics, however. The consequence might be nothing, or it might be the collapse of part of our universe into a 'black hole' which evaporates to seal-off the umbilical connection between our universe, and the baby universe.
Still, it's fun to imagine that there may still be interesting things in store for our universe as it becomes trillions of years old!
Copyright 1997 Dr. Sten Odenwald
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