Mesmeric Universes

It’s probably going to be difficult to describe what these images really are without going into enormous amounts of technical detail, but I think they are fun so I thought I’d put the pictures up with only a brief description. The remind me a little bit of the sort of hypnotic swirl sometimes used to put people under, although there’s a bit more to them than that.

According to our the standard “Big Bang” model, our Universe satisfies the Cosmological Principle which is that it is both homogeneous and isotropic, i.e. that it is the same in every location and looks the same in all directions. Of course we know our Universe isn’t exactly like that because it contains lumps of stuff called galaxies that correspond to variations in its density, but if look at sufficiently large scales it begins to look smooth. Sand is lumpy if you look close at it, but if you look at it from a long way away it looks smooth. The universe is supposed to be similarly smooth if you take a coarse-grained view.

The primary reason for incorporating the Cosmological Principle into models of the Universe is to make the mathematics simple. Einstein’s General Theory of Relativity is such a difficult theory that there are very few situations where the equations can actually be solved. One case where exact solution is relatively easy to achieve is that of homogeneous and isotropic space, which is such a symmetric state of affairs that much of the complexity of the Einstein equations disappears. Cosmological models based on this solution are generally called the Friedman models, after Alexander Friedman who first derived the solutions in the 1920s.

Despite their simplicity, the Friedman models turned out to be surprisingly accurate at describing our actual Universe which we now know to be very close to homogeneous and isotropic. Evidence for this comes from the Cosmic Microwave Background (CMB) which is astonishingly smooth across the sky. Variations in the sky temperature of the CMB are about one part in a hundred thousand of the mean temperature, which is smoother than the surface of a billiard ball.

However, it remains possible that our Universe may be slightly asymmetric and it is interesting to know what the CMB would look like if this were the case. Unfortunately there is no general cosmological solution available, so we have to tread slowly. One approach is to look at Universes which are homogeneous (the same in every place) but not isotropic (they look different in different directions). This might be describe the situation if the Universe were expanding more quickly in one direction that the others, or if it were rotating.

Actually the theory of homogeneous anisotropic universe models is quite well established and there is a full classification of all the possibilities, into the nine so-called Bianchi types. This is mathematically very complicated, so I won’t give details. However, my PhD student Rockhee has been calculating what the CMB pattern would look like in these models and the results are very pretty so I’ve included a few examples here. The little animated gifs show what the sky looks like as the Universe evolves in such cases. In all cases it starts as a pure quadrupole, i.e. a 90 degree variation across the sky. You might have to click on the image to see the animation.

The first one is Bianchi Type V. This is an example of a model in which the space is curved, so that as time goes on the initial quadrupole is focussed by gravitational effects into a smaller and smaller region of the sky. The preferred direction in this (and the other models) is picked to be in the centre of the image and the projection shows the whole sky. Hot spots are blue and cold spots are red, which is the way a physicist should plot temperature.

The next example is Bianchi Type VII_0 which is a flat Universe with rotation. What happens is that the initial quadrupole in this case gets twisted by the rotating space-time into a sort of spiral pattern. Late on in the evolution of such a Universe, an observer would see an interesting swirly structure in the cosmic microwave background.

The final example is my favourite, Bianchi Type VII_h. This one is a sort of combination of the two above examples. It has both rotation and curvature, so there is a swirly pattern which also gets focussed into a small bit of the sky. An observer living in such a Universe would see a prominent spot on the sky lying in the direction of the axis, which in this case is chosen to be in the centre of the diagram.

We’ve also been working out what the sky would look like in polarized light for these, but that’s even more complicated. If you’re really interested, I’ll post a link to the paper when it’s done…

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6 Responses to “Mesmeric Universes”

  1. [...] In the Dark A blog about the Universe, and all that surrounds it « Mesmeric Universes [...]

  2. Very interesting. Please do post the results.

    Lately I’ve been reading a lot about the anisotropy of the CMB. To an amateur like me there seems to be a fair amount of debate. Am I wrong?

  3. telescoper Says:

    I think most cosmologists regard these peculiar features as curiosities, worth bearing in mind but not getting particularly agitated about. I think we should keep an open mind about them and try to understand them better, but I don’t think they should cause us to throw away the whole theory. At least not yet.

  4. [...] 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. [...]

  5. […] 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. […]

  6. What a great resource. I like the fact that you make an attempt to reframe complex concepts using more accessible analogies.
    Q: If our models (even although based on inductive methods) are conceptual ones what, then, is the role of concept, or idea in the fabric of the universe? That we are given to dream and have ideas is not a phenomenon outside of our universe, rather, it is an effect of experiencing it in some way and this effect is, in turn, used to project or predict fundamental aspects of how the universe is. It is a lifted by the bootstraps approach but it seems the imagination is a hermeneutic key to unlock its mysteries. I read with some interest the recounting of the sailor, Johansen and how his fever dream was bent to an experience of warped spacetime.
    Your thoughts?

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