# Universe finite or infinite during the first instance of inflation?

1. Oct 24, 2013

### Herbascious J

-In the first few fractions of a second after the big bang, was the universe finite and closed during early inflation, before it smoothed out and became flat and infinite? I am wondering because I would like to know if the theory implies that the universe initially inflated with a finite volume, then became infinite. Or, did the universe come into being infinite, then went through a period of rapid inflation during the first few mili-seconds. Thanks!

2. Oct 24, 2013

### phinds

If it was finite then, it is finite now. If it was infinite then, it is infinite now. Things do not go from finite to infinite.

If you can figure out WHICH it was, I'm sure there's a Nobel Prize in it for you.

3. Oct 24, 2013

### Herbascious J

:D Thanks for the great reply. That's what I figured. I was struggling with the question because some explanations seemed to imply that the 'sphere' of the volume of the universe layed out into a flat sheet (perhaps bad analogies). Anyway, I couldn't get my mind comfortable with a finite sphere of matter, having any matter density at all after turning infinite. It seemed the finite energy would become totaly diffused once infinite, and there would be no galaxies at all. Thanks!

4. Nov 13, 2013

### goldust

An infinite series can either converge or diverge. By the same token, in my opinion, the universe could be considered either finite or infinite depending on how it expands. Just my 2 cents. :tongue:

http://en.wikipedia.org/wiki/Series_(mathematics)

Last edited: Nov 13, 2013
5. Nov 13, 2013

### Staff: Mentor

I don't see the connection between the way a series converges or diverges and the expansion of the universe.

6. Nov 13, 2013

### phinds

and in what way does that address my statement?

7. Nov 13, 2013

### h6ss

Be careful there. :tongue:

8. Nov 13, 2013

### phinds

I think it is clear from the context that I am talking about physical things, so I am confident that I do not need to be careful. It is an absolutely true statement.

9. Nov 13, 2013

### Herbascious J

Ok, final question... Does anyone on this thread think a suedo-sphere universe can later (after a few seconds) layout into a flat universe??

10. Nov 14, 2013

### Chronos

No, a flat universe is a natural result of inflation.

11. Nov 14, 2013

### goldust

Therein lies a twist. How can people ever know if the universe is flat? People once thought Earth is flat, yet Earth is round. Scientists now think the universe is flat, but how can they be sure they are right? No instrument in the world, no matter how accurate, can ever determine if something sufficiently big is perfectly flat. :tongue:

12. Nov 14, 2013

### goldust

We are on the same page that numbers are infinite even though we can count numbers? :tongue:

13. Nov 14, 2013

### bapowell

Try counting the reals between 0 and 1. Hop back on here when you've finished...

14. Nov 14, 2013

### bapowell

Cosmologists don't think the universe is flat. What they've done is measured the observable universe to be flat to within less than 1%. Of course, the universe could still be closed (spherical), with the observable universe only a small patch on this larger sphere. In this case, the analogy to humans on earth carries over quite nicely.

15. Nov 14, 2013

### bapowell

You would need some topology changing behavior. As far as I know, this is impossible in general relativity. There appears to be some degree of topology change permissible in speculative theories of quantum gravity (like string theory) but I don't know whether this is of the type needed for what you are asking. Unlikely, seeing as even after only a few seconds the universe is securely in the classical regime.

16. Nov 14, 2013

### phinds

What does this have to do with the real world of physical objects? Go back to my original statement in post #2 and see if you can find any correspondence between your comments and my statement. I can't see any at all.

17. Nov 14, 2013

### Herbascious J

Ok... I think that's what I was wondering about. It appears that the universe MUST be infinite at the moment when it comes into being, to remain infinite. If it is closed, it will remain, although vastly enormous, more than we can detect. So if it is infinite, then it was never the size of a nutshell (forgive the cliche). Thanks everyone!

18. Nov 14, 2013

### marcus

Universe finite or infinite during the first instants of inflation

Sounds like you have arrived at a clear satisfactory picture. Now keeping that basic idea intact I'd like to add some minor complications, in case they might interest you.

As far as I know, it is impossible in general relativity for the universe to "come into being". GR only applies, as a model, once the U has started expanding. But GR (a vintage 1915 pre-quantum theory, after all) is not the end of the story.

There is a sizable community of researchers working on modeling the U right around the start of expansion, often times extending back BEFORE the start (so that the U does not "come into being" when we are often told in the pop literature that it "came into being"). IOW some, perhaps the majority, of current models do not have a "singularity" and instead extend back before.

That line of research would come under the general heading of quantum cosmology. You can do a keyword search of recent research paper and scan the list just to get an idea. I don't mean delving into technical detail, just glancing to get an idea of what's out there. It means that the general concept of "big bang" is changing in the minds of those whose area of research it is.

Here are the "quantum cosmology" papers since 2009, ranked by number of times cited:
http://inspirehep.net/search?ln=en&...search=Search&sf=&so=d&rm=citation&rg=25&sc=0
Of those, here are the more recent ones, 2011 through 2013:
http://inspirehep.net/search?ln=en&...search=Search&sf=&so=d&rm=citation&rg=25&sc=0

If anyone wants the latest (Planck mission) 95% confidence intervals for Omega_k, which if negative indicates spatial finite U, but could be zero or positive which would indicate possibly infinite, they are on page 37 of this Planck report, see also pictures on page 36:
http://arxiv.org/pdf/1303.5076v1.pdf
http://arxiv.org/abs/1303.5076

Edit (afterthought) another curious bit of research: http://arxiv.org/abs/1311.3509

Last edited: Nov 14, 2013
19. Nov 16, 2013

### bcrowell

Staff Emeritus
It's true that realistic cosmological models don't switch between being spatially infinite and spatially finite. However, you seem to be claiming that this is obvious for elementary or philosophical reasons, and I don't think it is. This is an active area of research in GR, which you can find lots of information about by googling "general relativity" "topology change". A paper that gives a fairly recent summary is Borde, "Topology Change in Classical General Relativity," http://arxiv.org/abs/gr-qc/9406053 . Essentially topology change implies both kinematic problems (CTCs) and dynamical ones (violation of the WEC). None of this is obvious; it was worked out by Geroch and Tipler in the 60's.

20. Nov 16, 2013

### phinds

Interesting. I thought it was axiomatic that finite real things cannot become infinite in a finite amount of time. I still don't see how that could be possible.