# Most total e-folds from inflation

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1. Aug 4, 2014

### chasrob

I'm asking this just out of curiosity on my part.<grin> When I first heard of cosmic inflation, a long time ago, I went to the local university library to look at papers that made estimates of the total number of e-folds from various models. I'm not an expert in any area of science but I found the idea fascinating.

I found one in the popular mag Sky and Telescope that stated the early universe possibly went through 3000 e-folds and was now roughly ten to that power of light years across! The most inflation I found (and made a Xerox of) by Indian theorist T. Padmanabhan in the 1980's stated that, if a "natural" value of λ was used, there were 10720 e-folds and a resulting space e^10^720 cm across.

A more recent article concerning low scale inflation had 1028 e-folds if certain parameters were used.

I was wondering--as I say, just curious--if anyone had heard of similar ginormous (but not infinite) amounts of inflation en total.

2. Aug 4, 2014

### Chronos

It depends on the inflationary model. It is usually assumed the number of e-folds is between 30 and 60, but, is model dependent. For large field models, it can exceed 50, whereas small field models can get by with fewer e-folds. See http://arxiv.org/abs/1405.5538, How Many e-Folds Should We Expect from High-Scale Inflation?, for further discussion.

3. Aug 5, 2014

### Ich

That is $2\times10^{10}$, according to your link.

4. Aug 5, 2014

### chasrob

20 billion e-folds, wow. I guess it's not a big deal to most; the last 50-60 are the interesting ones.

5. Aug 5, 2014

### skydivephil

Some loop people have been estimating the number of e folds at around 145:
http://arxiv.org/abs/1301.1264

6. Aug 5, 2014

### Zag

chasrob, there is a difference between the total number of e-folds the Universe may have experienced and the observable number of e-folds we can infere from measurements.

The total number of e-folds - which is a measure of the amount by which the universe expanded since the start of inflation - can very well be as large as you want and it is not only model dependent but its value is also affected by how confident we are to assume that our high energy physics still works at very early times. The more you push the beginning of inflation to earlier times, the bigger will be the total number of e-folds you will get for a same model - but our physics may very well break down at extremmely high energies (very early times) and then whatever you came up with to model inflation won't be valid anymore at those very early stages. Naturally this total number of e-folds is still largely speculative since we still don't have a good physical description for the Universe at the moment it poped up into existence.

Now, what people usually talk about is the observable number of e-folds, and this one is constrained to be somewhere between 50 and 70 e-folds - but again values may vary inside this range according to your choice of inflationary model. This number of observable e-folds represents the amount of expansion the Universe experienced from the moment the largest scales we can observe today crossed the Hubble horizon (or Hubble sphere) until the end of inflation. A way of picturing it is the following: as our Universe expanded from a singularity, there was a time during inflation when the current observable Universe (which was contained in a much smaller region at that time) matched in size with the Hubble sphere, at that moment of crossing we would start our clock and only stop it at the end of inflation. This time interval measured by your clock would be analogous to the amount of observable inflation. And this number can actually be estimated based on observations! In fact, a very good paper by Liddle and Leach which makes estimates of the amount of observable inflation is the following: http://arxiv.org/pdf/astro-ph/0305263v2.pdf

I hope this was helpful! Best,
Zag

7. Aug 7, 2014

### chasrob

Thx for the links. What I meant in my last post was that, as Chronos says, the really interesting efolds are the last 30-60, which potentially can be studied by us.

I think it's interesting that all of our visible universe could have originated from such a infinitesimal space, far smaller than Planck size. After 20 billion efolds or even 10720. After all, if you efold an atom only about a 100 times it will be as big as the visible universe.

8. Jan 25, 2015