We may be living in a donut. It looks like Homer Simpson’s fever dream, but it could be the shape of the entire universe; to be exact, a hyperdimensional doughnut that mathematicians call 3 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 for Theoretical Physics in Madrid, a member of an international partnership called Compact (Collaboration on Observations, Models and Predictions of Anomalies and Cosmic Topology). In May, the Compact team announced that the question of the shape of the universe was still open and was exploring future possibilities to determine this question precisely.
“This is a high-risk, high-reward cosmology,” says team member Andrew Jaffe, a cosmologist at Imperial College London. “I would be very surprised if we found anything, but I would be extremely happy if we did.”
The topology of an object specifies how its parts are connected. The donut has the same topology as the teacup; the hole is equivalent to the handle: you can shape the clay donut into a cup shape without tearing it. Similarly, sphere, cube and banana have the same topology and do not have holes.
The idea that the entire universe could have a shape is difficult to imagine. In addition to topology, there is another consideration: curvature. In his theory of general relativity in 1916, Albert Einstein showed that space could be curved by massive objects, creating a gravitational force.
Imagine space as two-dimensional, like a sheet, rather than having all three spatial dimensions. Flat space is like a flat sheet of paper, while curved space can be like the surface of a sphere (positive curvature) or a saddle (negative curvature).
These possibilities can be distinguished by simple geometry. The sum of the angles of a triangle on a flat plate should be up to 180 degrees. But on a curved surface this is no longer the case. By comparing the actual and apparent sizes 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: like a flat sheet full of tiny pits where each star distorts the space. around.
“When you know what the curve is, you know what kinds of topologies are possible,” says Akrami. Flat space can go on forever, like an endless piece of paper. This is the most boring, insignificant possibility. But a flat geometry also obeys some topologies that cosmologists euphemistically call “trivial”; This means they are much more interesting and can be quite confusing.
For mathematical reasons there are exactly 18 possibilities. In general, they correspond to the universe having a finite volume but no edges: If you go further than the scale of the universe, you end up back where you started. It’s like the screen of a video game where a character that appears on the far right reappears on the far left; it’s as if the screen was twisted into a loop. In three dimensions, the simplest of these topologies is the 3-torus: It resembles a box that you can exit from any face and re-enter from the opposite side.
If you could look out into the universe, you would see endless copies of yourself in every direction, like a hall of 3D mirrors.
Such a topology has a peculiar meaning. If you could look at the entire universe – which would require the speed of light to be infinite – you would see endless copies of yourself in every direction, like a hall of 3D mirrors. Other, more complex topologies are variations on the same theme; for example, images may appear slightly shifted; you re-enter the box from a different location, or perhaps twist to turn left and right.
If the volume of the universe is not very large, we can see such duplicate images, for example, an exact copy of our own galaxy. “People started looking for topology at very small scales by looking for images of the Milky Way,” says Jaffe. But due to the finite speed of light, this is not entirely straightforward – “you have to look for them as they were a long time ago” – and so you may not recognize the copy. Also, our galaxy is moving, so the copy won’t be where we are now. And some of the more exotic topologies will replace it as well. In any case, astronomers have never seen such a cosmic replica.
On the other hand, if the universe is truly huge but not infinite, we may never be able to distinguish between the two, says Akrami. But if the universe is finite along at least some directions and not much larger than we can see, then we should be able to detect its shape.
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One of the best ways to do this is to look at the cosmic microwave background (CMB): the very faint glow of heat left over from the big bang that floods the cosmos with microwave radiation. First detected in 1965, the CMB is one of the most important evidence that the Big Bang took place. It is almost uniform throughout the universe. But as astronomers developed more sensitive telescopes to detect and map it in the sky, they found very small variations in the “temperature” of this microwave sea from place to place. These variations are residues of random temperature differences in the newly formed universe; These differences helped seed the emergence of structure so that matter in the universe is not spread evenly across the cosmos like butter on bread.
So the CMB is a kind of map etched into the sky around us, showing what the universe looked like at the earliest stage (about 10 billion years ago) that we can still observe today. If the universe has a non-simple topology that produces copies in some or all directions, and its volume is not significantly larger than the sphere we see projected by the CMB, these copies should leave traces in temperature changes. Two or more patches will match, like copies of fingerprints. But given that these changes are random and weak, and some topologies can swap copies, this is not easy to detect. However, we can investigate the statistics of small temperature changes and see if they are random. This is a search for patterns, like traders looking for non-randomness in stock market fluctuations.
The Compact team looked closely at any chance of finding anything. This showed that although non-random patterns were not yet seen in the CMB map, these were not ruled out. In other words, many strange cosmic topologies are still completely consistent with observed data. “We did not rule out interesting topologies as much as some had previously thought,” says Akrami.
Others outside the group agree. “Previous analyzes do not rule out the existence of observable effects that are likely due to the universe having a nontrivial topology,” says astrophysicist Neil Cornish of Montana State University in Bozeman, who devised such an analysis 20 years ago. “I think non-trivial topologies are still very much a possibility,” says astronomer Ralf Aurich of the University of Ulm in Baden-Württemberg, Germany.
But isn’t it a bit perverse to imagine that the infinitely large universe could have the shape of a twisted doughnut rather than have the simplest possible topology? Not necessarily. Going from nothingness to infinity in the big bang is a pretty big step. “Small things are easier to create than big things,” Jaffe says. “So it’s somehow easier to create a compact universe, and a non-trivial topology does that.”
Moreover, there are theoretical reasons to suspect that the universe is finite. There is no agreed-upon theory for how the universe emerged, but one of the most popular frameworks for thinking about this topic is string theory. But current versions of string theory predict that the universe must have at least 10 dimensions, not just four (space plus time’s three).
String theorists suggest that perhaps all other dimensions have become quite “compressed”: they are so small that we do not experience them at all. So why then did only six become finite while the others remained infinite? “I would say that it is more natural to have a compact universe, rather than four infinite dimensions and the others being compact,” Akrami says.
The ideal situation would be to combine everything that is observable, and we hope that this will give us a large signal of the topology.
Yaşar Akrami, cosmologist
If the search for cosmic topology shows that at least three of the dimensions are truly finite, this would rule out most possible versions of string theory, Aurich says.
“The detection of a compact universe would be one of the most surprising discoveries in human history,” says cosmologist Janna Levin of Barnard College in New York. Such searches are therefore “valuable, even though they threaten to disappoint.” But if he had to bet, he adds: “I’d bet against a small universe.”
Will we ever know the answer? “It’s quite possible that the universe is finite, but the topology scale is larger than we can examine through observations,” says Cornish. But he adds that some of the strange features in the CMB model are “exactly what you’d expect in a finite universe, so they’re worth further investigation.”
Cornish says the problem of looking for patterns in CMB is about how each of the 18 flat topologies can be modified: “There are an infinite number of possibilities to consider, each with its own unique predictions, so it’s impossible to try them out.” all out. Perhaps the best we can do is decide which possibilities seem most likely and see if the data fits them.
Aurich says a planned refinement of the CMB map in an international project called CMB phase 4, using a dozen telescopes in Chile and Antarctica, will aid the hunt. But the Compact researchers suspect that, unless we get lucky, the CMB alone may not allow us to answer the topology question definitively.
However, they say there is also a wealth of other astronomical data we can use: not just what is in the “sphere” of the CMB map, but also what is in the rest of space. “Everything in the universe is affected by topology,” says Akrami. “The ideal situation would be to combine everything that is observable, and we hope that this will give us a big signal about the topology.” He says the team wants to either detect this signal or show that it is impossible.
There are several instruments currently in use or under construction, such as the European Space Agency’s Euclid space telescope and the SKA Observatory (formerly the Square Kilometer Array), which launched last year, that will fill in more detail about what’s inside the volume of observable space. ), a radio telescope system built in Australia and South Africa. “We want to count all the matter in the universe,” says Jaffe, “which will allow us to understand the global structure of space and time.”
If we achieve this, and it turns out that cosmic topology makes the universe finite, Akrami imagines a day when we will have a kind of Google Earth for the entire universe, a map of everything.