# Did inflation itself make the universe bigger than what we currently observe

## Main Question or Discussion Point

Reading V.J. Stenger's "God: The Failed Hypothesis". He says that the observable size of the universe, 10^26 meters, is only 10^61 times bigger than the Planck distance, and he says inflation caused the universe to expand by a factor of 10(10^100) from whatever size it was before inflation, which I assume could not have been smaller than the Planck distance. Is he saying that the inflation itself made the universe bigger than what we can currently observe?

Feel free to point me to some remedial reading.

bapowell
Good question. Inflation doesn't change the size of the observable universe. The size of the observable universe is determined by the approximate distance that light has traveled since the end of inflation (the end of inflation is effectively the Big Bang, as it initiates the universe's expansion from a hot, dense state.) It is often said that inflation increases the size of the universe by 'X' amount. What people mean when they say this is that the scale factor, $$a(t)$$ (the function governing how lengths are measured in the universe) increases by a fantastic amount during inflation, by a factor of at least around $$10^{25}$$. The result is that inflation separates initially adjacent points to vastly separated regions of space. However, our observable universe, which, again, is determined by roughly how far a photon meanders by some initial time, does not increase as a result of this expansion. What inflation does for the observable universe is to leave behind a very smooth, homogeneous, flat region.

Good question. Inflation doesn't change the size of the observable universe.
My bad. I asked the question in an ambiguous way. Let me start over from scratch: I accept as fact that what we can observe is approximately 10^26 meters. I assume that 10^26 meters is probably something like 13.72Gly.

What I was really asking is whether the end result of inflation was a universe larger than 10^26 meters. In fact, if I read Stenger correctly, many, many orders of magnitude larger than 10^26 meters. Have I worded it clearly enough that now it's obviously a different question from the one you thought I was asking? Sorry. I'm a naif. I don't know the vocabulary or even how to formulate good questions.

bapowell
My bad. I asked the question in an ambiguous way. Let me start over from scratch: I accept as fact that what we can observe is approximately 10^26 meters. I assume that 10^26 meters is probably something like 13.72Gly.

What I was really asking is whether the end result of inflation was a universe larger than 10^26 meters. In fact, if I read Stenger correctly, many, many orders of magnitude larger than 10^26 meters. Have I worded it clearly enough that now it's obviously a different question from the one you thought I was asking? Sorry. I'm a naif. I don't know the vocabulary or even how to formulate good questions.
I guess the key point here is that the size of the universe is not known. Whether the universe extends beyond what we can observe seems extremely likely, but we simply can't know this. During inflation, space is stretched so rapidly that neighboring points are pulled outside the observable universe. After inflation ends, we slowly 'catch up' to these regions, and they re-enter the observable universe. Just after inflation ends, the universe has grown in size by an amount much larger than the observable universe has grown. If inflation lasted long enough, then there are regions of the universe outside our causal patch that we have yet to observe.

As an aid to understanding, check out this slide from one of my former adviser's talks: http://www.physics.buffalo.edu/whkinney/talks/Buffalo23JAN03/index.html [Broken]
Go to slide 17. This is meant to be an animation, but this version, unfortunately, doesn't run. But, what you see is the observable universe at some initial time (region surrounded by green circle) before inflation. The grid marks define a measure on the space. When inflation ensues, imagine the grid marks expanding rapidly, and the green circle expanding more slowly (the green circle is expanding at roughly the speed of light, but the grid is expanding much faster than this). So after inflation, the grid marks have grown to a very large size, but the green circle has not grown so much.

EDIT: It's important to keep in mind that the size of the universe has nothing to do with the size of the observable universe. The universe itself could well be infinite in extent. Inflation increases the size of the universe by stretching those grid marks -- it increases the distances between neighboring points. Since the size of the universe is unknown, the effect of inflation is given in terms of the scale factor I mentioned before. Inflation increases this scale factor exponentially.

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Whoa. Thanks, I think this is exactly what I needed, and it will probably keep me busy for a while!

How big did inflation make the universe? It suddenly went from being smaller than a neutron to what size? Grapefruit size? Big as a football field, as big as the solar system, a light year, a hundred light years?

bapowell