Dodecahedron universe after PLanck

[palmer eldtrich]

A number of years ago , it was conjectured that space was finite and shaped like a dodecahedron. The claim was
"data from the first year of the WMAP satellite – unveiled in February - agreed with the predictions of the standard big bang plus inflation model of cosmology for regions of space separated by small angles. However, on larger angular scales – greater than 60° - the WMAP observations were significantly lower than this model predicted".
http://physicsworld.com/cws/article/news/2003/oct/08/is-the-universe-a-dodecahedron

How does this conjecture stand in light of the Planck data ?

 

[phinds]

I find it very odd that anyone would ever have proposed a bounded shape for the universe because of the problems that raises by automatically positing an edge and a center. I don't know if "physicsworld.com" is a reliable source but even if it is, I still find this exceedingly odd.

 

[wabbit]

I find it very odd that anyone would ever have proposed a bounded shape for the universe because of the problems that raises by automatically positing an edge and a center. I don't know if "physicsworld.com" is a reliable source but even if it is, I still find this exceedingly odd.

From my recollection of that article at the time there were no edges, it was more "to a dodecahedron as a torus is to a cube", the shape obtained by gluing opposite faces of a dodecahedron.

Edit : the physicsworld piece seems to talk of what you say, though it has a picture consistent with my recollection - I would have to go back to the original, I suspect the journalist may have used sloppy wording in reporting on the article.

 

[phinds]

From my recollection of that article at the time there were no edges, it was more "to a dodecahedron as a torus is to a cube", the shape obtained by gluing opposite faces of a dodecahedron.

Ah, so it was in some way an unbounded topology. That makes much more sense, although to me it still seems unlikely. That's just a personal preference on my part to think that if it is finite but unbounded it must be some kind of smooth curve topology and I don't think of a dodecahedron as smooth in this sense.

 

[wabbit]

Agreed, seems a bit exotic - what would generate just that symmetry ?
It is both smooth and (can be) spatially flat though.

The original is here : Luminet, Dodecahedral space topology as an explanation for weak wide-angle temperature correlations in the cosmic microwave background (http://arxiv.org/abs/astro-ph/0310253)

He (Luminet) also has a more recent paper "Cosmic Topology : Twenty Years After"(http://arxiv.org/abs/1310.1245) which may be what palmer eldrich is looking for (didn't read it, if someone does I'd be happy to get the tl ; dr of it )

Edit : though not necessarly mainstream his line of inquiry (many other papers) is interesting, he doesn't AFAIK focus only on dodecahedra but questions what might be the global topology of the spatial universe, esp. considering bounded "perodic" torus-like(*) shapes with various symmetries and looking for cues in the CMB etc for such.

One characteristic signature of such shapes is "ghost images" of galaxies since looking in one direction we might observe the same galaxy at different ages.

(*) torus here means $\mathbb{R}^3/\mathbb{Z}^3$ , with a spatially flat metric (or some other one, not sure what the constraints are if not flat, though surely such spaces can be hyperbolic). Locally (up to scales of billions lightyears I think in Luminet's work) such flat torus-like spaces are exactly euclidian flat space, the only difference is the global topology. And they are strictly homogeneous, though not isotropic.

Edit : "torus-like" is just a word I made up, don't know if he uses it.

 

[palmer eldtrich]

Hi thansk for your reply, can I ask does the weak wide-angle temperature correlation remain in the Planck data, is of high sigma?
Didnt the PLanck team agree the universe is flat to the degree we can measure it?

 

[wabbit]

Sorry I don't know whether Planck results revised previous estimate to the extent of ruling out such models - have you looked at Luminet's 2013 review paper ? It went out 6 months after the Planck results were published so he might comment on that.

But I just wanted to point out again : the type of dodecahedral model we are talking about is perfectly compatible with flat space - where it differs is in its anisotropies.
Of course anisotropies were studied by the Planck team (see http://arxiv.org/abs/1303.5083) - I'm just unsure what the conclusions are regarding the possibilities discussed here.

Edit : he does indeed discuss Planck results at length. His conclusion seems to be that "at this stage, we don't know what the global topology of the universe is". He says a lot more, but I just skimmed it quickly.

 

[marcus]

Hi Wabbit, you got me to look up the relevant 2015 Planck release.
http://arxiv.org/pdf/1502.01593v1.pdf
Planck 2015 results. XVIII. Background geometry and topology of the Universe

I couldn't find the page where it discussed or constrained the dodecahedral idea, but I found these references at the end. So presumably it must discuss that somewhere in the 21 page article.

Lachieze-Rey, M. & Luminet, J., Cosmic topology. 1995, Physics Reports, 254, 135

Lehoucq, R., Lachieze-Rey, M., & Luminet, J. P., Cosmic crystallography. 1996, A&A, 313, 339, arXiv:gr-qc/9604050

Lew, B. & Roukema, B., A test of the Poincare ́ dodecahedral space topology hypothesis with the WMAP CMB data. 2008, A&A, 482, 747, arXiv:0801.1358

Luminet, J.-P., Weeks, J. R., Riazuelo, A., Lehoucq, R., & Uzan, J.-P., Dodecahedral space topology as an explanation for weak wide-angle temperature correlations in the cosmic microwave background. 2003, Nature, 425,

Haven't seen much about that beautiful Luminet idea recently. Johannes Kepler was enchanted by the platonic solids. http://en.wikipedia.org/wiki/Johannes_Kepler#Mysterium_Cosmographicum

 

[wabbit]

Ah thanks marcus - I was obstinately referring to the 2013 results only, obviously that's a bit dated now ! So now we need an update by Luminet or people working with him (My impression was that work in this area is fairly concentrated around one team, but to be honest that's just a vague impression - maybe others picked it up as well)

Perhaps also the observations aren't lending a lot of support, since there doesn't appear to be many recent articles.

Since you mention Kepler, Luminet wrote an article titled "Around Kepler's "Dream""
(http://arxiv.org/abs/1106.3639) though it doesn't seem to have much to do with dodecahedra - kindred minds perhaps more

Johann Kepler (1571-1630) is sometimes considered as a precursor of science-fiction novels with the writing of "Somnium, sive opus posthumum of astronomia lunaris". In this work published posthumously in 1634 by his son Ludwig, Kepler intends to defend the Copernican doctrine by detailing the perception of the world for an observer located on the Moon. Although Kepler was not the first to write the fantastic account of a voyage from the Earth to the Moon and "pass around a message", we show here that his "Dream" is made conspicuous under many aspects. Firstly, his author is one of the most remarkable minds of the history of sciences. Secondly, the "Dream" constitutes the missing link between the texts of pure imagination by Lucian of Samosata (IInd c. AD), and the fantasy novels based on scientific discoveries by Jules Verne, at the end of XIXth century. In the third place, the complete text presents an extraordinary structure in encased accounts, built on several series of explanatory notes drafted with the passing of years, as new astronomy progressed. Also it should be retained the dramatic role that its diffusion, although confidential during Kepler's lifetime, had on his own personal and family life, as well as the major influence this book exerted on a whole current of speculative literature devoted to space travel.

 

[wabbit]

Just had a brief look at the 2015 Planck paper. They have indeed an extensive section on topology with tests of various models (one recurring theme is "matched circles" with Luminet(2013) also mentions but I don't really know what they ccaracterize).
So at least this shows that interest in these ideas hasn't abated as I was suggesting in my previous post. They also appear to rule out the kind of periodic models discussed previously unless their dimension is very large.

 

[wabbit]

To me there is one big appeal for non-trivial topology models, which is that if the universe is spatially flat and simply connected, then it must be infinite (that is correct, right ? I oscillate between thinking this is obvious, and suspecting it might be false). And since the idea of an infinite universe seems very unnatural to me, "saving the finiteness" in the face of apparent (near-)flatness sounds like a big plus. Of course a small positive curvature would do as well and Ockham's razor might lead one to prefer that... As long as it's not infinite I'm fine with either : )

 

[Chronos]

The idea of an infinite universe is just as confounding as that of a finite universe, IMO. On the one hand you are faced with the prospect of an unlimited number of Earth's, even ourselves, cloned across an unending number of causally disconnected regions. On the other hand, a finite universe raises the specter our universe may be embedded in some vastly larger structure. Either way, it is difficult to escape the prospect of some version of a multiverse.

 

[wabbit]

Well to me it's very different, in part because I do not see any need for a finite universe to be embedded in a larger structure. What I meant is that I find it unnatural to think that there exist an infinite number of things, because I tend to think that infinity is "somehow" "unnatural". I shall stop here however because I am definitely straying into a philosophical matter and this is out of bounds in this forum, and in any case this is purely to me a matter of opinion, not fact, and your opinion is of course just as valid as mine. As Democritus said...

Edit : and what the fish said too : )

 

[phyzguy]

I thought Luminet's original idea was very interesting. This link is to one of his papers after WMAP. It seems there are three main predictions:

(1) A low value of the quadrupole in the CMB power spectrum.
(2) A slightly positive curvature. The best fit in the above paper is Ω_K=1.016, and Luminet says in the above paper, " A value lower than 1.01 will discard the Poincare space as a model for cosmic space, in the sense that the size of the corresponding dodecahedron would become greater than the observable universe and would not leave any observable imprint on the CMB, whereas a value greater than 1.01 would strengthen its cosmological pertinence."
(3) Six pairs of "matched circles" in opposite directions on the CMB. Roukema, et.al. in this paper actually claimed to find these circles in the WMAP data.

How do these three predictions hold up after Planck?

(1) I think if you look at Figure 1 of this paper on the Planck results, you see that the quadrupole point (the first data point) is below the model, but the statistical significance of this is low, and always will be. The statistics are limited by the "cosmic variance effect", which basically means we only have one universe to measure. So I don't think we can draw any conclusions on this one way or the other.

(2) The best fit curvature data from the above Planck paper, using all available data (not just Planck data), is a value of 1.000 +/- 0.005, so this would seem to rule out Luminet's model at 2σ, or at least say that, if Luminet's model is correct, the size of the recurrence is too large for us ever to observe.

(3) In this paper from the Planck collaboration they searched for the matched circles and they say, " We do not find any statistically significant correlation of circle pairs in any map."

So, it appears to me that there is no evidence that Luminet's beautiful idea applies in our universe.