# Scale Factor Ratio

1. Apr 27, 2007

### George Jones

Staff Emeritus
What is the ratio of the scale factor now to the scale factor at the end of the inflationary era?

Edit: In other words, what is the z value of the end of the inflationary era?

Last edited: Apr 27, 2007
2. Apr 27, 2007

### marcus

I've wondered about that, and whether there even is a unique prevailing estimate (with the amount of slack in the scenarios). I hope you get an answer.

3. Apr 27, 2007

### George Jones

Staff Emeritus
I'll be happy if someone gives $a$ and $b$ values for $10^x$ with $a < x < b$.

4. Apr 27, 2007

### marcus

there's a related question, GJ, which you may know the answer to.
(I think it has a definite answer and I may even have read an estimate, but if so it has faded from my memory)

there must be a moment when the CNB (cosm. neutrino background) was released and I wonder what the redshift of that is.

it would be a number much larger than 1100 by many orders magnitude,
but nevertheless somewhat analogous to 1100 as the z for the CMB.

I wonder if anybody here knows an estimate of that z.

5. Apr 27, 2007

### George Jones

Staff Emeritus
Cosmological Physics by Peacock say roughly 10^10.

6. Apr 27, 2007

### Garth

7. Apr 27, 2007

### pervect

Staff Emeritus
If inflation is to solve the flatness-oldness problems, inflation must have lasted for a minimum of "100 doublings",

http://www.astro.ucla.edu/~wright/cosmo_04.htm

That would be 10^30 or so.

I think there may be some constraints resulting from the COBE data, but I don't know what they are.

8. Apr 29, 2007

### George Jones

Staff Emeritus
Not quite what I asked , but the answer seems reasonable according to Figure 2. from Linweaver's paper on inflation. This figure shows the size of the universe (compared to now) when the Standard Hot Big Bang takes over after inflation. This is what I wanted.

This is the paper that marcus referenced in his Cosmological event horizon thread.

Thanks marcus, Garth, and pervect!

In a few days, I'll probably ask another question in this thread (my motivation for the first question), but, this time, I want to try and find the answer first!

9. Apr 29, 2007

### pervect

Staff Emeritus
Well, my reaction to your question and the answers was that I would and did want not only a number, but some idea of what observations gave rise to that number, some understanding of where the number came from.

Assuming that inflation is the reason we don't have a flatness-oldness problem gives at least a lower bound on how long inflation lasted. But what gives an upper bound?

I would expect that the duration (number of doublings) of inflation would have impact on the large scale structure formation, and on the observed slight variances in the CMB. But I'm not sure what assumptions are needed to work backwards from these sorts of observations to put some upper bound on how long (how many doublings) inflation lasted, or what papers might attempt this.

10. Apr 29, 2007

### George Jones

Staff Emeritus
Again, this is not what I asked for in my original post.

Let $a_{start}$ be the scale factor at the the beginning of the inflationary era, $a_{end}$ be the scale factor at the the end of the inflationary era, and $a_{now}$ be the scale factor at the present instant.

I asked for the value of $a_{now}/a_{end},$ not for the value of $a_{end}/a_{start},$ i.e., not for the growth during inflation.

Edit: both $a_{now}/a_{end}$ and $a_{end}/a_{start}$ can read off (for two infationary models) of Lineweaver's Figure 2.

Last edited: Jul 4, 2011
11. Apr 30, 2007

### pervect

Staff Emeritus
Well, the lower bound is still a lower bound :-) - i.e. if you need 100 doublings, during inflation, and then it expands more, you have more than 10^30.

But it makes it even harder to set an upper bound.

I'm not sure if we have a very strong experimental evidence for exactly when inflation occured (temperature, density, etc). The good news is that if we can come up with such data, we can use the Friedmann equations (assuming we believe them) to give us the early history of the universe. Of course, we need to add in the radiation terms to get the early history.

Last edited: Apr 30, 2007