One of the important features of the universe around us is that, on sufficiently large scales, it looks pretty much the same in every direction — “isotropy,” in cosmology lingo. There is no preferred direction to space, in which the universe would look different than in the perpendicular directions. The most compelling evidence for large-scale isotropy comes from the Cosmic Microwave Background (CMB), the leftover radiation from the Big Bang. It’s not perfectly isotropic, of course — there are tiny fluctuations in temperature, which are pretty important; they arise from fluctuations in the density, which grow under the influence of gravity into the galaxies and clusters we see today. Here they are, as measured by the WMAP satellite.
Nevertheless, there is a subtle way for the universe to break isotropy and have a preferred direction: if the tiny observed perturbations somehow have a different character in one direction than in others. The problem is, there are a lot of ways this could happen, and there is a huge amount of data involved with a map of the entire CMB sky. A tiny effect could be lurking there, and be hard to see; or we could see a hint of it, and it would be hard to be sure it wasn’t just a statistical fluke.
In fact, at least three such instances of apparent large-scale anisotropies have been claimed. One is the “axis of evil” — if you look at only the temperature fluctuations on the very largest scales, they seem to be concentrated in a certain plane on the sky. Another is the giant cold spot (or “non-Gaussianity,” if you want to sound like an expert) — the Southern hemisphere seems to have a suspiciously coherent blob of slightly lower than average CMB temperature. And then there is the lopsided universe — the total size of the fluctuations on one half of the sky seems to be slightly larger than on the other half.
All of these purported anomalies in the data, while interesting, are very far from being definitive. Although most people seem to agree that they are features of the data from WMAP, it’s hard to tell whether they are all just statistical flukes, or subtle imperfections in the satellite itself, or contamination by foregrounds (like our own galaxy), or real features of the universe.
Now we seem to have another such anomaly, in which the temperature fluctuations in the CMB aren’t distributed perfectly isotropically across the sky. It comes by way of a new paper by Nicolaas Groeneboom and Hans Kristian Eriksen:
Bayesian analysis of sparse anisotropic universe models and application to the 5-yr WMAP data
Sexy title, eh? Here is the upshot: Groeneboom and Eriksen looked for what experts would call a “quadrupole pattern of statistical anisotropy.” Similar to the lopsided universe effect, where the fluctuations seem to be larger on one side of the sky than the other, this is an “elongated universe” effect — fluctuations are larger along one axis (in both directions) as compared to the perpendicular plane. Here is a representation of the kind of effect we are talking about — not easy to make out, but the fluctuations are supposed to be a bit stronger near the red dots than in the strip in between them.
It’s not a very large signal — “3.8 sigma,” in the jargon of the trade, where 3 sigma basically means “begin to take seriously,” but you might want to get as high as 5 sigma before you say “there definitely seems to be something there.” However, the WMAP data come in different frequencies (V-band and W-band), and the effect seems to be there in both bands. Furthermore, you can look for the effect separately at large angular scales and at small angular scales, and you find it in both cases (with somewhat lower statistical significance, as you might expect). So it’s far from being a gold-plated discovery, but it doesn’t seem to be a complete fluke, either.
Remember, looking for any specific effect is quite a project — there is a lot of data, and the analysis involves manipulating huge matrices, and you have to worry about foregrounds and instrumental effects. So why were these nice folks looking for a power asymmetry along a preferred axis in the sky? Well, you might recall my paper with Lotty Ackerman and Mark Wise, described in the “Anatomy of a Paper” series of blog posts (I, II, III). We were interested in whether the (hypothetical) period of inflation in the early universe might have been anisotropic — expanding just a bit faster in one direction than in the others — and if so, how it would show up in the CMB. What we found was that the natural expectation was a power asymmetry along the preferred axis, and gave a bunch of formulas by which observers could actually look for the effect. That is what Nicolaas and Hans Kristian did, with every expectation that they would establish an upper limit on the size of our predicted effect, which we had labelled g*. But instead, they found it! The data are saying that
So naturally, Lotty and Mark and I are brushing up on our Swedish in preparation for our upcoming invitations to Stockholm. Okay, not quite. In fact, it’s useful to be very clear about this, given the lessons that were (one hopes) learned in John’s series of posts about Higgs hunting. Namely: small, provocative “signals” such as this happen all the time. It would be completely irresponsible just to take every one of them at face value as telling you something profound about the universe. And the more surprising the result — and this one would be pretty darned surprising — the more skeptical and cautious we have every right to be.
So what are we supposed to think? Certainly not that these guys are just jokers that don’t know how to analyze CMB data; the truth couldn’t be more different. But analyzing data like this is really hard, and other groups will doubtless jump in and do their own analyses, as it should be. It’s certainly possible that there is a small systematic effect in WMAP — “correlated noise” — rather than in the universe. The authors have considered this, of course, and it doesn’t seem to fit the finding very comfortably, but it’s a possibility. The very good news is that the kind of correlated noise one would expect from WMAP (given the pattern it used to scan across the sky) is completely different from that the we would worry about from the upcoming Planck mission, scheduled to launch next year.
Or, of course, we could be learning something deep about the universe. Maybe even that inflation was anisotropic, as Lotty and Mark and I contemplated. Or, perhaps more plausibly, there is some single real effect in the universe that is conspiring to give us all of the tantalizing hints contained in the various anomalies listed above. We don’t know yet. That’s what makes it fun.
Hans:
One last question. If you incorpoperated Sean”s model into the basic WMAP data analysis and estimated the model parameters as well as the three you used for Sean’s model what effect do you think it would have on the 2008 baseline parameter values and their error estimates (confidence levels)?
Cecil:
If we incorporated this model into, say Cosmomc, we would most likely observe very little changes in the “standard” model parameters. This is because the only parameter affecting the angular power spectrum is the anisotropy amplitude g*, and this would only alter the overall amplitude of the angular power spectrum (sigma_8, if you want). The anisotropy direction itself would not affect the angular power spectrum as it only contains isotropic contributions, and hence not contribute to shifting any of the remaining standard parameters (as all code / theories usually are based on an isotropic theory). Even more, in order to make the code consistent, we “re-scaled” the anisotropy amplitude g* such that it is not degenerate with the amplitude of the power spectrum any more.
Nicolaas
CMB 101, what is the wave lenght or frequency of the CMB photons? Are they line spectra like from individual atoms or continuous spectra with a median, mean and mode like molecualr spectra?
Celestial mechanician, The CMB photons have a continuous distribution of wavelengths (a blackbody to be specific). In accordance with Wien’s law, the peak of the distribution is at lambda = 1 mm because the temperature of the CMB is 3 K, but with a broad tail in both directions (especially toward longer wavelengths). Indeed one of the strengths of WMAP is that it can measure the CMB anisotropy at a range of wavelengths (3–13 mm) which helps to distinguish which signal is CMB and which isn’t. The Eriksen et al analysis was performed at both 3 and 5 mm (“W” and “V” bands respectively in microwavese).
Regarding the correlated noise: A common way to measure power spectra if you’re unsure about the correlated noise in your data is to do a cross-power spectrum between different maps (VxW; V1xV2, etc.) or between different years of data in which the noise model is only needed to estimate the error bars and optimize the estimator, and one is not biased by an incorrect noise model. (WMAP 1st year analysis did this.) It seems like the same type of procedure would work here. If one looks at the general quadrupolar anistropy in the primordial power spectrum, it is described by a traceless-symmetric tensor or 5 numbers g_{2M} (M=-2..2). (I realize the Eriksen et al analysis included only the cylindrically-symmetric mode and allowed its direction to vary, so they considered a 3D subspace of the full 5D space of possible quadrupole anisotropies; but nevertheless an analysis that measures all g_{2M}’s should see this anomaly if it’s real.) So if one looks at the covariance matrix of the a_{lm}’s, they now have off-diagonal as well as m-dependent entries proportional to the g_{2M}’s. (There are some cosmology-dependent coefficients in front of g_2M, but if the sky is really statistically isotropic then small errors in these coefficients won’t cause spurious detections as long as we estimate g_2M simultaneously with the C_l’s.) WMAP easily has enough signal/noise for these tests and if the anomaly survives a cross-power analysis then it’s not correlated noise.
That said, of the possible systematics that could produce an asymmetry in the power spectrum, the first one on my list would be beam ellipticity because WMAP does not hit each pixel at a uniform distribution of angles of attack. (Same will be true, more so, for Planck.) The cross-power analysis won’t solve this problem, ultimately one needs to simulate it using the known beam maps and see what happens.
Regarding the search in large scale structure: Anthony Pullen (here at Caltech) is working on it, so stay tuned. I’m sure there will also be a lot more poring over WMAP and soon Planck, and probably other LSS data sets shortly after that. I for one find the situation exciting. A few years ago I went to conferences where people presented “explanations” of the low-multipole anomalies that made no predictions that I could hope to see verified at many sigmas in my lifetime. Well, with this particular anomaly I hold out hope that in 5-10 years it will either have gone away or be seen at many sigma in both CMB and LSS …
Hi Chris!
A few comments to your posts:
1) The problem with a cross-correlation analysis (between, say, V and W) for this particular analysis is that it’s very difficult to handle the signal covariance matrix on a cut sky. The only reason it’s sparse in our analysis is that we’re using the Gibbs sampling algorithm, which essentially “fills in” the cut region. I don’t see many alternatives to this, really, if one wants to go to high l’s. However, the Gibbs sampler is an exact likelihood approach, and as such, intrinsically an auto-correlation method; it’s not straightforward to get rid of these auto-correlations, while still have a correct likelihood. Of course, the problem becomes smaller the more independent bands you have, but it’s always going to be there to some extent. But of course, in principle it’s of course possible that one may construct some “pseudo-Cl” approach for this particular model, but right now, I don’t see how.. For the moment, I think the best approach is simply to analyse realistic WMAP5 noise simulations, and see if something similar pops up.
2) Personally, I don’t think asymmetric beams is relevant for this result. The model signature has a substantial (as in several degrees, I’d say) correlation length along the plane normal to the preferred axis, and even though the WMAP beams are somewhat asymmetric, they’re not *that* asymmetric.. 😉 Correlated noise is definitely my biggest concern here.
and
3) Please note that the paper is “Groeneboom and Eriksen”, not “Eriksen et al.”… 🙂
Finally, I’m really looking forward to see what comes out of the LSS analyses! But do you think the current experiments are deep/wide enough to really get a good handle on this effect? Or do we need to wait for the next generation surveys?
Thanks!
Hans Kristian,
> Please note that the paper is “Groeneboom and Eriksen”, not “Eriksen et al.”…
Oops, my mix-up! (literally)
> But do you think the current experiments are deep/wide enough to really get a good handle on this effect?
At Fisher matrix level the SDSS photometric samples should be able to detect g* if it’s really 0.15 … at back of the envelope level since there are Fourier modes spanning a wide range of directions you need ~1/g*^2~44 linear modes to measure it. The factors of order unity are unfortunately not so kind: the Fisher matrix has a factor of 2/45 in it (because the variations in the power spectrum as a function of angle are 10^4 modes. BUT: No promises until the systematics tests are all in 🙂
Chris
I heartily agree with Sean, that a ‘3.8 sigma’ signal is certainly nothing to crow about & a more robust & unambiguous detection is needed before we look at this theory in more detail. BTW Sean, great article in Scientific American. I hope it made many readers give some serious thought to this ‘spontaneous inflation’ theory amongst the sea of other cosmological theories now in vogue. I think you’re on the right track, anyway.
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