We might be living in a donut. It sounds like a Homer Simpson fever dream, but that might be the shape of the entire universe – to be exact, a hyperdimensional donut that mathematicians call a tri-torus.

This is just one of many possibilities for the topology of the cosmos. “We are trying to find the shape of space,” says Yashar Akrami of the Institute of Theoretical Physics in Madrid, a member of an international partnership called Compact (Collaboration for Observations, Models and Predictions of Anomalies and Cosmic Topology). In May, the Accord team explained that the question of the shape of the universe is still wide open and surveyed the future prospects to pin it down.

“It’s a high-risk, high-value cosmology,” says team member Andrew Jaffe, a cosmologist at Imperial College London. “I’d be very surprised if we get anything, but I’ll be very happy if we do.”

The topology of an object specifies how its parts are connected. A donut has the same topology as a teacup, and the hole is the same as the handle: you can reshape a clay donut into the shape of a cup without tearing it. Similarly, a sphere, cube and banana have the same topology, without any holes.

The idea that the whole universe can have shape is difficult. In addition to the topology there is another aspect: the curvature. In his theory of general relativity in 1916, Albert Einstein showed that space can be curved by massive objects, creating a gravitational force.

Imagine that space is two-dimensional, like a sheet, rather than having all three spatial dimensions. Flat space is like a flat sheet of paper, while curved space might be like the surface of a sphere (positive curvature) or a saddle (negative curvature).

These possibilities can be distinguished by simple geometry. On a flat sheet, the angles of a triangle must add up to 180 degrees. But on a curved surface, that is no longer the case. By comparing the true and apparent size of distant objects such as galaxies, astronomers can see that our universe as a whole appears to be as close to flat as we can measure: it is like a flat sheet crowded with small bumps where each star deforms the space. around him.

“Knowing what the curvature is, you know what kinds of topologies are possible,” says Akrami. Flat space could go on forever, like an endless sheet of paper. That’s the most boring, trivial possibility. But smooth geometry also lends itself to some topologies that cosmologists call ruthlessly, which means that they are much more interesting and can be very seductive.

For mathematical reasons, there are exactly 18 possibilities. In general, they correspond to the universe with a finite volume but no edges: if you travel beyond the scale of the universe, you end up going back to where you started. It’s like a video game screen where a character that goes far to the right appears again to the far left – because there’s a twisted loop on the screen. In three dimensions, the simplest of these topologies is the 3-torus: like a box from which you re-enter through the other face and exit through any face.

If you could look out across the universe, you would see endless copies of yourself in every direction, like a 3D hall of mirrors

Such a topology has a curious implication. If you could look out across the entire universe – which would require the speed of light to be infinite – you would see infinite copies of yourself in every direction, like a 3D hall of mirrors. Other more complex topologies are variations on the same theme, where, for example, the images appear to be slightly shifted – you reinsert the box in a different place, or perhaps rotate it so that it becomes right to left.

If the volume of the universe is not too large, we may be able to see such duplicate images – an exact copy, say, of our own galaxy. “People started looking for topology on very small scales looking for images of the Milky Way,” says Jaffe. But it’s not entirely simple because of the limited speed of light – “you have to look for them as they were a long time ago” – so you may not recognize the duplicate. Also, our galaxy is moving, so the copy will not be in the same place as we are now. And some of the more exotic topologies moved it too. In any case, astronomers have not seen any such cosmic double.

If, on the other hand, the Universe is really massive but not infinite, we cannot distinguish between the two, says Akrami. But if the universe is finite, at least along some directions, and not much more than the distance we can see, then we should be able to detect its shape.

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One of the best ways to do that is to look at the cosmic microwave background (CMB): the tiny glow of heat left over from the big bang itself, which fills the cosmos with microwave radiation. First detected in 1965, the CMB is one of the main pieces of evidence that the big bang happened at all. It is almost uniform throughout the cosmos. But as astronomers have developed more accurate telescopes to detect and map it across the sky, they have found slight variations in the “temperature” of this microwave sea from place to place. These variations are remnants of random temperature differences in the expanding universe – differences that helped seed the evolution of structure, so that matter in the universe is not spread evenly throughout the cosmos like butter on bread.

So the CMB is a kind of map of what the universe looked like at the earliest stage that we can still see today (about 10bn years ago), imprinted on the sky around us. If the globe has a nontrivial topology that produces copies in some or all directions, and if its volume is not much greater than the sphere on which we see the projection of the CMB, then these copies should leave traces in the temperature variations. Two or more patches will match, like fingerprint duplication. But that is not easy to detect, since these variations are random and weak and the duplicates would be moved around in some topologies. However, we can search among the statistics of small temperature changes and see if they are random or not. It’s looking for a pattern, like traders looking for non-randomness in stock market fluctuations.

The Compact team has looked closely at their chances of finding anything. He pointed out that while no non-random patterns have yet appeared on the CMB map, they have not been ruled out either. In other words, many strange cosmic topologies are still completely consistent with the observed data. “We didn’t rule out as many interesting topologies as others thought,” says Akrami.

Others outside the group agree. “Previous analyzes have ruled out detectable effects due to the universe’s irregular topology,” says astrophysicist Neil Cornish of Montana State University in Bozeman, who devised one such analysis 20 years ago. Ralf Aurich, an astronomer at the University of Ulm in Baden-Württemberg, Germany, also says: “I think that nontrivial topologies still have a lot of potential.”

Isn’t it a bit perverse, however, to imagine that the universe could have some complicated doughnut shape rather than the simplest possible topology of infinite size? It is not necessary. Going from nothing to infinity in the big bang is quite a step. “Small things are easier to create than big things,” says Jaffe. “So it’s easier to create a universe that’s dense in some way—and a nontrivial topology does that.”

Moreover, there are theoretical reasons to doubt that the universe is finite. There is no agreed theory of how the universe came to be, but string theory is one of the most popular frameworks for thinking about it. But current versions of string theory predict that the universe should not have just four dimensions (three space, plus time) but at least 10.

String theorists argue that all the other elements may have become very “condensed”: they are so small that we do not perceive them at all. But then why would only six or so be finite and the others infinite? “I would say it’s more natural to have a compact universe, rather than four infinite dimensions and the others compact,” says Akrami.

The ideal situation is to put all observables together and hopefully it will give us a big indication of the topology.

Yashar Akrami, cosmologist

And if the search for cosmic topology shows that at least three of the dimensions are indeed finite, says Aurich, it would rule out many of the possible versions of string theory.

“The detection of a dense universe would be one of the most significant discoveries in human history,” says cosmologist Janna Levin of Barnard College in New York. That’s why a search like this is so worthwhile, “even though they disappoint.” But if she had to bet, she says: “I would bet against a small globe.”

Will we ever know the answer? “The universe is probably finite, but the topology scale is larger than what we can probe with observations,” says Cornish. But he says the CMB pattern has some odd features “just as you would expect in a finite universe, so it’s worth further investigation”.

The problem of looking for patterns in the CMB, according to Cornish, is how each of the 18 flat topologies can be changed, “there are an infinite number of possibilities to consider, each with its own unique predictions, so it’s impossible to try remove them. all out.” Perhaps the best we can do, then, is to decide on the most likely possibilities and see if the data fits them.

Aurich says a planned improvement to the CMB map in an international project called CMB phase 4, using a dozen telescopes in Chile and Antarctica, should further the hunt. But the Accord researchers suspect that, unless we’re lucky, the CMB alone may not allow us to answer the topology question definitively.

However, they say there’s plenty of other astronomical data we can use too: not just what’s on the “sphere” of the CMB map but what’s inside it, in the rest of space. “Topology affects everything in the universe,” says Akrami. “The ideal situation is to put all the observables together and hopefully it will give us a big signal of the topology.” The team is trying to detect that signal, he says, or show that it is impossible.

A number of instruments are now in use or under construction that will fill in more details about what lies within the extent of observable space, such as the European Space Agency’s Euclid space telescope, launched last year, and the SKA Observatory (formerly the Square Kilometer Array). ), a system of radio telescopes under construction in Australia and South Africa. “We want to take a census of all the matter in the universe,” says Jaffe, “which will enable us to understand the global structure of space and time.”

If we manage that – and if the cosmic topology of the universe turns out to be finite – Akrami envisions a day when we have a kind of Google Earth for the entire cosmos: a map of everything.