No. The Big Bang Theory predicts an infinite future (and heat death) for the universe but says nothing about what might have come before inflation, so an eternal universe is possible although I believe it is considered unlikely. It would require some kind of fundamental state change, since the universe before the singularity would have to have been different in some significant way than the current universe, otherwise the singularity would not have happened (we see no singularity in the future of the current universe). I'm not widely read in this but I have never encountered a theory of an eternal universe that seemed to be anything other than pop-sci blather.
I believe the historical idea of an eternal universe is one that is static, unchanging, and has no beginning and no end. The big bang theory absolutely rules this specific type of eternal universe out, as it says that at every scale the universe is neither static nor unchanging but has a very dynamic existence. At its largest scales it expands and at smaller scales it experiences huge changes from the formation and evolution of galaxies, stars, planets, and other bodies. What the BBT doesn't say is whether or not the universe has a beginning or an end. The fact that the BBT predicts a singularity doesn't mean that it has a beginning, it means that the theory can no longer be used at that point. Another one must be found. As for an ending, there isn't one predicted by the BBT, but who's to say our current understanding of physics is sufficient to predict what will happen hundreds of billions of years from now?
It means that before approx 14bn years ago, nothing of our present observable Universe existed.
This does not rule out the existence of some kind of Universe beyond the observable.
However if something does exist beyond that it probably never can be observable, thus is not something which science can address.
There are all manners of metaphysical speculations, but they really don't explain anything.
Back when I was about 2nd year in high school, my English/Spanish/History teacher knew of my interest in science, and he gave me a paperback book by Fred Hoyle on the Steady-State Universe. He said, "This is an old theory that has now been proven wrong, but it is still an interesting read". I really enjoyed the book, and it motivated me to go on and learn more about the BBT and more modern understandings.
Hawking and Penrose showed that given certain assumption the big bang is associated with a spacetime singularity which marks the beginning of the universe. However these assumptions are no longer considered realistic and so its quite possible that the universe existed eternally into the past. there is no reason to either confirm nor deny that possibility. What most cosmologists agree is necessary is quantum theory of gravity to be able to probe this further. There are no theories of quantum gravity that have passed experimental verification. But there are some that theorists think have a lot going for them. When applied to the big bang these theories seem to suggest the universe existed before the big bang. Perhaps eternally into the past. I think these are the best bets we have at the moment, but they are not more than that. good bets but not verified experimentally. It is not impossible that we will be able to probe this experimentally and there are suggestions for how to do this. but it hasn't been done yet. So we dont know.
The universe will expand forever into the future assuming dark energy is a cosmological constant. There is always the possibility that dark energy is not a constant in which case the future of the universe is more uncertain.
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