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 Originally Posted by NightGizmo
Wait... if the expansion of the universe is accelerating, how can it be asymptotically limited in size?
The problem is that we do not know much about dark energy at all. We think we know that the universe started with the Big Bang, then gradually expanded for a while. Then it underwent expansion. Very little is known about this, but it makes sense of some observations about the large-scale structure of the universe. Then the expansion ended and the universe began to slow down in it's rate of expansion.
Now it's accelerating again.
If it keeps accelerating, then it's Heat Death for the universe, which is the idea that if gravity loses the fight and the universe keeps expanding, eventually all the stars will burn out, all the galaxies will spin apart, all the Black holes will have evaporated... and nothing but a thin atmosphere of ever-cooling atoms is left.
Bottom line is that we just don't know the time-dependent nature of dark energy.
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The notion that the universe is flat from a GR perspective is perhaps in question. That statement is based on the value of the cosmological constant... which is presumed to not change in time, and thus constant... but it is not clear whether or not Einstein's cosmological constant is the whole story behind dark energy.
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