WMAP Summary: Our Universe


by SpaceTiger
Tags: summary, universe, wmap
SpaceTiger
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Mar24-06, 05:13 PM
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Quote Quote by Garth
The point about the BSE analogy was to show that two equally scientific answers can be valid even though they have the opposite effect. The answer depended on the question asked.
The analogy seems to imply that the question the WMAP team has chosen to answer is somehow deceiving the public, yet the question you have chosen to ask:

"Are the positions of the low-l mode anisotropies consistent with non-random alignment?"

will always be answered in the positive, regardless of the results. This seems to me much more deceptive. I don't disagree with you that it's important what question we ask, but that argument seems to weaken your own position, not that of the WMAP team.


I could respond by saying they are 'hawking' GR, but I will not.
But that is not because they have vested interest in GR, it is because GR has been successfully tested on numerous occasions. It is of little concern to David Spergel (for example) whether or not GR is the correct theory of gravity, he's just testing the theories that are of the most interest to the scientific community. You, however, obviously have a lot to lose or gain from the success of your own theory. I think your "vested interest" argument is also coming back to bite you in the butt.


The legitimate requirement for high-sigma verification of a statement is a desire to avoid false positives, however it has the inevitable consequence of increasing the chance of false negatives.

We just need to be aware of that fact.
Their position is that more evidence is required, which seems to be taking that fact fully into account. Perhaps you should be more clear on your position and why you think it's superior.
Garth
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Mar24-06, 05:51 PM
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Quote Quote by SpaceTiger
Their position is that more evidence is required, which seems to be taking that fact fully into account. Perhaps you should be more clear on your position and why you think it's superior.
My point is, as far as testing for the existence/non-existence of the AoE is concerned, given the context of observations that "If we were eager to claim evidence of strong non-Gaussianity, we could quote the probability of this occurring randomly as less than 2%.", the consequence of requiring more evidence to reduce the chance of a false positive (if it really doesn't exist) also increases the chance of a false negative (if it really does exist).

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wolram
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Mar24-06, 06:35 PM
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Interesting paper on the a of e.

http://arxiv.org/PS_cache/astro-ph/pdf/0502/0502237.pdf

Authors: Kate Land, Joao Magueijo
Comments: Small corrections introduced
Report-no: Imperial-TP
Journal-ref: Phys.Rev.Lett. 95 (2005) 071301

We examine previous claims for a preferred axis at $(b,l)\approx (60,-100)$ in the cosmic radiation anisotropy, by generalizing the concept of multipole planarity to any shape preference (a concept we define mathematically). Contrary to earlier claims, we find that the amount of power concentrated in planar modes for $\ell=2,3$ is not inconsistent with isotropy and Gaussianity. The multipoles' alignment, however, is indeed anomalous, and extends up to $\ell=5$ rejecting statistical isotropy with a probability in excess of 99.9%. There is also an uncanny correlation of azimuthal phases between $\ell=3$ and $\ell=5$. We are unable to blame these effects on foreground contamination or large-scale systematic errors. We show how this reappraisal may be crucial in identifying the theoretical model behind the anomaly.
SpaceTiger
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Mar24-06, 08:23 PM
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Quote Quote by Garth
My point is, as far as testing for the existence/non-existence of the AoE is concerned, given the context of observations that "If we were eager to claim evidence of strong non-Gaussianity, we could quote the probability of this occurring randomly as less than 2%.", the consequence of requiring more evidence to reduce the chance of a false positive also increases the chance of a false negative.
It's not a "negative" result, it's an "inconclusive" result. They're suggesting that more evidence is required to reach a conclusion, not that they will reach the opposite conclusion until that evidence is acquired. This is why citing the axis of evil is such a poor way to approach the problem, because it doesn't, by itself, give useful information.

The approach we take to scientific problems, particularly theoretical ones, is very important. I tend to think of three types:

Worst approach: Scour observational data for something that looks unusual and then make a lot of noise about it. Quote the most dramatic a posteriori probabilities you can compute.

Bad approach: Look for something unusual in the data (or something you find philosophically disturbing) and make a theory such that it can be explained. Pay no heed to the testability of your theory.

Good approach: Learn as much as you can about the observational evidence available, look for statistically significant deviations from standard theory, and try to concoct a testable alternative than can explain at least two separate phenomena.

The first approach is just useless, IMO, and the second approach is extremely unlikely to succeed. If we want to have productive discussions about a scientific problem, I think it's always best to focus on theories that have taken the third approach. Depending on who's discussing it, the "axis of evil" falls into either the first or second category. I don't think it should be forgotten or ignored, but I don't see that there's much to be learned from it at the moment. If we find further deviations from standard theory, particularly on that scale, then it may evolve into a more powerful line of evidence against the standard model of cosmology.
Garth
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Mar25-06, 01:37 AM
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ST, then we agree on the 'good approach'.

However, I understand it to be the case that in accordance with the first half of that strategy:
Learn as much as you can about the observational evidence available, look for statistically significant deviations from standard theory
those deviations are already statistically significant.

wolram thank you, I was already aware of that 2005 Land & Magueijo paper and their conclusion that
The multipoles' alignment, however, is indeed anomalous, and extends up to [itex]\ell=5[/itex] rejecting statistical isotropy with a probability in excess of 99.9%. There is also an uncanny correlation of azimuthal phases between [itex]\ell=3[/itex] and [itex]\ell=5[/itex].
However, in this discussion I wanted to work with the more recent, weaker and less controvertable conclusions of WMAP3:
the probability of this occurring randomly as less than 2%
Of course these two statements are not inconsistent with each other.

One problem of course is that, because these low-l modes are relatively few in number, and they are not point sources like stars so their positions cannot be determined as accurately, then "the probability of this occurring randomly as less than 2%" may be all that will ever be statistically inferable. Nevertheless, this is still noticeably significant beyond the 95% confidence level.
[EDIT]
As a 'gedankenexperiment', and for the sake of argument assume that this WMAP3 conclusion is all that we will ever be able to say about it.

On the one hand, if it is maintained that "even more compelling evidence is required" for the existence of the AoE to be confirmed, is there not a large chance (>98%) of making a false negative?

Or on the other hand, if it is maintained that the above evidence is sufficient for the existence of the AoE to be confirmed, is there not only a small chance (<2%) of making a false positive?

On the balance of probabilities which is the prudent response? Perhaps the present result is not as "inconclusive" as the Spergel WMAP3 paper makes out?

Garth
SpaceTiger
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Mar25-06, 11:09 AM
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Quote Quote by Garth
On the one hand assume the AoB does not exist. Will we not then have a small chance (<2%) of making a false positive.

Or, on the other hand assume the AoB does exist. Will we not then have a large chance (>98%) of making a false negative?
This is completely wrong. Didn't we just agree that these a posteriori statistics are not reliable?
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Mar25-06, 11:49 AM
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Quote Quote by SpaceTiger
This is completely wrong. Didn't we just agree that these a posteriori statistics and not reliable?
Sorry, you caught me in the middle of an edit when my computer went down. I have now been able to rephrase the latter part of my argument in the way I want it.

We agreed that a posteriori statistics are less reliable, but it does depend on the actual probabilites and the structure within the alignments. Whether they reject statistical isotropy with a probability in excess of 99.9% or only 98% confidence level, these are formiable odds to explain as a statistical 'fluke'.

I am not alone in thinking that there is something there!
On the large-angle anomalies of the microwave sky

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SpaceTiger
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Mar25-06, 12:29 PM
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Quote Quote by Garth
On the one hand, if it is maintained that "even more compelling evidence is required" for the existence of the AoE to be confirmed, is there not a large chance (>98%) of making a false negative?

Or on the other hand, if it is maintained that the above evidence is sufficient for the existence of the AoE to be confirmed, is there not only a small chance (<2%) of making a false positive?
No, if I'm understanding what you mean by "false positive" and "false negative", that's still incorrect. The statistics refer to the probability of this occurring in a hypothetical random generation of the CMB (with the same power spectrum). They don't, however, give the probability that the feature is real because they don't (and can't) consider the selection bias.


I am not alone in thinking that there is something there!
Certainly not. This has been circulating in what I would call the semi-mainstream. A few theorists have jumped on it in the hopes that it will turn out to be significant, but the overwhelming majority (in my experience) still view it as insufficient evidence for anything useful.
Garth
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Mar25-06, 12:38 PM
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Quote Quote by SpaceTiger
No, if I'm understanding what you mean by "false positive" and "false negative", that's still incorrect. The statistics refer to the probability of this occurring in a hypothetical random generation of the CMB (with the same power spectrum). They don't, however, give the probability that the feature is real because they don't (and can't) consider the selection bias.
Ah - the selection bias!

Thank you ST for an informative discussion!

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Garth
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Mar25-06, 03:08 PM
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Quote Quote by SpaceTiger
No, if I'm understanding what you mean by "false positive" and "false negative", that's still incorrect. The statistics refer to the probability of this occurring in a hypothetical random generation of the CMB (with the same power spectrum). They don't, however, give the probability that the feature is real because they don't (and can't) consider the selection bias.
ST, for clarity let me expand on my gedankenexperiment and see where we differ.

For a statistical experiment we envisage an ensemble of say 200 separate and independent universes, each with a CBM with anisotropic fluctuations similar to ours and in which one intelligent species has made similar observations as WMAP3 of their CMB.

The null hypothesis to be tested is the CMB fluctuations are all random, that they are Gaussian at all modes in the power spectrum.

In 100 of these universes (sub set A) the anisotropies are completely random, in the other 100 (sub set B) there is a deficiency in the low-l modes and a real AoE caused by some unknown non-cosmological process. The resultant power spectrums of all universes are similar.

In sub-set A most CMB anisotropies look completely random to the inhabitants of the respective universes, however in 2 of these universes there is a statistical quirk and the low-l modes appear aligned in an 'AoE'.

In sub-set B the low-l modes of all the CMB anisotropies appear aligned in an 'AoE'.

In A 98 species do not observe an alignment and consider their CMB Gaussian and they all are correct, but 2 do observe an alignment and aren't sure.

Of these 2, if they both maintain that "even more compelling evidence is required" for the existence of the AoE to be confirmed, i.e. the null hypothesis is true, they will be correct. Or on the other hand, if they both maintain that the evidence is sufficient for the existence of the AoE to be confirmed, i.e. the null hypothesis is false, they are mistaken.

In B all 100 aren't sure. If they each maintain that "even more compelling evidence is required" for the existence of the AoE to be confirmed, i.e. the null hypothesis is true, they all will be incorrect. Or on the other hand, if they each maintain that the evidence is sufficient for the existence of the AoE to be confirmed, i.e. the null hypothesis is false, they all are correct.

Now we are in the group of 102 that do observe an apparent low-l mode alignment.

Of those 102:

If they each maintain that "even more compelling evidence is required" for the existence of the AoE to be confirmed, 2 will be correct and 100 will be incorrect.

However, if they each maintain that the evidence is sufficient for the existence of the AoE to be confirmed, then 2 will be incorrect and 100 correct.

My preference is for the stratergy that has the greatest chance of giving the correct answer, given that an apparent AoE has been observed in our sky.

I will be interested to see where I am mistaken in my thinking.

Garth
SpaceTiger
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Mar26-06, 12:06 AM
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Quote Quote by Garth
In sub-set A most CMB anisotropies look completely random to the inhabitants of the respective universes, however in 2 of these universes there is a statistical quirk and the low-l modes appear aligned in an 'AoE'.
The problem is here. The statistics aren't saying that two of these universes would appear to be aligned in an 'AoE', they are saying that only two of them will appear to have an axis with these properties (along the ecliptic plane). The real question we're interested in here is not the probability that the multipoles will be aligned to the ecliptic plane, but the probability that the standard model is wrong about the low multipoles.

To attempt to answer this, we might come up with another thought experiment. Let's say, hypothetically, that the standard model is right and we generate 100 random universes, as in your prescription. Now, let's ask the question, what is the probability that, after looking at the low multipoles, someone will notice something in that data that's seemingly inconsistent with the standard model. We could start by just looking at all possible alignments -- the ecliptic plane, the galactic plane, the supergalactic plane, earth's axis of rotation -- I could go on, but let's stop there for now. Let's say (rather arbitarily) that there is also a 2% chance of notable alignment with any of these axes. That brings us up to 8 universes.

What about them? In 8 of these universes, someone will have noticed an alignment that they felt brought the standard model into question. But why should we stop at alignments? Perhaps we should also consider anti-alignments -- now we're up to 16 universes. But wait, what about preferred axes in the instrument itself? 20 universes? Perhaps they would have brought it up at less significance -- 30 universes?

So how many universes have apparent discrepancies with the standard model? I don't know, nobody does. That's the problem. There's just no way to compute these probabilities because there's no way to know what astronomers would have noticed in these hypothetical universes. What makes things worse is that the people who found the axis of evil weren't looking for it where it was -- they were looking for signs of alignment with the galactic and supergalactic planes. This makes the argument even more a posteriori.

How could we get around this problem? Well, at the moment, it's awfully hard. If, based on other compelling evidence, someone had concocted a self-consistent model of the universe that predicted the measurements of the low-l multipoles to give low power, the arguments would be a lot more convincing. If, after seeing the low-l modes of the power spectrum, someone had made up a theory to explain it and immediately checked for the axis of evil where it was, that would also be more convincing.

Given that neither of these things happened, however, we're in a tougher position. I agree with what the WMAP folks said -- more compelling evidence is required.
Garth
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Mar26-06, 04:30 PM
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If we are looking for arbitrary alignments, such as say the three stars of Orion's belt, the clue indicating that they are random is the fact that there are about 2,000 naked eye stars that are not aligned. Even restricting ourselves to stars as bright as the belt there are many 100's non-aligned stars. With the quadrupole and octupole alignments all the multipole vectors are part of the alignment.

The question of the direction of the alignment perceived a posteriori becomes significant if a reasonable cause could be identified that would produce such an alignment. Land & Magueijo:
The axis of evil
It has been suggested that a preferred direction in CMB fluctuations may signal a non-trivial cosmic topology (e.g. [1, 12, 13, 14]), a matter currently far from settled. The preferred axis could also be the result of anisotropic expansion, possibly due to strings, walls or magnetic fields [15], or even the result of an intrinsically inhomogeneous Universe [16]. Such claims remain controversial; more mundanely the observed “axis of evil” could be the result of galactic foreground contamination or large scale unsubtracted systematics (see [17, 18, 19, 20] for past examples).
Also they report structure in the alignments:
There is also an uncanny correlation of azimuthal phases between ℓ = 3 and ℓ = 5.
Also Chris Vale's LOCAL PANCAKE DEFEATS AXIS OF EVIL provides an enticing possibility, that is a lensing of the CMB dipole by the Solar system moving relative to a local mass.


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SpaceTiger
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Mar26-06, 04:48 PM
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Quote Quote by Garth
The question of the direction of the alignment perceived a posteriori becomes significant if a reasonable cause could be identified that would produce such an alignment.
But that's just the point of my selections (galactic plane, supergalactic plane, etc.), they are all planes of symmetry along which we might expect contamination. If I truly wanted to be arbitrary, I had a limitless number of planes from which to choose.

The fact that there exist multiple plausible reasons for the alignment should be another clue. If there was one glaring possibility that stood up above the rest, that would lend weight to the significance of the "axis", but all these possible causes indicates a large theoretical degeneracy and a large space of potential alignments that would be deemed significant.
Nereid
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Mar26-06, 07:32 PM
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Sorry to take introduce a new element into this thread, but the 3-year WMAP results are just so rich.

I have several questions, to anyone interested in answering:
  • to what extent can the Planck mission be tweaked, to take account of the WMAP results?
  • ditto, other CMB projects?
  • What are the CMB projects, already under-way or in an advanced stage of planning, that will reduce the error bars in the high-l modes?
  • To what extent can/has the WMAP results significantly advanced our understanding of (local) galactic foregrounds - dust, gas, free-free transitions, ...? extra-galactic foregrounds - Local Group dust (for example), dust (etc) in the LMC, SMC, M31, ...?
  • What do these results have to say about the ISW?
  • There are some ~300 point sources in these data, up from ~200 in the year-1 data. How consistent are these (observed) (extragalactic) point sources with the (observed - SDSS/2dF etc) P(k)?
Garth
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Mar27-06, 04:46 AM
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Quote Quote by Nereid
Sorry to take introduce a new element into this thread, but the 3-year WMAP results are just so rich.

There are some ~300 point sources in these data, up from ~200 in the year-1 data. How consistent are these (observed) (extragalactic) point sources with the (observed - SDSS/2dF etc) P(k)?
Hi Nereid! Yes, we have been rather hogging the discussion!

I think that the large-l modes are interesting. Whereas the WMAP2 power spectrum indicated the rise to the third peak it did not continue far enough to mark that peak, WMAP3 does continue into
l > 800 yet does not show the peak at all, its error bars are too large and even then do not cross the predicted curve. What is there seems to 'plateau out'. WMAP has a noise problem at the high-l end. (Hinshaw et al. Three-Year Wilkinson Microwave Anisotropy Probe (WMAP1) Observations: Temperature Analysis page 75.)

That third peak, important to determine [itex]\Omega_b[/itex], has to be determined by other experiments: Acbar, Boomerang, CBI, VSA.

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Mar27-06, 01:05 PM
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The Planck mission was almost certainly designed to look for things we expect from the standard model and, since the standard model hasn't been called into question by WMAP, I wouldn't expect a shift in the Planck design. They're primarily planning to look at angular scales of l < 2000, if I remember correctly, and the interesting range will be between 1000 and 2000, where WMAP hasn't covered. It may seem like a small range, but it's about a million modes on the sky, so there's much to be learned.

If the standard model holds, there aren't a lot of new results to be garnered from the primary anisotropies -- smaller error bars and a possible detection of B mode polarization from gravitational waves. Some of the most interesting results ought to come out of the secondary anisotropies, which include the Sunyaev-Zeldovich effect and extragalactic sources.

There are a lot of WMAP results concerning the galaxy and dust, but I haven't had time to review them. Dr. Spergel gave a talk about it this past Wednesday and it seemed that one of the main results was the confirmation of emission from spinning dust grains.
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Mar29-06, 12:45 AM
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I think the thrid peak in the power spectrum has been nailed down in the WMAP release, and is well explained by the LCDM model. There will be several more papers on this in the year to come . . . IMO.
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Bernui, Mota, Reboucas, & Tavakol have today updated their paper
Mapping the large-scale anisotropy in the WMAP data to include WMAP 3 data.

They previously had described another method of measuring large-scale anisotrophies:
Introduction

Here we propose a new indicator, based on the angular pair separation histogram (PASH) method [20], as a measure of large-scale anisotropy. An important feature of this indicator is that it can be used to generate a sky map of large-scale anisotropies in a given CMB temperature fluctuations map. This level of directional detail may also provide a possible additional window into their causes.
With the result:
Conclusions

We have proposed a new method of directionally measuring deviations from statistical isotropy in the CMB sky, in order to study the possible presence and nature of large-scale anisotropy in the WMAP data.
The use of our anisotropy indicator has enabled us to construct a map of statistical deviations from isotropy for the CMB data. Using this σ–map we have been able to find evidence for a large-scale anisotropy in the WMAP CMB temperature field. In particular we have found, with high statistical significance (> 95% CL), a small region in the celestial sphere with very high values of σ, which defines a direction very close to the one reported recently [6, 10].
This result persists even after attempts to explain it away as an artefact of the data processing or foreground cleansing procedures:
We have shown that the results reported here are robust, by showing that the σ–map does not significantly change by changing various parameters employed in its calculation. We have also studied the effects of different foreground cleaning algorithms, or absence thereof, by considering in addition to LILC also the TOH and WMAP CO-ADDED maps. We have found again that the corresponding σ–maps remain qualitatively unchanged. In particular the hot spot on the south-eastern corner of the σ–map remains essentially invariant for all the maps considered here. This robustness demonstrates that our indicator is well suited to the study of anisotropies in the CMB data.
Now that result has been preliminarly updated by the WMAP3 data:
Finally, we add that after our paper was submitted, the three year WMAP CMB data was released [28]. As a preliminary check, we have calculated the σ−map for the new three year WMAP CO-ADDED map, which is depicted in Fig. 6. As can be seen the hot spot found in the first year σ−map in the south eastern corner of the sky, remains qualitatively unchanged with an axis also in agreement with that found for the first year data. In this way our results are also robust with respect for the three year WMAP CMB data. A complete and detailed analysis of the three year WMAP data using our indicator will be presented elsewhere.
There are three questions to ask:
1. "Is the distribution of anisotropies in the WMAP data non-Gaussian?",
2. "Is there an alignment in the non-Gaussianity?" and
3. "Is any such alignment identifable with local geometry, such as motion through the CMB, the galactic plane etc.?"

The interpretation of the statistical significance of the result depends on the question asked.

Garth


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