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.JesseM said:
Ah, you're right. I found the link to that paper on this page, which seemed to say that Luminet and Tegmark had opposing conclusions:Spin_Network said: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?
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.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 . 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 .
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 :
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  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 . 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  techniques.