Confused about implications of flat universe

[GreatBigBore]

I recently saw a YouTube video of a 2009 lecture by Lawrence Krauss. He says that we now know unambiguously that the universe (and I just mean the universe that we can see, back to the big bang, not the multiverse or the foam or any of that) is flat. But it seems to me that a flat universe with a boundary has a center, as far as I can tell. As usual, I can't do a great job imagining curved 3D space, but I can refer back to the nice 2D surfaces that Krauss used to demonstrate open, flat, and closed universes. The closed universe, represented by a sphere where the inhabitants are aware only of the 2D surface of the sphere, clearly has no edge and no center. But the flat universe, if it is finite (which it seems it must be), also has a center, yet I still hear people saying that there's no center. Krauss made one quick comment but never elaborated on it: he said something about the flat universe being "infinite in extent". I'm wary of this, because I don't know what "infinite in extent" could mean in a real universe, not to mention that lots of people seem to be confident that our universe has a finite size. So is there a center, or is it infinite in extent? And if infinite, what does that mean in practical terms? Can anyone help me to understand what I'm missing?

 

[Chalnoth]

I recently saw a YouTube video of a 2009 lecture by Lawrence Krauss. He says that we now know unambiguously that the universe (and I just mean the universe that we can see, back to the big bang, not the multiverse or the foam or any of that) is flat.

Flat to within experimental errors, which is really really flat. Doesn't mean it's absolutely flat, and if you listen carefully to the words he uses, he doesn't claim it is either. But it is extremely flat.

But it seems to me that a flat universe with a boundary has a center, as far as I can tell.

1. What boundary?
2. A "center" is a point of symmetry. The center of a sphere is a point about which you can rotate the sphere any which way and get the same thing, for instance. So far as we know, our universe is, on average, completely uniform in all directions, which means there is no special point that we might call a center.

But also, consider a torus: a torus is topologically flat, but still wraps back on itself: like the surface of a sphere, it is finite and clearly has no center.

Krauss made one quick comment but never elaborated on it: he said something about the flat universe being "infinite in extent". I'm wary of this, because I don't know what "infinite in extent" could mean in a real universe, not to mention that lots of people seem to be confident that our universe has a finite size. So is there a center, or is it infinite in extent? And if infinite, what does that mean in practical terms? Can anyone help me to understand what I'm missing?

There are some pretty good arguments to our universe being quite infinite, mainly dealing with inflation.

 

[Skolon]

1. A torus have some symmetries, I suppose. So, if the Universe have a torus like "shape" we can found somehow this kind of symmetries. Don't we?

2. What can we tell about Universe at BB initial moment? It was finite or not? If not, the BB Theory is describing just a part of whole Universe?

 

[bapowell]

If the universe is in fact a torus, then its nontrivial topology might have observational consequences. It depends on how large our observable universe is as compared to the torus. If our universe is just a small patch on a huge torus, then we'll observe a nearly flat universe -- nothing fancy. However, if the horizon of our universe is as large as one of the circumferences of the torus, then the universe will be periodic in this direction. See, for example, http://arxiv.org/abs/astro-ph/0310233" .

As far as the big bang is concerned, it doesn't care whether the universe started out infinite or not. This is because the big bang occurred everywhere in space -- it was not concentrated at some specific location.

 

[Chalnoth]

This is because the big bang occurred everywhere in space -- it was not concentrated at some specific location.

I really really dislike this description. It can be extremely misleading, because it sounds like it presupposes that whatever event started our region of space-time started everything off, which is by no means certain (I wouldn't even consider it remotely likely).

I think perhaps a better way of putting is that whatever event started our region of space-time, whether it was some quantum tunneling event or vacuum fluctuation or whatever, that event likely produced an extremely small region of space-time. However, its properties were such that it rapidly underwent cosmic inflation, which caused this tiny region of space-time to become huge.

 

[bapowell]

Chalnoth, thanks for your comment. I am certainly not trying to suggest that I know what process began our universe (or our patch of the universe, or whatever). I am mostly rebuking the misconception that the big bang was a singular event occurring in an already existing spacetime (the cosmic egg, for example), which is what I think was leading to Skolon's confusion.

My definition of the big bang should be thought of merely as an operational definition, applicable to your suggested scenario as well -- our little patch pops into existence and begins to expand (inflation or no inflation). My point is that this expansion occurs everywhere across the spacetime patch, and the moment that the patch begins its expansion is effectively a big bang.

 

[Chalnoth]

Chalnoth, thanks for your comment. I am certainly not trying to suggest that I know what process began our universe (or our patch of the universe, or whatever). I am mostly rebuking the misconception that the big bang was a singular event occurring in an already existing spacetime (the cosmic egg, for example), which is what I think was leading to Skolon's confusion.

It's entirely possible that whatever event it was that birthed our universe occurred within a pre-existing space-time. If so, it would have looked like a microscopic black hole that would have quickly evaporated soon after it was produced: the entire new bit of space-time would have started off inside this microscopic black hole, and, once that had evaporated, would have been forever cut off from its "parent" universe.

My definition of the big bang should be thought of merely as an operational definition, applicable to your suggested scenario as well -- our little patch pops into existence and begins to expand (inflation or no inflation). My point is that this expansion occurs everywhere across the spacetime patch, and the moment that the patch begins its expansion is effectively a big bang.

Well, I guess I personally just don't like that terminology.

 

[bapowell]

It's entirely possible that whatever event it was that birthed our universe occurred within a pre-existing space-time. If so, it would have looked like a microscopic black hole that would have quickly evaporated soon after it was produced: the entire new bit of space-time would have started off inside this microscopic black hole, and, once that had evaporated, would have been forever cut off from its "parent" universe.

I don't know what this has to do with the discussion. To the parent universe, there's no big bang -- just a black hole that evaporates. The relevant universe is the daughter universe, which is ours. This daughter universe will undergo expansion, which presumably had a beginning. That's our big bang, or perhaps "initial moment of expansion" (used in lieu of the term "big bang"). It is non-local, occurring everywhere in the spacetime.

 

[Chalnoth]

I don't know what this has to do with the discussion. To the parent universe, there's no big bang -- just a black hole that evaporates. The relevant universe is the daughter universe, which is ours. This daughter universe will undergo expansion, which presumably had a beginning. That's our big bang, or perhaps "initial moment of expansion" (used in lieu of the term "big bang"). It is non-local, occurring everywhere in the spacetime.

I'm not so sure that last part can be true. So far as we know, all forces of nature are quite local. Yes, it is true that this is what our simplest models say, but then our simplest models don't include any sort of physical process to start off a region of space-time like our own. I strongly suspect that any real physical process that does so doesn't involve any sort of weirdness like non-local expansion suddenly popping up.

 

[bapowell]

As an example, and believe me, this is just an example: consider two infinitely flat planes colliding. This collision would create a non-localized energy density across each plane. Perhaps I should have said "not localized", rather than "non-local" which carries a specific connotation in physics.