## Why the Universe is (probably) not rotating

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.

### 10 Responses to “Why the Universe is (probably) not rotating”

1. Anton Garrett Says:

Rather than say that the universe is (or might be) rotating, I’d prefer to say that a cosmological solution to Einstein’s field equations has a constant of integration that corresponds to nonzero intrinsic angular momentum, because this phrasing overcomes the “rotating relative to what” issue. (The universe IS everything.) It’s a bit like explaining that the expansion of the universe is not expansion into any other space, but an increase in distances between objects.

Ockham’s Razor tells you how to distribute probability between a theory in which angular momentum is strictly zero, and a theory in which it may be nonzero but has a value that is too small to be measured by today’s instruments. If the strictly-zero hypothesis is strongly preferred then an explanation should be sought, since GR is silent on the question. Is there one?

I hope as a Bayesian non-cosmologist that this is a sensible question…

• Which choice is suggested to you by Ockham’s razor?

What about a universe in which the axes of rotation of galaxies are not distributed randomly (thus with no preferred direction on average)? This would also be a case of non-zero total angular momentum, but one couldn’t speak of the entire universe rotating in any meaningful sense.

• Anton Garrett Says:

“Which choice is suggested to you by Ockham’s razor?”

I don’t know the noise stats for the data. On that depends the answer. I’m talking about a formal Bayesian calculation, although in some situations the answer is obvious.

“What about a universe in which the axes of rotation of galaxies are not distributed randomly (thus with no preferred direction on average)?”

I don’t understand the question Phillip. If the distribution is non-random then surely there WILL be overall be a preferred direction?

• “I don’t understand the question Phillip. If the distribution is non-random then surely there WILL be overall be a preferred direction?”

Sorry, the parenthetical expression applies to “randomly”, not to “not distributed randomly”.

• telescoper Says:

As a cosmologist I prefer not to think about the Universe, but about fluid elements. In a homogeneous universe these must all behave the same way at the same time (defined by the surfaces of homogeneity). Fluid elements can change in three ways: volume expansion, rotation and shear. If all the fluid elements on a hypersurface rotate in the same way then there is a net cosmological rotation.

The Cosmological Principle doesn’t allow a net rotation (because that would imply a preferred direction), so your question is why the Cosmological Principle should hold. There are two ways of answering this: (i) by appealing to initial conditions (which we don’t understand); (ii) by assuming that something homogenized, isotropized (and put the brakes on the rotation of) the Universe. Inflation is a model that works via (ii): inflating an anisotropic universe redshifts away the shear and rotation of the fluid elements, leaving only the volume dilation. But this doesn’t mean that they are identically zero, just very small relative to what’s left, i.e. the isotropic expansion of the Universe.

• “As a cosmologist I prefer not to think about the Universe”

That’s one to add to my collection of quotes.

“I don’t know much about music. In my line of work, you don’t have to.”

—Elvis Presley

• “Inflation is a model that works via (ii): inflating an anisotropic universe redshifts away the shear and rotation of the fluid elements, leaving only the volume dilation.”

It definitely works. However, does one need some improbable initial conditions in order to get inflation to work? Some claim this is so. Also, even if it works, one needs to be sure that it really happened. The CMB observations are now becoming detailed enough to lend support to inflation (e.g. the amount and direction of tilt is about right). To me, the main argument for it is that there seems to be no other believable way to solve the isotropy problem. But it would be nice to have direct evidence for inflation, rather than believing it because it works.

Time to quote Jim Peebles:

“And for a long time it seemed that we were going to have to accept inflation by default. We have these deep puzzles, inflation offers a solution, we have no other solution, so by default we accept it. That’s not the way I like to do physics. I like to have an experiment that forces us to accept it.”

—Jim Peebles [http://www.aip.org/history/ohilist/25507.html]

• telescoper Says:

Very much agree with Jim Peebles. The question you pose about initial conditions is impossible to answer really because we don’t know how to define an appropriate measure to define the probability.

• I see that the AIP has changed some URLs; here’s the correct one (at least for now) for the transcript with this Peebles quote. Note that there are three separate interviews with Peebles here, and a huge number of interviews with other folks. Worth checking out.

2. Erik Andrulis Says:

The Universe is moving and not moving at the same time. You call Yourself the Unmoved Mover for a good reason. Just sayin’.