IF YOU had met physicist Dmitry Sokoloff in the early 1970s and asked him what he was doing, you might have thought he'd gone off the rails. Sokoloff was sifting through catalogues of distant galaxies trying to find our own Galaxy. He was looking for us, here, out there—but in an era long gone by. On a planet called Earth in this galactic ghost, maybe hundreds of millions of light years away, human life would eventually evolve, two world wars would rage across the globe, and 1998 years after a fabled prophet was said to have been born, a country called France would win the soccer World Cup.

Sokoloff never found an image of the Milky Way in its youth. But the idea wasn't as far-fetched as it sounds. Since the beginning of this century, astronomers have pondered the possibility that light in the Universe moves in mysterious ways, creating multiple images of every bright object inside—including our own Galaxy. We can now be pretty sure that no Milky Way lookalikes exist nearby. But they may lurk in distant corners of the cosmos, and scientists plan to look for them using satellites due for launch in the next few years. Early next century, we may learn that the Universe is a giant hall of mirrors where you can't always believe your eyes.

If evidence does show multiple images of galaxies in space, that would reveal some important things about the Universe. "We'd know for certain that the Universe is finite," says astrophysicist Neil Cornish of the University of Cambridge. It could also help us extend Einstein's celebrated theories about gravity. And if our telescopes can pinpoint an image of the Milky Way somewhere in the sky, we might even be able to watch our own history as it evolves. "The possibilities are truly mind-blowing," he says.

The issue of multiple images in space began to be taken seriously as a result of Einstein's general theory of relativity. This confirmed speculation by several 18th-century scientists that space might not be flat. The gravity of stars and galaxies can warp space, making light rays bend around them. Alexander Friedmann, a Russian physicist, showed in the 1920s that there were a variety of options for the geometry of space. Which one applies depends on one unknown quantity: the total amount of matter in the Universe.

If there is relatively little mass in the Universe, space will have a hyperbolic geometry. In other words, initially parallel light rays will diverge as they journey through space. "The Universe would act like a concave lens," says Joseph Silk, an astrophysicist at the University of California at Berkeley. With a bit more mass—at some critical value—space will be flat, and light will travel in parallel lines as we intuitively imagine it does. In the third kind of universe that Friedmann teased out of Einstein's equations—one that contains more mass than this critical value—parallel light rays will gradually converge.

Einstein's equations lay down the laws about the local geometry of space in such universes. But they say nothing about their overall shapes, or topologies. What's more, though the universe in which light converges has to be finite in size, the other two can be either finite or infinite. Einstein's theory cannot say. "In that sense, his theory is incomplete," says Janna Levin, a colleague of Silk's at Berkeley. "The whole issue is still shrouded in ambiguity."

Observations over the past decade or so have almost ruled out the idea that the Universe is massive enough to square with Friedmann's converging Universe (see "To infinity and beyond", New Scientist, 11 April, p 26). As far as we can tell, space is hyperbolic or flat. But more than 80 years after Einstein penned his theory of gravity, the jury is still out on whether the Universe is finite or infinite.

Physicists believe that in any finite universe, space curves back on itself, never reaching any kind of "edge". And what a weird kind of cosmos this would be. A light ray travelling through space in what seems to be a straight line could eventually end up back roughly where it started. It's rather like circumnavigating the Earth. Whatever direction you set off in, if you carry on for long enough you'll find yourself back home. If you keep going, you will see the same landmarks over and over. Similarly, if you travel in a straight line through a finite Universe, you will see the same pattern of stars and galaxies repeated time and again, as if you were moving through an endlessly repeating set of identical regions of space (see Diagram). In this curious cosmos, light from the Milky Way will wrap right round the Universe and find itself back at Earth, creating the illusion that there is a copy of our own Galaxy in the sky.

Tall order

That's what inspired Sokoloff to hunt for a "ghost" of the Milky Way among the galaxies that clutter the heavens. In the early 1970s, Sokoloff was a student at Moscow State University, where he is now professor of mathematics. With physicist Vitia Shvartsman, he looked through catalogues of astronomical objects to see if any galaxies might be a phantom image of the Milky Way with an almost identical shape. "Vitia was hopeful," Sokoloff says, "but I was more sceptical."

Sokoloff had good reason not to raise his hopes too high: finding a ghost of the Milky Way was a tall order. The Galaxy's light would have navigated much of the dusty Universe, so the ghost would probably be vanishingly faint. And because the light would have taken millions or even billions of years to make its way around the Universe, the ghost would be far younger than the real thing.

"The ghosts are pictures of galaxies at a very different age," says Levin. "It's much like getting some baby pictures and trying to match them with pictures of old people." Besides, adds Cornish, even our picture of what the Galaxy looks like today is more sketchy than we'd like it to be: "We live in the Milky Way—it's hard to know what it looks like from outside."

Perhaps because of these difficulties, Sokoloff and Shvartsman didn't manage to find a youthful Milky Way, and all attempts since have also failed. But the search will soon begin again. If researchers find these ghostly galaxies, they would not just prove that the Universe is finite: they could also reveal its shape.

Theorists have come up with a host of different shapes that could correspond to a flat or hyperbolic finite universe. For instance, says Levin, a flat space can be built from repeating brick-shaped blocks, skewed rectangular blocks (parallelepipeds), or even hexagonal prisms that twist round by 120 degrees as light passes from one prism to the next. And there are plenty of ways of designing a hyperbolic, finite Universe by tiling space with identical polyhedrons. Among them are regular icosahedrons (solids with 20 sides), and irregular polyhedrons with 18 sides. Each of the myriad shapes would scatter light from galaxies throughout space in different ways. Measuring the distribution of galactic images in the sky would reveal whether the Universe really does have one of these exotic shapes—or even something quite different.

Astronomers now know there are no images of our Galaxy nearby. But there could yet be some lurking farther afield, beyond the range of existing telescopes, and finding these could soon be possible. In 2000, NASA plans to launch its MAP (Microwave Anisotropy Probe) satellite, and in 2006, the European Space Agency will launch Planck (see "Genesis to Exodus", New Scientist, 19 October 1996, p 31). "These will give us insight into the Universe on such huge scales," says Cornish. With David Spergel of Princeton University in New Jersey, he will be part of the team that analyses the first MAP data.

Both satellites will take a hard look at the most distant detectable "object" in the Universe—the cosmic microwave background radiation, a relic of the big bang. The expanding fireball of the early Universe kept all radiation trapped within it until its density fell to a certain point. At that time, which theory deems to be about 300 000 years after the big bang, the Universe became transparent, and the radiation began to journey through space. We can see it still. "This remnant of the hot big bang offers a remarkably rich site for cosmic archaeology," says Levin.

The background radiation pervades the whole Universe and travels in all directions. But the only photons we see on Earth are the ones arriving here and now. They have all been travelling since the Universe became transparent—very roughly, 13 billion years ago. And because the speed of light is constant, they have all travelled the same distance since that time. Because of the expansion of the Universe, space has stretched during that time, and the distance the radiation has travelled is farther than you'd expect—something like 30 billion light years. So the photons we see have come from a distant sphere in the sky with a radius of about 30 billion light years.

The radiation carries ripples—slight changes in its wavelength or "temperature". These variations, first detected by the cosmic microwave background explorer (COBE) satellite in 1992, reflect small changes in the density of the big bang fireball when the radiation escaped.

In 1996, Cornish, with Spergel and Glenn Starkman of Case Western Reserve University in Cleveland, Ohio, worked out a simple way to use these photons to find the telltale signs of repeating galaxies (Physical Review Letters, vol 77, p 215). To picture how this works, imagine how our view of the microwave background radiation would compare with that of aliens living on a planet in a galaxy billions of light years away.

Just as our radiation sphere is centred on us, aliens in a distant galaxy would see a sphere of radiation centred on themselves, also with a radius of about 30 billion light years. If the aliens are too far away from us, their radiation sphere will not overlap with our sphere. But if their galaxy lies less than about 60 billion light years away, our sphere will intersect with theirs (see Diagram). When two spheres intersect, they share common points around a circle. So looking towards the aliens, we would see a ring of ripples in the radiation that are identical to those the aliens would see if they looked in the opposite direction, towards us.

But what if the alien galaxy is just an image of the Milky Way, and what if the aliens are us? This is exactly what could happen if the Universe was made of identical, repeating copies of itself. We would then have both the aliens' view and our own. In other words, we would see identical ripples in the cosmic radiation along a ring facing our galaxy, and along a ring in some other direction. With an infinitely repeating pattern of ghost images there would be many such rings—and the exact pattern would depend on exactly how the images are dotted through space. This pattern would hold the key to the exact shape of the cosmos on the largest scale.

MAP and Planck will have the chance of spotting the matching circles for the first time. Both satellites will take a far more detailed look at the microwave background than COBE. "In one COBE pixel you could fit 400 Moons," says Cornish. "MAP has much better resolution, just a quarter of a Moon for each pixel."

Cornish and his colleagues have already worked out a strategy for trawling through the data to see if matching circles turn up. They need only find three pairs to work out the exact shape of the Universe. "If we find the circles, it is very easy to reconstruct the topology," says Cornish. Jeff Weeks, a freelance mathematician in Canton, New York, has already designed computer code that can work out the topology in a few seconds. It would then be easy to predict where all the other circles should lie, and hunt them down in the satellite data. That's if there are circles (see "Warped horns and squashed corners").

It's perfectly possible, of course, that MAP and Planck will come back empty-handed. Perhaps the Universe is infinite after all, and contains no Milky Way clones. Or perhaps our clones do exist, but the Universe is so large that they are enormously remote and the cosmic background radiation spheres around them do not intersect with our own. In that case, the radiation won't betray the shape of the Universe. "It is possible that both topology and curvature are on such huge scales that we will simply never see either," Levin says. "It's similar to wrongly concluding that the Earth is flat and unconnected just because we couldn't see it curve over into a sphere."

But if we find that the Universe really is a giant kaleidoscope, we would know for the first time where our galaxy lies in relation to the Universe as a whole, a concept that till now has made no real sense: "You could actually say where in the Universe you live," says Cornish.

It could also trigger a breakthrough in ideas about gravity. "If we observe topology directly, this would be in some sense the first observation of a theory of gravity beyond Einstein's," says Levin. For decades, physicists have been trying build on Einstein's theory by bringing gravity into the fold of quantum theory, which describes how the other forces in nature—strong, weak and electromagnetic—exert their power. Gravity has been reluctant to comply. According to John Barrow of the University of Sussex, knowing the overall shape of the Universe would provide a strong constraint on the plethora of candidates for quantum theories of gravity. "This would be a very definite thing for a quantum gravity theory to shoot at," he says.

Perhaps most gripping is the hope that we might be able to see our own Galaxy as it was in its youth. We might find ourselves watching our own past unfold in a seemingly far-off galaxy. Mysterious, distant beacons might be exposed as images of neighbouring galaxies. As Cornish says, a small universe can't hide any secrets.

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