How space can fold back on itself is described by the mathematics of topology. Imagine the Universe is shaped like a cube (topologists imagine far more complicated things, but a cube will do for now). If you were a fly trapped in a cubical box, you could buzz around within the box, but never cross the walls. But if the sides of the cube were multiply connected in a simple way, when you flew up out of the top of the box you'd re-enter from the bottom. If you flew across the right hand (RH) wall, you'd return via the left hand (LH) wall. It isn't that the cube is bent round to join up on itself: rather, the left and right walls are in the same place as each other, as are the floor and ceiling. It's a bit like some computer games, where a spaceship flies off the right of the screen and instantly back on from the left. If you looked straight out of the RH wall, you'd see the back of your own head, as light from it would have exited via the LH wall and in from the right. But add a little more complexity, let the cube be twisted and space bent, and stranger things happen. Now, light from the front of your face may go out via the RH wall and follow a curved path on a circuitous route round back to your eyes. In a multiply connected Universe (if it is small enough) you'd look straight ahead and see your own face looking back at you - but it may be distorted, or bigger or smaller, just as in the hall of mirrors.
Curved space is a clue to why people take such ideas seriously. Albert Einstein explained gravity in terms of curved space. His general theory of relativity is a geometrical theory, but it doesn't say anything about topology - it assumes space isn't topologically interesting. But physicists searching for a theory of everything find that they have to invoke complex topologies involving things called superstrings on scales (quantum scales) far smaller than those of particles such as electrons. Quantum gravity seems certain to involve interesting topology - so, many cosmologists believe, that means we ought to consider large-scale topology interesting too. Janna Levin, of the University of Sussex, says: "Ignoring the topology of space time is like assuming the world is flat - just a cultural prejudice."
But where's the evidence? Look for images of the same galaxy in different parts of the sky - like looking for different views of your own face. The snag is that, as the light arrives by different routes, it takes longer (maybe billions of years) to travel some routes than others. And since galaxies, like faces, change as they age, we can't be sure whether a young galaxy in one part of the sky really is the same as an old one in another part. But Princeton University researchers say that we may be able to see the effects at work in two years, when the next generation of microwave satellites launch.
Neil Cornish and David Spergel have calculated how the Universe's topological structure could affect the way we see the microwave background radiation itself - famously mapped by the Cobe satellite. As light (or radio) waves travel repeatedly through the same box of space as time passes, they're in effect travelling through the Universe at different stages of its own evolution. How the light is deflected on curving paths produces an effect rather like that of the gravitational lens, when light from a very distant object (eg a quasar) travels by different routes around a galaxy lying between us and the quasar, and makes several images in our telescopes. Different topologies produce different patterns of spots embedded in the overall pattern of microwave background radiation; detecting such spots would tell us that we really do live in a small, perfectly formed and multiply connected Universe.
This has been known for a couple of years, but the surprising thing about Cornish and Spergel's work - recently posted on the Internet - is that a statistical analysis of the pattern of this radiation as observed by Cobe really does match the predictions for a Universe with the simplest possible multiply connected topology better than it does the conventional model of an infinitely big Universe. At least, it does so if the Universe has a relatively low density, so that it is going to expand for ever, as gravity will never be able to pull everything back into a Big Crunch; Einstein's terminology calls space "negatively curved". The latest observations of the way galaxies move suggest the overall density is indeed low enough: so Big Bang radiation would pass through about 500 copies of the Universe (or rather, via the same Universe 500 times at different ages) before being captured by our radio telescopes. But statistical evidence alone never entirely convinces.
Like all good scientific theories, though, this one makes a prediction. The simple topology ought to produce ring-shaped patterns in the microwave background radiation, but too faint to have been detected yet. The satellites MAP and Planck, due to launch early next decade, should be sensitive enough to detect any such rings. Levin stresses this is a real possibility, and "the exploration of the Universe for signs of topology is really just beginning."
Since the favoured Big Bang explanation, called "inflation", tries to describe how the Universe grew out of a seed on the quantum scale, there may be a direct link between superstrings topology and the topology of the Universe at large. So - most aptly - watch this space.
The writer is author of `The Birth of Time' (Weidenfeld & Nicolson)