Why not a flat but finite spatial universe?

[nomadreid]

In the Wiki article on the FLRW metric, http://en.wikipedia.org/wiki/Friedmann–Lemaître–Robertson–Walker_metric
it says "the universe is nearly an isotropic and homogeneous FLRW spacetime".

OK, so spacetime is globally flat, which implies that space is too. This is backed up by
http://www.isciencetimes.com/articl...ed-perfect-accuracy-infinite-flat-eternal.htm
which states
" The scientists [at the Apache Point Observatory] translated the data into a 3-D map of the universe. What they discovered is that the universe is 'flat'..."

In the same article the team leader David Schlegel says "...it's likely the universe extends forever in space..."

But in a 2001 interview http://www.esa.int/Our_Activities/S...ite_or_infinite_An_interview_with_Joseph_Silk
Prof. Joseph Silk pointed out that a spatially flat universe could be either infinite or finite (with the surface of a torus as an example of a flat finite space), but that the Planck satellite might be able to distinguish between the two possibilities.

So, has the Planck satellite findings or Apache Point Observatory data cleared this up? If so, how? If not, why does Schlegel (and other sites) say that the universe is "probably" infinite?

 

[Simon Bridge]

You mean, how would we be able to tell one from the other?
Because the answer to the stated question is: "no reason".

The "global" topology of the Universe is an area of active research and there are no positive conclusions so far.
Wikipedia has a brief overview of a bunch of possibilities:
http://en.wikipedia.org/wiki/Shape_of_the_universe#Flat_universe

Both authors are speculating on their favorite models.

 

[nomadreid]

Thank you, Simon Bridge. Since, as you say, between the two possibilities for models of a flat universe, there is no reason to choose one over the other at the moment (and possibly never), it is curious that most articles on the Internet (sorry, this is a subjective impression) seem to favor the "spatially infinite" model. Whereas science is not a democracy, I wonder what the appeal of that model over the other one is.

 

[Bill_K]

Whereas science is not a democracy, I wonder what the appeal of that model over the other one is.

Simplicity. In a finite model, space would exhibit an apparent periodicity: you'd see the same galaxy repeated endlessly, in different equally spaced locations. The images of the galaxy would form a 3-D lattice.

But note that in such a model there is no way to preserve isotropy. Although the expansion rate could still be isotropic, the distance associated with the periodicity would necessarily be different in different directions. As a result, the universe would have a principal set of axes.

 

[nomadreid]

Thanks again, Bill_K. Very well explained. Fascinating!

 

[timmdeeg]

... it is curious that most articles on the Internet (sorry, this is a subjective impression) seem to favor the "spatially infinite" model. Whereas science is not a democracy, I wonder what the appeal of that model over the other one is.

In contrast to the infinite plane the torus is a non-trivial solution, perhaps that's why people don't prefer it.

 

[nomadreid]

Thanks, timmdeeg. An interesting consideration.

 

[timmdeeg]

But note that in such a model there is no way to preserve isotropy. Although the expansion rate could still be isotropic, the distance associated with the periodicity would necessarily be different in different directions. As a result, the universe would have a principal set of axes.

Would this mean that the cosmological principle isn't preserved in the special case of the 3-torus, though being a FRW universe.

 

[George Jones]

Would this mean that the cosmological principle isn't preserved in the special case of the 3-torus, though being a FRW universe.

Yes, a torus violates the cosmological principle because it is not isotropic.

It is possible for a spacetime that has an FLRW metric to have toroidal spatial sections, but such a spacetime usually is not considered to be an FLRW universe. The usual definition of an FLRW universe is a spacetime that has an FLRW metric, and that is spatially isotropic and homogeneous.

 

[timmdeeg]

Ah, good to know. Thanks, George.

 

[Chalnoth]

OK, so spacetime is globally flat,

This is false. Space-time is most definitely curved. It is possible to select time slicings where all three spatial dimensions are flat, but there is still curvature between the space and time dimensions. We see this curvature as the expansion of our universe.

 

[Chronos]

Even if space is infinite, there are regions that will remain forever unobservable. See; http://arxiv.org/abs/astro-ph/0310808, Expanding Confusion: common misconceptions of cosmological horizons and the superluminal expansion of the Universe, for discussion.

 

[nomadreid]

Thanks to all; a couple of replies:
Chalnoth: I stand corrected, that should have been that spacetime is asymptotically flat.

Chronos: good article, a summary of which should be included in standard physics courses.

 

[Mordred]

You may be interested in this article I regularly post, as it expands on George Jones post in the torus shape. The article covers different geometries in a fairly easy to understand metric. Largely based from Barbera Ryden.


https://www.physicsforums.com/showpost.php?p=4687696&postcount=10

editops wrong article lol, long day

https://www.physicsforums.com/showpost.php?p=4697773&postcount=30

 

[nomadreid]

Mordred, thanks. The second article (or past post) is quite nice. It would have been even nicer if the last section (FLRW metric) had been expanded upon a bit.

As to the first, mistaken post: I started reading it before I saw your edit, and would just note the following point on that: http://cecelia.physics.indiana.edu/life/redshift.html

 

[Chalnoth]

Thanks to all; a couple of replies:
Chalnoth: I stand corrected, that should have been that spacetime is asymptotically flat.

Not at all. If I remember correctly, the space-time curvature is proportional to $H^2$, which doesn't tend towards zero (It's been a while since I worked it out, but I'm sure it's at least proportional to some power of the expansion rate...).

 

[Mordred]

glad you enjoyed it, the cutoff point on the 4D metric was due to length, to properly cover the 4D section for each geometric shape would of nearly doubled its length. However the metrics covered is usually sufficient to get the concept of universe geometry across.

 

[nomadreid]

Thanks for the correction, Chalnoth. Oops, I was thinking of the point of view from Special Relativity, rather than General. I stand even more corrected.