Inflation and the size of the Universe

[Ranku]

By how many times is the size of the observable universe larger than expected because of inflation?

 

[phyzguy]

By how many times is the size of the observable universe larger than expected because of inflation?

Whether or not there was a period of inflation does not alter the current size of the observable universe. The inflation hypothesis simply helps to explain a number of observed features of the current universe, like its flatness and spatial uniformity. If inflation happened, it occupied only an extremely brief period of time at the very beginning of the period of expansion, so the current age of the universe is not significantly altered. It is the current age that determines the size of the observable universe.

 

[PeterDonis]

larger than expected

What is "expected"?

 

[Grinkle]

By how many times is the size of the observable universe larger than expected because of inflation?

Your question implies that you think the size of the OU is evidence to support that our early universe underwent an inflationary period.

I think inflation theories are consistent with the observed geometric flatness and uniformity of the OU. I don't think size of the OU per se comes into it. If you have seen discussion to the contrary, please link them - I'd be interested.

 

[bahamagreen]

By how many times is the size of the observable universe larger than expected because of inflation?

When you ask about "the size of the observable universe" you need to be more clear whether you mean the size now of what used to be the size of the observable universe then before inflation (which is now beyond our observable universe now), or whether you mean what we see now.

This is somewhat further confounded by how we might define an observable universe because if it is defined in terms of "light from far away", then that definition encounters the time of last scattering (380,000 years after the big bang) before which light was unable to enjoy any cosmological mean free path. One could try to figure the potential size of the observable universe prior to the time of last scattering by ignoring it and calculating how far light sources could be if space was clear, but that sort of defeats the definition and the reality.

So if you mean what we see now, then it is just the age. However; I think it is possible to ask how big the size of what used to be the observable universe before inflation has become now, understanding that we can't observe it now. This is another way of asking how much inflation had to occur in order to result in the way things look now so that the fine tuning problems of horizon, flatness, etc. are resolved by the present observable universe having originated within a boundary of causal space. This is often answered as the number of e-folds - the time interval in which an exponentially growing quantity increases by a factor of e (2.718281828). I have seen about 60 e-folds as a popular figure for a while.

 

[Ranku]

Your question implies that you think the size of the OU is evidence to support that our early universe underwent an inflationary period.

I think inflation theories are consistent with the observed geometric flatness and uniformity of the OU. I don't think size of the OU per se comes into it. If you have seen discussion to the contrary, please link them - I'd be interested.

The horizon problem is a problem if we believe that there is no reason for the universe to have been always homogenous. If the universe was always homogenous, then homogeneity over superluminal scale would be natural. However, if the universe was originally inhomogenous, to explain superluminal scale homogeneity requires inflation, whereby originally inhomogeous regions in proximity had the opportunity to homogenize, and inflation blew up those regions whereby there is homogeneity over superluminal scale.
Now, regardless of whether the universe was always homogenous or not, whether inflation occurred or not, either way we observe homogeneity over superluminal scale. We can therefore compare between a universe which was always homogenous and in which homogeneity would be observed at superluminal scale of a certain order of magnitude, and a universe which was originally inhomogenous and which inflation enables to be homogenous over superluminal scale of a certain order of magnitude. If there is a difference in order of magnitude between the two superluminal scales of homogeneity, would that not be proof of inflation?

 

[Grinkle]

This -

a difference in order of magnitude between the two superluminal scales of homogeneity

Seems to me different than this -

the size of the observable universe

Which is, for me, is part of a healthy discussion - sometimes (often) in this forum folks refine wording and thinking in B level discussion. I definitely do. So no criticism intended.

Am I missing something about your post 1, or are you refining what your question is? If the latter, then imo you need to add the evidence of initial in-homogeneity to logically move towards proof.

As an aside - scientific experiment usually either falsifies or stays consistent with theories. Proof is very hard to claim because one never knows what new experiment or observation might come along to falsify a previously very well supported theory. That is pretty off-topic, though. Thanks for the explanation in post 6 - very helpful for me.

 

[phyzguy]

The horizon problem is a problem if we believe that there is no reason for the universe to have been always homogenous. If the universe was always homogenous, then homogeneity over superluminal scale would be natural. However, if the universe was originally inhomogenous, to explain superluminal scale homogeneity requires inflation, whereby originally inhomogeous regions in proximity had the opportunity to homogenize, and inflation blew up those regions whereby there is homogeneity over superluminal scale.
Now, regardless of whether the universe was always homogenous or not, whether inflation occurred or not, either way we observe homogeneity over superluminal scale. We can therefore compare between a universe which was always homogenous and in which homogeneity would be observed at superluminal scale of a certain order of magnitude, and a universe which was originally inhomogenous and which inflation enables to be homogenous over superluminal scale of a certain order of magnitude. If there is a difference in order of magnitude between the two superluminal scales of homogeneity, would that not be proof of inflation?

So it appears your original question has been answered and now you have a new question. Is that correct? However, I am having trouble understanding your new question. When you say, "If there is a difference in order of magnitude between the two superluminal scales of homogeneity...," which two scales are you referring to? We only have one universe to measure. What test are you proposing to do that would be "proof" of inflation?

 

[timmdeeg]

Now, regardless of whether the universe was always homogenous or not, whether inflation occurred or not, either way we observe homogeneity over superluminal scale.

I'm not sure if you are aware of the Flatness problem which is a fine-tuning problem and which was solved by assuming inflation too.

https://en.wikipedia.org/wiki/Flatness_problem

 

[Ranku]

Upon re-reading Alan Guth's book The Inflationary Universe, I find that my OP question has indeed been answered: The size of the observable universe is the same for both a universe with inflation and a universae without inflation. So the size of the observable universe cannot be a test for whether inflation occurred or not.
As for comparing superluminal scale homogeneity, since that sits within the observable universe, so there will be no difference there either, between a universe with or without inflation.