# Toroidal universe?

## Main Question or Discussion Point

Toroidal universe????

I just came across a paper from 2003 describing an analysis of early results of CMB from WMAP. In it were speculations that the universe could be toroidal rather than Euclidean in spatial shape. Since then, has the idea been further developed or simply shut down?

tiny-tim
Homework Helper
Hi mathman!

I've never seen this paper (btw, what paper?), but isn't "toroidal" just another way of saying flat, like a 3D "Asteroids" screen?

I'm pretty sure that the upcoming LISA, laser interferometer space array, will create a large perfect triangle which will add up to 180*, greater than 180*, and less than 180* for a flat, positively curved, or negatively curved spacetime respectively. There are other agendas for it as well but that should provide strong evidence for any of those cases. It will be interesting nonetheless to discover which type of curvature our universe takes. As far as that paper goes I'm not familiar with it but I have only begun reading scientific journals. If you have a link that would be great.

Joe

i say this with all due respect, but why does it matter if the universe is flat, curved, circle, etc? Does the shape of the universe predict when or how the universe began? is that why we should care about this topic. Again, i do not mean to be disrespectful, but i am curious why so many people care about the shape of the universe.

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Yes. It is a part of the solution in GR
For example (if we ignore the dark energy) curvature is positive, then universe is finite and closed and it will collapse. So the future fate of the universe is precoded in the current curvature.

Dark Energy makes such things much more complicated, however.

bapowell

i say this with all due respect, but why does it matter if the universe is flat, curved, circle, etc? Does the shape of the universe predict when or how the universe began? is that why we should care about this topic. Again, i do not mean to be disrespectful, but i am curious why so many people care about the shape of the universe.
Why do you care only about the beginning of the universe? That doesn't sound very scientific to me...

bapowell

Hi mathman!

I've never seen this paper (btw, what paper?), but isn't "toroidal" just another way of saying flat, like a 3D "Asteroids" screen?
This might be the 2003 paper: http://arxiv.org/abs/astro-ph/0310233" [Broken]
There's an earlier one by the same authors: http://arxiv.org/abs/astro-ph/9801212" [Broken]

It's a very interesting proposal! Enjoy!

And, yes, it's flat. But they investigate what happens if the distance to last scattering (the distance a photon travels from the time the CMB is created up to now) is larger than the radii of the torus, so that that we on earth would see multiple intersecting copies of the CMB sky. It's really fascinating stuff!

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Why do you care only about the beginning of the universe? That doesn't sound very scientific to me...
Why does that not sound scientific? Does the beginning of the universe not involve quantum fluctuations and singularities? I am interested in understanding the origin of the universe. Are you afraid that it may invoke, dare i say it, "god". Don't worry, i wont be a party pooper. I just want to understand physics at Plank's time that's all.

bapowell

No, I just think it's funny that you judge the importance of the topology of the universe on whether it has any bearing on its origin, as if that's the only thing worth studying. The universe is a fascinating place, and it's important to understand its many properties. Who knows...the topology of the universe may well shed light on its origins. Without a UV completion of gravity, who's to say?

That was my point. Can topology of the universe help us understand the origin of the universe?

bapowell

That was my point. Can topology of the universe help us understand the origin of the universe?
Sure! The geometry and topology of spatial dimensions is critically important in string theory!

The paper I had been reading was a news article. New York Times, March 11, 2003, "Universe as Doughtnut: New Data, New Debate" by Dennis Overbye.

In it he refers to a paper on the subject:http://arxiv.org/pdf/astro-ph/0302496. The authors are Tegmark, Oliveira-Costa, and Hamilton.

I've been following this theory since the late 1970s/early 1980s. According to this the Big Bang was more of a big through; singularity more like circularity. It is dangerous to talk about shapes of course even in analogy, but it may be also like a sphere the centre of which radiates everywhere and is located in 2D as the hole in/through the doughnut. As the grains of sugar move outward around the cosmological confectionary they separate from one another until on the other side (so to speak) they grow closer. It has been theorised that this means the production of possibly endless universes existing in parallel. A possible geometric building block of the universe - the interlocking sphere where surface and centre (essence and manifestation/experience) exist everywhere is supposed to fit with this model somehow, but it all sounds a more than a little mystical and difficult to comprehend. The Donut theory itself is rooted in more sound science. I hope this doesn't sound too crackpot.

skippy1729

I just came across a paper from 2003 describing an analysis of early results of CMB from WMAP. In it were speculations that the universe could be toroidal rather than Euclidean in spatial shape. Since then, has the idea been further developed or simply shut down?
This is still an active field of research and will probably remain so until (if) it is solved. Einsteins equations do not fix the global topology of the universe unless we make the assumption that it is simply connected. Toroidal is only one of an infinite number of possibilities. In the general case the universe can be closed and compact for any of the three possible spatial curvatures flat, spherical and hyperbolic. While we know that it is almost flat, the hyperbolic and spherical cases are not ruled out. Flat means EXACTLY 1, not 1.0000001 or 0.9999999. There are several methods being used to search for an answer: multiple images in widely separate positions in the sky, "fingerprints" in the CMB spectrum for example. It is possible that the entire universe (not just the observable universe) is SO large that the question will never be answered. And, of course, there is the possibility that it is literally infinite which some people (like me) find philosophically repulsive. But there is no reason why the universe needs to conform to my whims.

Two comprehensive reviews are:

Topology and the CMB, Janna Levin http://arxiv.org/abs/gr-qc/0108043

Cosmic Topology, Lachieze-Rey & Luminet http://arxiv.org/abs/gr-qc/9605010

Skippy

Given that I personally find everything infinitely interesting I am not, myself, philisophically repulsed by the idea of an infinite Universe, which could be limited and contained in one sense and infinite in another - certainly in possibilities : )

That was my point. Can topology of the universe help us understand the origin of the universe?
Yes, the topology of our universe can help us understand our origin. Big problem is to understand that topology (i.e. finite in space and time, or infinite in both?)

Chronos