I Inflation "cooled Universe from 10^27 to 10^22 kelvins" why?

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I've seen numerous descriptions of inflationary phase a-la "The universe was supercooled from about 10^27 down to 10^22 kelvins".

However, I do not understand what is the basis for such estimation. We do not even know with any certainty how long the inflationary phase lasted. For one, "eternal inflation" theories even say that it may be lasting something like billions of years.

If it lasted even "only" a few seconds, the inflationary vacuum expansion surely diluted all preexisting particles to zero density. Thus, temp in this case should not be 10^27 or 10^22 K. It should be zero.

Then decay of the false vacuum does create a new hot and dense state. _Now_ it can be at ~10^22 K (if you know a paper where it is estimated to be about this temp to match observations, please post a link).

So, to me, the sequence of events in inflation theories should be:
[whatever] -> temp and density rapidly falls, possibly even to zero -> decay of vacuum, reheating to high temp (10^22K?) -> "normal Big Bang" scenario.
 
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Please give an appropriate source for this statement.
 
My Google-fu finds that it originated from "Phase transitions in the very early universe" by Guth.

http://adsabs.harvard.edu/abs/1983veu..conf..171G

Tried to find it online, no luck so far.
 
I believe the final temperature in the Guth statement refers to the inflationary patch post-reheating. After the super-cooled phase transition completes, the latent heat is released, reheating the system. Not certain about this, though.

This reference might be helpful: https://journals.aps.org/prl/pdf/10.1103/PhysRevLett.44.631
 
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