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But if you accept the Big Bang theory, ie that the universe had a start, then you have to concede that it must also have a finish. It's possible that they've reached the boundaries of what we define as the universe.
As for this, not necessarily. The universe has expanded in a double inflationatory model, and can continue to do so. In this case the end of the universe would be that everything continues to drift apart with a lower and lower temperature, until it (the temperature) evens out between matter and energy. It would still expand forever.