According to general relativity theory, which says that space itself can curve, the cosmos can take one of three forms: flat like a sheet of paper, closed like a sphere, or open like a saddle. This astronomical geometry is no trivial matter — the fate of the cosmos depends on it.
As Princeton University cosmologist David Spergel puts it, “The shape of the universe tells us about its past and its future.” The shape of the cosmos determines whether it will expand indefinitely or eventually collapse, as well as whether it is finite or infinite.
For a matter that bears on such grand questions, its components are remarkably simple. The eventual structure of the cosmos is governed by only two factors: its density and its rate of expansion.
Closed, open or flat universe?
Roughly 68 percent of the universe is dark energy and 27 percent is dark matter. The remainder is ordinary matter, which includes planets, stars, and other bodies. The density of the cosmos refers to how much matter is packed into a given volume of space.
If the density of the universe is high enough for gravity to overcome the force of expansion, the cosmos will curl into a ball. This is known as the closed model, and it has a positive curvature equal to that of a sphere. A mind-boggling property of this universe is that it is finite, yet it has no bounds. An intergalactic Ferdinand Magellan could circle it forever, never hitting a wall or falling over an edge.
Space will warp in the opposite direction if the universe’s density is low and unable to stop the expansion. This would form an open universe with a negative curvature resembling a saddle.
There is also a Goldilocks universe scenario, which scientists believe is the most plausible. Most cosmological evidence points to the universe’s density as being just right — the equivalent of around six protons per 1.3 cubic yards — and that it expands in every direction without curving positively or negatively. To put it another way, the universe is flat. (Perhaps this will come as some consolation to anyone disappointed by our planet’s roundness.)
Flat in 3D
What does a flat universe mean, though? This flatness isn’t the two-dimensional variety we’re used to seeing in everyday life, but it can be imagined using a few analogies.
Say you’re standing in one corner of a square room. Turn 90 degrees after walking 10 feet along the wall to the next corner. Then turn 90 degrees and walk another 10 feet. Do this twice more and you’ll find yourself back where you started — you’ve completed a square. This is normal Euclidean geometry, which we all learnt in high school, and adding one more dimension results in a flat cosmos.
But conducting this experiment on a positively curved space that’s representative of a closed universe would create a different outcome. Start at the equator and walk to the North Pole this time. Then, walk back to the equator by turning 90 degrees. Return to your starting place by rotating 90 degrees. It takes four rotations in the flat universe example to get back to where you started, but only three in the closed universe example.
If you’re still confused (understandably), here’s another example: Two rockets flying close to each other will always remain parallel in a flat universe. This is unlike a closed universe, in which the paths of these two rockets will diverge, trek along the curvature of space, and eventually loop around to meet where they started. In a negatively curved, open cosmos, the rockets will split up and never meet again.
The cosmic microwave background (CMB), the afterglow of the Big Bang that radiates toward us from all directions, has the best clues about the form of the universe. Over the last two decades, scientists have routinely measured temperature fluctuations in the CMB — effectively performing trigonometry on the largest possible scale — and found almost no curvature at all.
The standard cosmological model, commonly known as the Lambda cold dark matter (ΛCDM) model, includes a flat universe as a key component. (Λ is the Greek letter for lambda, which symbolizes dark energy.) However, in late 2019, Alessandro Melchiorri of Sapienza University of Rome and his colleagues authored a paper concluding that Planck space observatory CMB measurements reveal a closed universe.
They measured the amount of gravitational lensing — how much light from the CMB has been deflected by the gravity of matter in its path — and found that it was greater than expected by the CDM model. If you remove the assumption of a flat universe, instead of “trying to fit the data to the wrong model,” he says, the deviation disappears.
The Planck collaboration (of which Melchiorri is a part) also detected a lensing anomaly but didn’t find it as significant. “It’s something you can live with quite easily,” says Antony Lewis, a cosmologist at the University of Sussex in Brighton, England, and a member of the Planck team. He, like most researchers, believes the gap is due to error margins. “If you get a big dataset and you look for weirdnesses,” Lewis says, “you’re bound to find it.”
Melchiorri admits to “playing devil’s advocate,” but he believes scientists should be humble and not dismiss Planck data outright. His thesis isn’t so much that the universe is closed as it is that this inconsistency may be telling us something. He also recognizes the implications of that statement. It was called a “cosmological crisis” by him and his co-authors. “Once you assume a closed universe it’s a bit of a catastrophe,” he says, “because there are many data sets that start to be in tension with [the Planck data].”
Flat as far as the eye can see
If true, it would overturn decades of astronomical findings. Aside from this evidence, there is no reason to question the universe is flat. All other CMB measurements, such as those taken by Chile’s Atacama Cosmology Telescope (ACT) and the Wilkinson Microwave Anisotropy Probe, are consistent with flatness. Other data, most notably baryon acoustic oscillations — the imprints left on galaxies by primordial sound waves that happened after the Big Bang — also point to flatness.
Most scientists would be wary of a single outlier if a theory was backed by such overwhelming data. “The Melchiorri paper’s not ridiculous,” Spergel says, in that it really does describe a feature of the Planck data that favors positive curvature. “But,” he adds, “when you go and get more data, you see a pretty consistent picture of a flat universe.”
In a paper published in December, Spergel and dozens of other researchers associated with the ACT combined their own data and other datasets with the Planck data. They found “no evidence of deviation from flatness, supporting the interpretation that the [Planck deviation] is a statistical fluctuation.” Since the publication of Melchiorri’s study, several analyses, including one last February by University of Cambridge cosmologists George Efstathiou and Steven Gratton, have drawn the same conclusion. As far as they’re concerned, there’s no need to update the ΛCDM model.
So, at least for now, the universe seems to be a three-dimensional sheet of paper. But, just as Melchiorri does not say it is closed, not all scientists insist it is flat – that’s just how it appears from our viewpoint. Our observations are, by definition, limited to the observable universe, so we could be missing something.
If the universe is curved, though, it must be so colossal that the entire 93 billion light-years we can see isn’t a large enough portion to reveal the curvature. To use Earth as an example, Gratton suggests that we could be standing in a fog, unable to see beyond a small, flat land area — but somewhere out of sight, the horizon proves we live on a sphere. “When we say the universe is flat,” he says, “what we’re saying is, of the little bit of the universe we can see, it’s consistent with being part of a [3D analogue of a] flat surface.”