Exploring the Shape of the Universe: A Fascinating Look at Recent Research

[Spin_Network]

This recent paper is interesting:http://arxiv.org/abs/physics/0509171

It has some interesting images, and it offers some conceptual thinks.

 

[JesseM]

On the other hand, this paper argues that the WMAP evidence rules out the dodecahedral model:

http://www.arxiv.org/abs/astro-ph/0307282

 

[Spin_Network]

On the other hand, this paper argues that the WMAP evidence rules out the dodecahedral model:

http://www.arxiv.org/abs/astro-ph/0307282

There is a :N.B. that our results do not rule out the recently proposed dodecahedron model of Luminet, Weeks, Riazuelo, Lehoucq & Uzan, which has a 36 degree twist between matched circles.

If one looks closely in the link you provided?

 

[JesseM]

There is a :N.B. that our results do not rule out the recently proposed dodecahedron model of Luminet, Weeks, Riazuelo, Lehoucq & Uzan, which has a 36 degree twist between matched circles.

If one looks closely in the link you provided?

Ah, you're right. I found the link to that paper on http://www.mathaware.org/mam/05/shape.of.universe.html, which seemed to say that Luminet and Tegmark had opposing conclusions:

Astronomers have analyzed the WMAP data and they have obtained conflicting results. Jean-Pierre Luminet and his colleagues proposed that the data seemed to best fit a universe that was a spherical space formed by identifying opposite faces of a dodecahedron in a three-dimensional sphere [10]. You can build a dodecahedron, a polyhedron with 12 pentagonal faces, to see that the faces cannot be glued straight across without first using a twist. Other mathematicians and physicists, such as Max Tegmark and his colleagues, assert that the WMAP data in fact rules out a finite universe, and that measurements point to a flat Euclidean space which is infinite [11].

But I guess the person who wrote the page didn't notice that note, or that the N.B. was only added in a later draft.

 

[JesseM]

I just looked over the actual paper though, and it says:

Our results also rule out other models that predict
back-to-back matched circles. However, they do not rule
out the recently proposed dodecahedron model of [35]:
although this model predicts six pairs of diametrically
opposed circles of radius about 35°, the circles have a 36°
twist relative to their twin images, thereby eluding our
search method. After the original version of this paper
had been submitted, a more thorough analysis by Cornish
and collaborators [36] confirmed our findings and
improved them to rule out this and other twisted backto-
back models as well.

A maximally ambitious six-parameter “everything
bagel” circle search, corresponding to the general case
of arbitrary topologies, is currently being carried out
by Spergel and collaborators, and will be presented in
a forthcoming paper [37]. This should provide decisive
evidence either for or against the small universe hypothesis.
If this circle search confirms our finding that small
universes cannot explain the anomalies, we will be forced
to either dismiss the anomalies as a statistical fluke or to
search for explanations elsewhere, such as modified in-
flation models [21–26]. Even the fluke hypothesis might
ultimately be testable, since it may be possible to improve
the signal-to-noise of the large scale power spectrum
beyond the WMAP cosmic variance limit by employing
cluster polarization [38, 39] or weak gravitational
lensing [40] techniques.

 

[Garth]

There is a problem, not generally acknowledged, with the standard model interpretation of the WMAP/BALLOON/COBE data, that of the deficit of the low-l modes. While the standard model can explain this deficit as a statistical "fluke" as there are so few of these modes, the correlation between their positions and local geometry has led to their alignment being called "the axis of evil".
If this "AOE" is explained by local contamination of the data, or by a lensing of the cosmological dipole, then the deficit is made even worse.

Therefore these low-l modes (large angle anisotropies) may indeed be not consistent with the standard LCDM model prediction of a flat or open and therefore infinite universe but rather with a finite universe. Yet the data of l ~50 peak appears also consistent with a flat universe, so how can this be reconciled? By a model in which the universe is flat yet finite, such as the dodecahedron model, or by a conformally flat model.

Is this the reason WMAP2 is so long in being published?

Garth

 

[marcus]

In case it might be helpful in this thread, here is Niel Cornish homepage
http://www.physics.montana.edu/faculty/cornish/
and a sample article
http://arxiv.org/abs/astro-ph/0310233
"Constraining the topology of the universe"
I think he has considered the possibility that the U might have an unexpected topology, but (apologies) I'm a bit vague about this.

 

[Chronos]

I agree with Spin. The dodecahedral model has not been ruled out. I was pretty sold on the Cornish explanation until recently. The paper Spin referenced is worth a look. So is this:

W Aurich et al. 2005 CMB anisotropy of the Poincaré dodecahedron
arXiv.org/abs/astro-ph/0412569