Hi Paul,
On Tue, 19 Feb 2008, Paul Parsons wrote:
I'm just getting in touch as I'm writing a piece for Focus magazine
[to others on cosmo-media: this is BBC Focus magazine: http://en.wikipedia.org/wiki/BBC_Focus ]
about cosmic topology. Jean-Pierre Luminet sent me a press release about some work he's involved with on Poincare Dodecahedral Structure. In it, he cites a 2008 paper with your good self as lead
i think you mean PDS = Poincare Dodecahedral Space
author - just wondering if I could run a few quick questions past you about this...
Sure.
What do you think of the idea that we live in a universe with dodecahedral structure?
What do i think of the idea that we live in a PDS universe?
My general impression is that the CMB data seem to be successively pointing more and more towards the PDS model.
Firstly, COBE hinted at a lack of structure on the largest scales. WMAP, with better resolution, confirmed a lack of structure on the largest scales (more than 10 Gpc/h), especially when we think in terms of three-dimensional space rather than just in terms of angles. The next clue was that WMAP in combination with various other experiments have continually indicated a positive curvature with the total density parameter Omega_total somewhere around a few percent above the density for a perfectly flat universe. Among the positive curvature models consistent with this estimate, the PDS is probably the most credible. Thirdly, there have been studies by several groups using different methods, including our latest work in Torun, which used a method of analysing the WMAP map which was most likely (if we assume that the PDS model is wrong) to give evidence *against* the PDS model, but instead, it gave a valid PDS solution.
So the PDS model does seem to be the more natural interpretation of the data at the moment. However, we cannot yet say that the infinite flat model is ruled out to high significance by the data: there are analyses suggesting that the lack of structure above 10 Gpc/h is just coincidence, and the Omega_total estimates do not rule out the flat model to high significance.
What will the universe look like if our universe really does have this dodecahedral topology?
We should find that very high redshift (very distant) objects in some parts of the sky, seen with our telescopes as they looked a long time in the past, can be seen in other parts of the sky as they appeared even earlier, as regions of slightly high density which have not yet gravitationally collapsed, observed as the "cosmic microwave background". In other words, we could see a single physical region - traced by filaments of large scale structure including galaxy clusters and the most massive galaxies - in two different directions on the sky as they looked like at two different epochs: firstly at a very early epoch seen as temperature fluctuations, and secondly at an epoch a billion years or so later when some of the galaxies and galaxy clusters have just started to form and give off starlight.
The PDS model is not yet well enough constrained to give precise coordinates for these matching objects. In our paper (astro-ph/0801.0006) you'll find our present best estimates together with some discussion of other groups' work, which give some estimates of the coordinates needed to calculate this, but from our present results, these are only approximate.
I understand that your own work has revealed evidence for this cosmic topology in the WMAP data? Tell me more about that.
The full answer is here: http://arXiv.org/abs/0801.0006 e.g. start from the abstract.
This irc log might help too: http://cosmo.torun.pl/pipermail/cosmo-media/2008-January/000070.html http://cosmo.torun.pl/pipermail/cosmo-media/2008-January/000071.html
i assume you want a short, layperson's summary. Let's try the following.
Matched circles are the set of pairs of points at which two "topologically lensed" copies of a single physical point are seen in apparent space, on the surface of last scattering, observed as the cosmic microwave background (CMB), at what seem to be two different space points, but are really, physically, identical.
We extend this idea by considering pairs of points where two points distant from one another on the CMB (in the apparent space[1]) are two points in space which in reality are not exactly identical, but are just physically *near* to one another (in the fundamental domain[1]). This allows us to use a larger number of data points in the maps than for a "pure" circles method, since there are many more pairs of points which are near to one another rather than exactly at the same position. We know that points near to each other should be (statistically) correlated to one another: the temperature fluctuations should (statistically) be similar to one another at a pair of close points. So although individual pairs of points with this new method should not match as well as pairs of points on matched circles, they should still match fairly well, and there are many more of them. Also, small errors in choosing the correct orientation and exact geometry of the dodecahedron should be less important this way.
Using this idea, we searched for the best orientation of a PDS model which gives high cross-correlations of such would-be nearby pairs in the WMAP maps. If the PDS model is wrong, then these cross-correlations should, most of the time, be weak, since the points in a pair are *observed* in apparent space to be quite far from each other, in which case the correlations have been measured to be statistically close to zero.
We also allowed for an arbitrary twist angle to be used when matching opposite faces of the dodecahedron. This meant that if our search algorithm (a Markov Chain Monte Carlo method) found any strong signal, then it would be more likely to find a wrong twist angle than a correct twist angle for the PDS - unless the PDS model is really correct.
The result was that both a clear best solution was found, in which pairs of apparently distant points are in fact strongly correlated to one another for one particular orientation of the dodecahedral face centres, and the twist angle for this solution is 39 plus or minus 2.5 degrees, which is surprisingly close to what is required for the PDS model.
So the PDS had two quantitative predictions for our method: that a strong correlation should be found for some PDS orientation, and that the twist angle for this strongest correlation should be close to either plus or minus 36 degrees. Both were satisfied.
[[1] Since you're writing a general article on cosmic topology, i presume you'll explain near the beginning what the fundamental domain and apparent space (covering space) are.]
PS - one additional question to the ones I sent before... I gather David Spergel and Neil Cornish have already tried looking for matching circles in the CMB, but found nothing. So how did you and your team manage to get a positive result? How does your team's method differ?
Are there really matched circles in the WMAP data? Will you be able to check this to a higher degree of confidence when the Planck data are released?
In our new paper we use a different (though related) method, which we think is more robust than the matched circles method - in some sense you could say that it uses thickened matched circles, i.e. annuli, even though this is an *interpretation* of the method, not the calculation method itself. Since we did find a best solution, and that solution has the correct twist angle within the uncertainty estimate, and since the cross-correlations for that solution are strong, you could loosely say that yes, there really are matched annuli in the WMAP data.
Whether these annuli can be thinned down into matched circles may not be as straightforward as it was thought earlier. i think the main argument comes from the Ulm group (Aurich, Lustig & Steiner): there are problems trying to go to "high" resolution. We extended from the circles method to using "nearby" pairs of points and are starting from the moderately large scale signal rather than the small scale signals. Other groups have done some work on the very largest scales, those which have been causing the most controversy since the WMAP data and analyses first became publicly available.
If the coordinates of our best estimate solution are correct to within our stated precision, then future work will eventually have to thin the annuli down to "circles". However, for several different reasons, this may not be as easy as it might seem.
Planck data will certainly help, but data from many different ground telescope surveys will probably also be necessary to correct the maps for various contaminants which are generally thought to be in the maps.
Our own 32m radio telescope at the Torun Centre for Astronomy is being used for the OCRA (One Centimetre Receiver Array) project together with support from Jodrell Bank, for removing foregrounds at very high resolution: galaxy clusters seen due to the Sunyaev-Zel'dovich effect. OCRA may contribute by helping to get high resolution coordinates of the PDS model after (if!) the low resolution model continues to get more observational support.
How might we find out the topology of our universe? What experiments can we do? Again, will the Planck mission help? Will any other future missions help, eg CMBPol?
It's hard to predict which experiment will give a result of high enough significance to convince the cosmological community (assuming that the model is indeed correct). It was not easy to predict ahead of time that the supernovae Type Ia surveys would give the most convincing evidence in favour of a cosmological constant/dark energy. Planck will help, ALMA and SKA will help, at very high resolution, OCRA will help, but most probably it will be a combination of data from several different space and ground-based telescopes, along with careful, thorough analyses of the data, making as few arbitrary assumptions as possible. Possibly one particular experiment may get the most publicity as "discovering the PDS", but in terms of real science rather than media attention, my speculation is that it would most likely be a combination of many different data and analyses, just like for dark energy.
To me, the universe wrapping round on itself seems much more natural than it being infinite. What do you think?
i agree. i think it is most natural to consider the Universe as a physical object. After all, the alternative would seem to be... a spiritual object, in which case we're no longer doing science if we try to study it. Paraphrasing Janna Levin, most physical objects we know of have finite masses and sizes; so why should the Universe be an exception?
What do you think the next big thing in cosmic topology will be?
Predicting the future in fundamental scientific research, especially on such a deeply fundamental question, is close to useless IMHO. Grant committees want that, but i'm not the person who'll give it to them. If we know the answers ahead of time, then it's not research.
On the other hand, i think most people in the cosmic topology community would agree that any particular cosmic topology candidate is, given successively better and better data and analyses, highly falsifiable: the astronomical coordinates representing the model imply predictions, which if satisfied should lead to more precise estimates of the coordinates, which in turn should enable more precise predictions, creating a tightening cycle of constraints. If successive steps follow this cycle, then probably most of them could be considered as "big things".
Hope these answers help... i'd be happy to comment on a draft of the article before it gets published.
You should see this email on the mailing list archive: http://cosmo.torun.pl/pipermail/cosmo-media/2008-February/thread.html
cheers boud