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During inflation, expansion happens at a very rapid rate.

How many years of expansion did it fast forward through?

Meaning, if it weren't for inflation, how many years would it take for the universe to expand at its basic rate from the big bang to the size of the universe after inflation?

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    $\begingroup$ The expansion that the Universe went through during inflation isn't usually measured in 'years-at-normal-rate', presumably because it doesn't make any sense to talk about a normal rate when that's simply not what happened. It is measured in e-folds; experimental data requires that inflation lasted for about $60$ e-folds, aka the Universe expanded by a factor $e^{60}$ or more. $\endgroup$ – Danu Mar 6 '14 at 6:53
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    $\begingroup$ There are a lot of different models though, and the number of e-folds they are capable of producing can easily go up to $100$ or maybe even more: we are unable to observationally tell the difference anyhow because of the limited size of the observable Universe. $\endgroup$ – Danu Mar 6 '14 at 7:20
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Assuming we have the correct value for the cosmological constant the doubling time, that is the time it will take for the universe to double in size, is around 11.4 billion years.

We have few hard theories about inflation, but suppose the universe expanded by $e^{60}$ as Danu suggests in his comment, then the number of doubling times is $60/ln(2) \approx 87$. The time it will take the current universe to double in size 87 times is about 990 billion years.

You can obviously adapt this sum for whatever number of $e$-foldings your preferred theory of inflation predicts.

Footnote: the doubling time really only applies once the universe has expanded enough to make the density of matter negligable compared to the cosmological constant. However we aren't far off that stage and given how approximate this sum is I don't think it really matters.

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  • $\begingroup$ So... inflation fast forwards through 990 billion years of expansion? $\endgroup$ – MikeHelland Mar 10 '14 at 13:54
  • $\begingroup$ @John Rennie : I am not so sure about this. $\\$ The Hubble Time, 11.4Gyrs that you refer to, is the time that it would take the universe to expand by one e-fold today. This is not a constant number, but a timescale that changes with the scale of the universe. Namely, the time that it would take the universe to expand by one e-fold tomorrow will be (slightly) bigger. So your calculation is incorrect I think. Please correct me if I am wrong... $\endgroup$ – Flint72 May 9 '14 at 15:06
  • $\begingroup$ @Flint72: because of dark energy the universe is asymptotically approaching a de Sitter geometry. I probably ought to sit down and think hard about this, but off the top of my head I believe this means the doubling time is actually decreasing slightly with time, but tending to a constant value. You are correct to say the doubling time will change a bit in the future, but given how rough the above calculation is I don't think we are committing any great scientific sins by approximating it as a constant. $\endgroup$ – John Rennie May 9 '14 at 15:34

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