The shape of the universe could be far more complex than anybody had ever imagined

About 2,500 years ago humanity began to recognize that our planet earth is round—though a few “flat Earth” supporters still refute this today. The shape of our cosmos is not clear, however. Previous studies have proposed that the universe probably has a fairly simple shape, like the 3D equivalent of a spherical surface or a plane. But this view may be erroneous, according to cosmologists from the COMPACT (Collaboration for Observations, Models and Predictions of Anomalies and Cosmic Topology). In a paper published in April 2024, they proposed that the shape of the cosmos could be considerably more complex than previously assumed.

Earth also seems flat at first glance. This is because its radius is so huge that the surface’s curvature is hardly perceptible. To demonstrate it’s a sphere, you would just have to walk. If you were to travel straight ahead without ever turningyou would certainly return to the start at some point.Cosmologists gather similar clues to determine the shape of the cosmos. They could dispatch a spaceship out to traverse the universe. Instead they gaze into the night sky and scrutinize traces of the oldest light that reaches us from the depths of the universe. This radiation was produced around 300,000 years post the big bang. Although photons had existed even prior to that, matter was so densely packed into what was in that period a small universe that the light quanta had no opportunity of traveling freely. Eventually, nevertheless, the universe cooled down to such an extent that it got transparent. The photons were able to spread freely through space—and still do today.

Photons from this early time in the cosmos reach us as cosmic background radiation. Almost the same pattern of old light comes from every corner of the universe. This radiation offers clues to the shape of the universe. If, for instance, the curvature of the cosmos were to change at one point, the cosmic background radiation would not be as consistent as we observe it. Experts therefore assume that the cosmos is either curved in the same manner everywhere—or is completely flat.

A WEALTH OF LIKELIHOODS

It is hard to imagine the cosmos having no curvature or constant curvature. That’s why it helps to use 2D examples. In this particular analogy, to fit the homogeneous patterns of cosmic background radiation, the cosmos can be in fact flat like a flat sheet of paper (no curvature), correspond to the 3D counterpart of a spherical surface (positive curvature) or form a kind of 3D saddle surface (negative curvature). In all of the three cases, the curvature is constant everywhere.

But this still does not disclose what the cosmos as a whole looks like. For instance, space could be curved in the same manner everywhere and still have a hole. The mathematical discipline of topology can be employed to differentiate between such cases. Topologists classify geometric figures based on rough categories, such as the number of holes in them, so as to create a catalog of shapes. Cosmologists target to assign one of these shapes to the cosmos.

As mathematicians have been able to prove, there are an infinite number of distinct categories (topologies) of curved 3D surfaces. So if spacetime in fact saddle-shaped or spherical, then there are theoretically any number of shapes that the cosmos can take on, each of which is very dissimilar from the other. Cosmological observations to date, nevertheless, point to a flat cosmos without curvature. If correct, this insight narrows the search for the topology of the cosmos: as mathematician Grigori Perelman deduced in 2003, the catalog of flat 3D surfaces is very small, with only 18 different categories.