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‘We’re trying to find the shape of space’: astrophysicists wonder if the cosmos is like a doughnut

Rather than stretching to infinity and beyond, the universe may have a topology that can eventually be mapped

We may be existing in a doughnut. It may sound like Homer Simpson’s fever dream, but that could in fact be the shape of the entire cosmos – to be precise, a hyper-dimensional doughnut that mathematicians term a 3-torus.This is just one of the many likelihoods for the topology of the universe. “We’re trying to find the shape of space,” says YasharAkrami(Assistant Research Professor of Theoretical Physics (Cosmology) at the Institute for Theoretical Physics, Madrid), a member of an international collaboration called Compact (Collaboration for Observations, Models and Predictions of Anomalies and Cosmic Topology). In May, the Compact team opined that the question of the shape of the cosmos still remains wide open and charted the future prospects for pinning it down.

Isn’t it, however, a little bit perverse to envisage that the cosmos may have some twisted-doughnut shape instead of having the simplest possible topology of infinite size? Not essentially. Going from nothing to infinity in the big bang is quite a step. “It’s easier to create small things than big things,” says Compact team member Andrew Jaffe (a cosmologist at Imperial College London). “So it’s easier to create a universe that is compact in some way – and a nontrivial topology does that.”

Moreover, there are theoretical reasons to suspect that the cosmos is finite. There is no settled theory of how the universe originated, but one of the most widely accepted frameworks for thinking about it is string theory. But present versions of string theory predict that the cosmos shouldn’t have merely four dimensions (three of space, plus time) but at least 10.

String theorists argue that perhaps all the other dimensions became highly “compactified”: they are so miniscule that we don’t experience them at all. But then why would merely six or so have become finite while the others stayed infinite? “I would say it is more natural to have a compact universe, rather than four infinite dimensions and the others compact,” says Akrami.And if the search for cosmic topology indicated that at least three of the dimensions are indeed finite, says Ralf Aurich (an astronomer at Ulm University in Baden-Württemberg).

“A detection of a compact universe would be one of the most staggering discoveries in human history,” says Janna Levin (cosmologist from Barnard College in New York). That’s the reason why searches like this, “though they threaten to disappoint, are worthwhile.” But if she in fact had to place a bet, she adds: “I would wager against a small universe.”

Will we ever know the answer? “It is quite likely that the cosmos is finite, but with the topology scale larger than what we can probe with observations,” says Neil Cornish (astrophysicist of Montana State University in Bozeman). But he also adds that some odd features in the CMB pattern “are exactly the kind you would expect in a finite universe, so it is worth probing further”.

The problem with seeking patterns in the CMB, Cornish states, is how each of the 18 flat topologies can be diverse, “there are an infinite number of possibilities to consider, each with its own unique predictions, so it is impossible to try them all out.” Perhaps the best we can do, then, is decide which likelihoods seem most probable and see if the data fits those.


Aurichstates that a planned upgrading of the CMB map in an international project called CMB stage 4, using a dozen telescopes in Chile and Antarctica, should aid the hunt. But the Compact researchers suspect that, except if we get lucky, the CMB alone may not let us to answer the topology question definitively.

Nevertheless, they say there is abundance of other astronomical data we can use too: not merely what’s on the “sphere” of the CMB map but what’s inside it, in the rest of space. “Everything in the universe is affected by the topology,” says Akrami. “The ideal case will be to combine everything that is observable and hopefully that will give us a large signal of the topology.” The team desires either to detect that signal, he says, or demonstrate that it’s impossible.

There are quite a few instruments now in use or in construction that will offer more details of what is inside the volume of observable space, such as the ESA’s Euclid space telescopeand the SKA Observatory (formerly the Square Kilometre Array), a system of radio telescopes being fabricated in Australia and South Africa. “We want 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 it in fact turns out that the cosmic topology makes the cosmos finite – Akrami envisages a day when we have a kind of Google Earth for the entire universe: a map of everything.


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