[Cosmo-media] Cosmic topology

[Boud Roukema]

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