Interpretation of the WMAP data

Garth Antony Barber
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Interpretation of the WMAP data

Post by Garth Antony Barber » July 20 2005

Is there a problem with a deficiency of low modes in the WMAP power spectrum? The data is normally said to be consistent with a flat spatial topology.

The WMAP data is angular in nature, i.e. a comparison of the depth against the angular size of an anisotropy.

Conformal transformations of the metric
[tex]{g}_{\mu \nu }\rightarrow \tilde{g}_{\mu \nu }=\Omega ^{2}{g}_{\mu \nu }[/tex]
leave angles invariant.

Therefore the WMAP data might also be said to be consistent with a conformally flat topology, such as Einstein's original model of a cylindrical topolopy. Such a topology would be finite though unbounded and would be expected to be deficient in the low modes as there would not have been enough room in the early universe for these anisotropies to form.

Therefore might the data, both of the positions of the peaks and of the low mode deficiency, be informing us that the universe is of a finite conformally flat topology?

Christopher Gordon
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Interpretation of the WMAP data

Post by Christopher Gordon » July 20 2005

If the universe was cylindrical and the
radius of the cylinder was small enough to explain the low multipoles then one should also see circular patterns in the CMB. These
have not be seen. A reference for this is:
N.J.Cornish, D.N.Spergel, G.D.Starkman and E.Komatsu,
``Constraining the Topology of the Universe,''
Phys.\ Rev.\ Lett.\ {\bf 92}, 201302 (2004)
[arXiv:astro-ph/0310233].
%%CITATION = ASTRO-PH 0310233;%%

Garth Antony Barber
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Interpretation of the WMAP data

Post by Garth Antony Barber » July 20 2005

But surely only if the topology is multiply connected?
In a simply connected topology would not the single ‘circle in the sky' be cosmologically lensed and magnified to fill the whole celestial sphere?

But my first question was: "Is there a problem with the low modes in the power spectrum?"

Christopher Gordon
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Interpretation of the WMAP data

Post by Christopher Gordon » July 20 2005

As I understand it, a cylindrical topology would imply two matched circles at opposite sides of the sky.

Hans Kristian Eriksen
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Re: Interpretation of the WMAP data

Post by Hans Kristian Eriksen » July 20 2005

Garth Antony Barber wrote:But my first question was: "Is there a problem with the low modes in the power spectrum?"
It depends on what you mean. There is not a problem in the power spectrum (Slosar and Seljak 2004; O'Dwyer et al. 2004), unless you think a 5-10% effect or so is a problem, but the morphology of some low-ell modes look funny.

For instance, there appears to be an alignment between the l=2 and 3 modes (although the very conservative approach taken by Slosar and Seljak casts doubts on that too), and the l=5 and 6 modes also look funny (Eriksen et al. 2004 -- ILC paper). So there are a number of odd things going on, but it's difficult to say how significant they are.

Garth Antony Barber
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Interpretation of the WMAP data

Post by Garth Antony Barber » July 20 2005

If the low mode morphology is aligned to Magueijo's 'axis of evil', might the CMB power spectrum be contaminated with a local signal? If this contamination is then removed would that not then leave an even greater deficiency at these modes?

Garth Antony Barber
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Re: Interpretation of the WMAP data

Post by Garth Antony Barber » July 20 2005

Christopher Gordon wrote:As I understand it, a cylindrical topology would imply two matched circles at opposite sides of the sky.
I disagree by my understanding; is it not that in a simply connected, finite, universe there is surely only one cosmological lens, the universe itself, and the footprint of our light-cone is enlarged to cover the celestial sphere once and once only?

Fergus Simpson
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Interpretation of the WMAP data

Post by Fergus Simpson » July 20 2005

As far as I know, thats true, but then that wouldnt be a flat universe. I thought that for a universe to be flat and finite you need to be multiply connected. Otherwise there would be edges! :)

Christopher Gordon
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Re: Interpretation of the WMAP data

Post by Christopher Gordon » July 20 2005

Garth Antony Barber wrote:
Christopher Gordon wrote:As I understand it, a cylindrical topology would imply two matched circles at opposite sides of the sky.
I disagree by my understanding; is it not that in a simply connected, finite, universe there is surely only one cosmological lens, the universe itself, and the footprint of our light-cone is enlarged to cover the celestial sphere once and once only?
The cylinder has to have a small enough radius that our light cone wraps around it. Else there will be a negligable effect on the low-l.

Garth Antony Barber
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Re: Interpretation of the WMAP data

Post by Garth Antony Barber » July 21 2005

Fergus Simpson wrote:As far as I know, thats true, but then that wouldnt be a flat universe. I thought that for a universe to be flat and finite you need to be multiply connected. Otherwise there would be edges! :)
But my main point is the question of whether the WMAP data is consistent with a conformally flat universe.

Christopher Gordon, thank you for your comments but such a conformal transformation could have the effect of enlarging the radius to encompass our light cone, could it not?

Christopher Gordon
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Interpretation of the WMAP data

Post by Christopher Gordon » July 21 2005

Yes, but then there would be no observational effect.

Garth Antony Barber
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Re: Interpretation of the WMAP data

Post by Garth Antony Barber » July 21 2005

Christopher Gordon wrote:Yes, but then there would be no observational effect.
Except that of a WMAP power spectrum that gives the first peaks consistent with a flat universe yet be deficient at the low mode tail?

Christopher Gordon
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Interpretation of the WMAP data

Post by Christopher Gordon » July 21 2005

No, you only get the low-l if the radius is smaller than the light cone.

Christopher Gordon
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Re: Interpretation of the WMAP data

Post by Christopher Gordon » July 26 2005

Hans Kristian Eriksen wrote:
Garth Antony Barber wrote:But my first question was: "Is there a problem with the low modes in the power spectrum?"
It depends on what you mean. There is not a problem in the power spectrum (Slosar and Seljak 2004; O'Dwyer et al. 2004), unless you think a 5-10% effect or so is a problem, but the morphology of some low-ell modes look funny.
Slosar and Seljak find the probability of the data, given the Lambda CDM prediction, to be lower than observed to be between 3 and 4%, see table 2. They find the probability of the true value being higher than the Lambda CDM prediction given the data to be between 5 and 10%. But, this second measure is very sensitive to the prior chosen for the data. This is different to the case of parameter estimation where the results are fairly prior insensitive, provided the prior is broader than the likelihood. So in my opinion, the first result of 3-4% is more reliable. Of course this is still not particularly anomalous, but the fact that it is associated with the largest length scales observable, which is also the scale of the dark energy, makes it suggestive of a possible physical cause rather than a statistical fluke.

Anze Slosar
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Re: Interpretation of the WMAP data

Post by Anze Slosar » July 26 2005

Christopher Gordon wrote: Slosar and Seljak find the probability of the data, given the Lambda CDM prediction, to be lower than observed to be between 3 and 4%, see table 2. They find the probability of the true value being higher than the Lambda CDM prediction given the data to be between 5 and 10%. But, this second measure is very sensitive to the prior chosen for the data.
Well, there is no such thing as priorless claim... And the frequentist approach does seem to change data while fixing the model, which definitelly sounds much more wrong than fixing the data and changing the model..., but I do not want to start yet another pointless freq/bayes war... My personal perference is the 5-10% from Bayesian approach... Anyway, this is discussed very nicely in [astro-ph/0306431]

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