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In their article at bigthink.com "Surprise: the Big Bang isn't the beginning of the universe anymore", the writer articulated an alternative theory that suggests inflation didn't begin at a singularity, but continued back in time ad infinitum. This is a popular science website, so the article is written for a general audience, even though the writer is "a Ph.D. astrophysicist and science communicator", and therefore the descriptions may be embellished a little. However, in the second last paragraph, he wrote "When inflation ended, the universe reheated to a high, but not arbitrarily high, temperature, giving us the hot, dense and expanding universe that grew into what we inhabit today."

I am not quite sure whether this statement was part of the theoretical framework of the new concept of eternal inflation, or if it is part of all inflation theories. Is it part of the incumbent inflation theory? If so, where is the reheating coming from? And wouldn't this reheating wipe out the very thing that inflation was theorized to fix, that is scale of the fluctuations in the distribution of matter/energy throughout the universe (an annealed universe, to use a materials physics analogy)?

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Reheating is part of standard inflation and is not unique to eternal inflation. See Wikipedia.

I am not sure what you mean by "scale of the fluctuations in the distribution of matter/energy throughout the universe", but it is not one of the standard things inflation is theorized to fix - these are the horizon problem, the monopole problem, and the flatness problem.

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