Archive for Bianchi cosmologies

Why the Universe is (probably) not rotating

Posted in Cosmic Anomalies, The Universe and Stuff with tags , , , , , on October 1, 2013 by telescoper

Just a quick post to point you towards a nice blog post by Jason McEwen entitled Is the Universe rotating? It’s a general rule that if  an article has a question for a title then the answer to that question is probably “no”, and “probably no” is indeed the answer in this case.

The item relates to a paper by McEwen et al whose abstract is given here:

We perform a definitive analysis of Bianchi VII_h cosmologies with WMAP observations of the cosmic microwave background (CMB) temperature anisotropies. Bayesian analysis techniques are developed to study anisotropic cosmologies using full-sky and partial-sky, masked CMB temperature data. We apply these techniques to analyse the full-sky internal linear combination (ILC) map and a partial-sky, masked W-band map of WMAP 9-year observations. In addition to the physically motivated Bianchi VII_h model, we examine phenomenological models considered in previous studies, in which the Bianchi VII_h parameters are decoupled from the standard cosmological parameters. In the two phenomenological models considered, Bayes factors of 1.7 and 1.1 units of log-evidence favouring a Bianchi component are found in full-sky ILC data. The corresponding best-fit Bianchi maps recovered are similar for both phenomenological models and are very close to those found in previous studies using earlier WMAP data releases. However, no evidence for a phenomenological Bianchi component is found in the partial-sky W-band data. In the physical Bianchi VII_h model we find no evidence for a Bianchi component: WMAP data thus do not favour Bianchi VII_h cosmologies over the standard Lambda Cold Dark Matter (LCDM) cosmology. It is not possible to discount Bianchi VII_h cosmologies in favour of LCDM completely, but we are able to constrain the vorticity of physical Bianchi VII_h cosmologies at $(\omega/H)_0 < 8.6 \times 10^{-10}$ with 95% confidence.

For non-experts the Bianchi cosmologies are based on exact solutions of Einstein’s equations for general relativity which obey the condition that they are spatially homogeneous but not necessarily isotropic. If you find that concept hard to understand, imagine a universe which looks the same everywhere but which is pervaded by a uniform magnetic field: that would be homogeneous (because every place is identical) but anisotropic (because there is a preferred direction – along the magnetic field lines). Another example of would be s a universe which is, for reasons known only to itself, rotating; the preferred direction here is the axis of rotation. The complete classification of all Bianchi space-times is discussed here. I also mentioned them and showed some pictures on this blog here.

As Jason’s post explains, observations of the cosmic microwave background by the Wilkinson Microwave Anisotropy Probe (WMAP) suggest  that there is something a little bit fishy about it: it seems to be have an anomalous large-scale asymmetry not expected in the standard cosmology. These suggestions seem to be confirmed by Planck, though the type of analysis done for WMAP has not yet been performed for Planck. The paper mentioned above investigates whether the WMAP asymmetry could be accounted for by one particular Bianchi cosmology, i.e. Bianchi VII_h. This is quite a complicated model which has negative spatial curvature, rotation (vorticity) and shear; formally speaking, it is the most general Bianchi model of any type that includes the standard Friedmann cosmology as a special case.

The question whether such a complicated model actually provides a better fit to the data than the much simpler standard model is one naturally answered by Bayesian techniques that trade off the increased complexity of a more sophisticated model  against the improvement in goodness-of-fit achieved by having more free parameters.  Using this approach McEwen et al. showed that, in simple  terms, while a slight improvement in fit is indeed gained by adding a Bianchi VII_h component to the model,  the penalty paid in terms of increased complexity means that the alternative model is not significantly more probable than the simple one. Ockham’s Razor strikes again! Although this argument does not definitively exclude the possibility that the Universe is rotating, it does put limits on how much rotation there can be. It also excludes one possible explanation of the  peculiar pattern  of the temperature fluctuations seen by WMAP.

So what does cause the anomalous behaviour of the cosmic microwave background?

I have no idea.

The Cold Spot

Posted in Cosmic Anomalies, The Universe and Stuff with tags , , , , on August 16, 2009 by telescoper

Musing yesterday about the rapidly approaching restart of the academic year reminded me that I really ought to get on and finish the bunch of papers sitting on my desk and on various computers. I’ve also got a book to finish before October so I’d better get cracking with that too.

More importantly, however, it reminded me to congratulate my PhD student Rockhee Sung who has just had her first paper published (in the journal Classical and Quantum Gravity). The paper is available online here and it’s free to download for a month even if you don’t have a personal or institutional subscription to the journal.

The idea of this paper came a while ago but it has taken us a long time to get everything in place to start writing it up. In the meantime other papers have been written on the subject, but Rockhee and I have done this our own way – or rather she has, as she put most of the hard work into actually doing the calculations.

About four years ago, during the course of careful statistical analysis of data from the Wilkinson Microwave Anisotropy Probe (WMAP), a group based in Santander (Spain) published a paper drawing attention to the existence of an anomalous “Cold Spot” in the data. This phenomenon has now acquired its own Wikipedia entry (here), so I won’t repeat all the details except to say that it is about 5° across and that it is colder than one would expect if the temperature fluctuations are Gaussian, as is predicted in the simplest models of the early Universe involving cosmological inflation. The spot is to the bottom right, and is marked with an arrow on the picture below.

It’s worth digressing a little here to explain that a fluctuating field of course contains both hot spots and cold spots. Because there CMB temperature fluctuations comprise a wide range of wavelengths there are also spots on different scales. Assessing the statistical significance of a single isolated feature like the cold spot is not particularly easy. Based on the brute force method of simulating skies according to the Gaussian hypothesis and then repeating the approach that led to the original discovery, the result is that around 1% of Gaussian CMB skies have a cold spot as cold as that observed in the real data. Before the non-Bayesians among you get too excited, I’ll remind you that this means that the probability of a Cold spot given the standard model is about 1%, i.e. P(Cold Spot | Standard Model)=0.01. This is NOT the same as saying that the probability of the standard model being correct is 0.01…

A probability of 1% is an in-between kind of level: not too small to be decisive, and not too large to be instantly dismissed as just being a chance fluctuation. My personal opinion is that the Cold Spot is an interesting feature that deserves to be investigated further, but is not something that in itself should cause anyone to doubt the standard model. I include it among the list of cosmological anomalies that I’ve blogged about before (for example, here, here and here). I find them interesting but don’t lose sleep worrying that the standard model is about to fall to pieces. Not yet, anyway.

Not all theorists are as level-headed as me, however, and within weeks of the discovery of the cold spot suggestions were already being put forward as to how it could be “explained” theoretically. Some of these are described in the Wikipedia entry, so I won’t rehash the list. However, one suggestion not included there was the idea that the anomalous cold spot might be there because the Universe were not isotropic, i.e. if the Cosmological Principle were violated.

Way back when I was a lad doing my own PhD, my supervisor John Barrow had been interested in globally anisotropic (but nevertheless homogeneous) cosmologies. These are models in which any observer sees different things in different directions, but the pattern seen by observers in different places is always the same. I never worked on these at the time – they seemed a bit too esoteric even for me – but I remembered bits and pieces about them from conversations.

A complete classification of all the space-times  possessing this property was completed over a hundred years ago (before General Relativity was invented) by the Italian mathematician Luigi Bianchi, and cosmological models based on them are called the Bianchi models.

This isn’t the place to go into detail about the Bianchi models: the classification is based on the mathematical properties of Lie groups, which would take me ages to explain. However, it is worth pointing out that only five Bianchi types actually contain the cosmologically principled Friedmann-Lemaître-Robertson-Walker universe as a special case: I, V, VII0 ,VIIh and IX. If you really want to know what the classes are you’ll have to look them up! Since we know our Universe is very close to being homogeneous and isotropic, it seems reasonable to look at those models capable of describing small departures from that case so the above list provides a useful subset of the models to explore.

Rockhee’s PhD project was to explore  the patterns of cosmic microwave background  fluctuations that can arise in that set of Bianchi cosmologies, not just in the temperature (which had been done before) but also in polarization (which hadn’t). I’ve already posted some of the temperature patterns Rockhee computed here.

The reason for extending wanting to extend this work to include polarization was the following. The microwave background radiation is partly linearly polarized because of the way radiation is scattered by electrons. If an electron is immersed in a radiation bath which is isotropic there is no net polarization, but if the radiation field is anisotrpic – in particular if it varies on an angular scale of 90º (i.e. a quadrupole) – then the scattered radiation will be partly polarized. In the standard cosmology the variations in the radiation field are random fluctuations so each electron “sees” a different quadupole. The net polarization field is therefore produced incoherently, by adding stochastic contributions. In  a  Bianchi model the situation is different. Each electron in this case sees the same quadupole. The polarization pattern produced is therefore coherent. Not only do anisotropic universes produce characteristic radiation patterns, they also produce a corresponding pattern in polarization.

So what does this all have to do with the Cold Spot? Well, in anisotropic spaces that are also curved, it is possible for light rays to get focussed in such a way that the entire pattern of flucuations present at least-scattering winds up concentrated in a small patch of the sky as seen by a late-time observer. for this to happen the space has to be negatively curved. Only two of the Bianchi types can do this, as there are only two that are both near-FLRW and negatively curved: V and VIIh. Both of these models could, in principle, therefore produce a cold spot by geometrical, rather than stochastic means. In the little figure below, taken from our paper, you can see examples of Bianchi VIIh (top) and Bianchi V (bottom) showing the temperature (left) and polarization (right) in each case. We’ve oriented the model to put the cold spot in approximately the right location as the observed one.

 

cold

 

The point is that there is a pretty heavy price to be paid for producing the cold spot in this way: an enormous, coherent signal in the polarized radiation field.

As often happens in such situations, somebody else had the idea to investigate these models and we were scooped to a large extent by Andrew Pontzen and Anthony Challinor from Cambridge, who recently published a paper showing that the polarization produced in these models is already excluded by experimental upper limits. They concentrated on the Bianchi VIIh case, as this appears to have a more general structure than V and it was the model first advocated as an explanation of the cold spot. In this model the combined effect of vorticity and shear introduces a swirly pattern into the radiation field that you can see clearly in the top two panels of the figure as well as focussing it into a small patch. Bianchi V doesn’t produce the same kind of pattern either in temperature or polarization: it looks more like a simple quadrupole squeezed into a small part of the sky. A particularly interesting aspect of this is that the Bianchi VIIh case clearly has a definite “handedness” while the Bianchi V one doesn’t.

The moral of all this is that the polarization of the cosmic microwave background provides key additional information that could prove decisive in eliminating (or perhaps even confirming) models of the Universe more exotic than the standard one. That’s one of the areas in which  we expect Planck to produce the goods!

In the meantime Rockhee and I will be submitting a couple of much larger papers in due course, one containing a wider discussion of the possible pattern morphologies that can be produced in these models, and another about their detailed statistical properties.