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Heat death is the predicted fate of the universe.

Eternal inflation theory states that new hydrogen atoms are created in each pocket universe so that means new hydrogen atoms are still being created somewhere in the multiverse.

I’ve read that most of inflationary models are eternal. So if eternal inflation is correct, does it mean the multiverse as a whole won’t ever suffer heat death?

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Well, this is really two things that are being mushed together here.

Eternal inflation for a single universe just means that the universe will continue to inflate forever. The universe in this case will reach heat death, or as close to it as quantum mechanics allows. The formation of new "hydrogen atoms" (actually, I'd suspect merely sub-atomic particles would be formed, but regardless) is part of that quantum-induced difference, it's because quantum mechanics doesn't allow real heat death.

However, eternal inflation is usually a part of a multiverse theory, implying the constant formation of bubble universes. This multiverse as a whole does not reach heat death, or close to it - bubbles within it are constantly collapsing into slower-inflation, forming new universes. So the multiverse does not reach a heat death, but this has little to do with the formation of particles out of vacuum in each universe within it.

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