Published online 23 May 2008 | Nature | doi:10.1038/news.2008.854
Corrected online: 28 May 2008


Doughnut-shaped Universe bites back

Astronomers say Universe is small and finite.

torusMmm... Universe. Calculations show it really might be shaped like the snack favourite.

The doughnut is making a comeback – at least as a possible shape for our Universe.

The idea that the universe is finite and relatively small, rather than infinitely large, first became popular in 2003, when cosmologists noticed unexpected patterns in the cosmic microwave background (CMB) – the relic radiation left behind by the Big Bang.

The CMB is made up of hot and cold spots that represent ripples in the density of the infant Universe, like waves in the sea. An infinite Universe should contain waves of all sizes, but cosmologists were surprised to find that longer wavelengths were missing from measurements of the CMB made by NASA’s Wilkinson Microwave Anisotropy Probe.

One explanation for the missing waves was that the universe is finite (see 'Universe could be football-shaped').

A mirror ball

“You can think of the Universe as a musical instrument - it cannot sustain vibrations that have a wavelength that is bigger than the length of the instrument itself,” explains Frank Steiner, a physicist at Ulm University in Germany.

Cosmologists have suggested various 'wrap-around' shapes for the Universe: it might be shaped like a football or even a weird 'doughnut'. In each case, the Universe would appear to be infinite, because you would never physically reach its edge - if you travelled far enough in any direction you would end up back where you started, just as if you were circumnavigating the globe.

But the notion soon suffered a setback. Cosmologists predicted that a wrap-around Universe would act like a hall of mirrors, with images from distant objects being repeated multiple times across the sky. Glenn Starkman at Case Western Reserve University in Cleveland, Ohio, and his colleagues searched for the predicted patterns, but found nothing.

Undeterred, Steiner and his colleagues have re-analysed the 2003 data from NASA's Wilkinson Microwave Anisotropy Probe, looking for different shapes, including the so-called '3-torus', also dubbed the 'doughnut universe'.

Despite its catchy nickname, this shape is tough to visualize, says Steiner. The 3-torus is an extension of the familiar doughnut shape and can be formed from a rectangular piece of paper. You can imagine gluing together first one set of opposite edges to make a cylinder, and then the second set of opposing edges to make a doughnut shape, explains Steiner.

The 3-torus is formed in a similar way, but you begin with a cube and glue together each of the opposite faces. So if you were to attempt to exit one of the cube's faces, you would immediately find yourself entering again through the opposite one.

Other shapes are possible

Steiner’s team used three separate techniques to compare predictions of how the temperature fluctuations in different areas of the sky should match up in both an infinite Universe and a doughnut one. In each case, the doughnut gave the best match to the Wilkinson Microwave Anisotropy Probe data. The team has even been able to pin point the probable size of the Universe, which would take around 56 billion light years to cross.

Jean-Pierre Luminet at the Paris Observatory in France, who proposed the football-shaped universe in 2003, likes Steiner's work. He agrees that the analysis shows that the doughnut is still a likely candidate, but adds that other shapes are also possible. “One must remember that the (football universe) is still alive and well,” says Luminet.


Starkman, however, is not convinced that Steiner’s team has done enough to win people over. “It could be true that the Universe is small,” he says, “but this doesn’t provide an answer one way or the other.”

Steiner believes that new and more precise measurements of the cosmic microwave background to be made by Europe's Planck satellite, which is due to be launched later this year, will help answer the question.

“Philosophically, I like the idea that the Universe is finite and one day we could fully explore it and find out everything about it,” Steiner says. “But since physics cannot be decided by philosophy, I hope it will be answered by Planck.” 


The final quote of this article was mistakenly attributed to Glenn Starkman. It is now correctly attributed to Frank Steiner.
  • References

    1. Aurich, R., Janzer,H. S., Lustig, S. & Steiner, F. Class. Quant. Grav. (in the press). Preprint at (2008).
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