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WMAP Summary: Our Universe 
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#37
Mar2406, 05:13 PM

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"Are the positions of the lowl mode anisotropies consistent with nonrandom 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. 


#38
Mar2406, 05:51 PM

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Garth 


#39
Mar2406, 06:35 PM

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Interesting paper on the a of e.
http://arxiv.org/PS_cache/astroph/pdf/0502/0502237.pdf Authors: Kate Land, Joao Magueijo Comments: Small corrections introduced Reportno: ImperialTP Journalref: 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 largescale systematic errors. We show how this reappraisal may be crucial in identifying the theoretical model behind the anomaly. 


#40
Mar2406, 08:23 PM

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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. 


#41
Mar2506, 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: wolram thank you, I was already aware of that 2005 Land & Magueijo paper and their conclusion that One problem of course is that, because these lowl 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 


#42
Mar2506, 11:09 AM

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#43
Mar2506, 11:49 AM

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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 largeangle anomalies of the microwave sky Garth 


#44
Mar2506, 12:29 PM

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#45
Mar2506, 12:38 PM

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Thank you ST for an informative discussion! Garth 


#46
Mar2506, 03:08 PM

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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 lowl modes and a real AoE caused by some unknown noncosmological process. The resultant power spectrums of all universes are similar. In subset 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 lowl modes appear aligned in an 'AoE'. In subset B the lowl 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 lowl 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 


#47
Mar2606, 12:06 AM

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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 antialignments  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 selfconsistent model of the universe that predicted the measurements of the lowl multipoles to give low power, the arguments would be a lot more convincing. If, after seeing the lowl 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. 


#48
Mar2606, 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 nonaligned 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 Garth 


#49
Mar2606, 04:48 PM

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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. 


#50
Mar2606, 07:32 PM

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Sorry to take introduce a new element into this thread, but the 3year WMAP results are just so rich.
I have several questions, to anyone interested in answering:



#51
Mar2706, 04:46 AM

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I think that the largel 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 highl end. (Hinshaw et al. ThreeYear 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. Garth 


#52
Mar2706, 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 SunyaevZeldovich 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. 


#53
Mar2906, 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.



#54
Apr606, 02:29 AM

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Bernui, Mota, Reboucas, & Tavakol have today updated their paper
Mapping the largescale anisotropy in the WMAP data to include WMAP 3 data. They previously had described another method of measuring largescale anisotrophies: 1. "Is the distribution of anisotropies in the WMAP data nonGaussian?", 2. "Is there an alignment in the nonGaussianity?" 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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