Stars and Planets are Spherical, But What Shape is the Universe?
Donuts are famous not only for their sweet flavor but also for their distinctive shape, which in mathematical language is referred to as the topology of the toroidal donut. If we assume that our universe has a complex structure similar to that of a donut, an astronaut could theoretically leave from a point, travel far and long, and return to the exact starting point.
Theoretical physicists believe the universe could look like this.
Essentially, no one can assert that the universe does NOT possess complex topological shapes (geometry and topology are two distinct fields). This is the conclusion presented in a scientific report published in Physical Review Letters this past April.
Topology is a branch of mathematics that studies properties of spaces that do not change when they are continuously deformed, such as stretching or bending, but not cutting or gluing.
Topology has numerous applications across various scientific fields, including physics, chemistry, biology, and computer science. It provides a language and tools for studying complex systems and abstract geometric structures.
A cup transforming into a donut shape (torus); this deformation is one of the properties of topology.
On a conventional geometric structure like a sphere, any two points on the surface can be contracted to a single point. For example, you can travel all the way around the equator and return to your starting point, and this distance can be contracted to a single point when both the starting and ending points are brought to the North Pole.
However, a donut does not possess a conventional geometric structure; it has complex topological properties. A loop on the surface of the donut cannot be contracted to a point because the hole in the center of the donut limits its ability to be shrunk.
In the scientific community, there exists a widespread belief that the universe has a geometric structure that is not too special. However, the research team that published the report argues that no one has definitively confirmed this.
“I find it very intriguing, the possibility that the universe could have an unusual and strange topology, and the most interesting part is that we can measure it,” said cosmologist Dragan Huterer from the University of Michigan, who did not contribute to the new research.
An unusual topological universe can be compared to the classic game world of Pac-Man, where the main character can move from the right edge of the screen to the left. Therefore, the Pac-Man world cannot be contracted to a single point either.
Pac-Man traveling between two edges of the screen.
Scientists are searching for signs that the universe possesses complex topological properties by studying the cosmic microwave background (CMB, which is the microwave radiation that fills the visible universe and is what remains from when the universe was only about 380,000 years old). If the universe truly has a complex topology, the potential for space to self-loop would leave distinct imprints in various locations.
In their research efforts, scientists have sought matching circles in two different locations in the universe while also looking for points in space that have certain similarities.
So far, these search efforts have been in vain. However, according to theoretical physicist Glenn Starkman and his colleagues, there is still a possibility that the universe takes the shape of a donut, as previous studies have only considered a small set of possible shapes of the universe.
Among the shapes that have been considered is a topological shape called the 3-torus, or three-dimensional torus. In 1984, the 3-torus was proposed by physicists Alexei Starobinsky and Yakov Zeldovich as one of the possible shapes of the universe. In this structure, leaving any one face would lead you to the opposite face. However, the search for evidence that the universe is a simple 3-torus has not yet yielded results.
View from inside a 3-torus. All the cubes in the image are one cube, as light in this space loops around to form closed rings.
However, researchers have yet to consider variations of the 3-torus, such as a 3-torus where one face is twisted corresponding to another face. In this structure, if one leaves the upper face, they would move straight to the lower face and would be rotated at a certain angle.
In the new study, scientists proposed a total of 17 possible shapes of the universe. Most of these unusual topological shapes have not been ruled out in previous scientific reports. The study presents identifying signs in case the universe takes on one of the 17 proposed shapes. Future analyses may help scientists find evidence of these strange topological structures, thus determining the shape of the universe.
The search for the shape of the universe will require significant computational power, and may even need machine learning technology to speed up calculations. According to theoretical physicist Starkman, the lead author of the new scientific report, we have compelling reasons to endeavor to find the unusual topological shape of the universe.
Previously, some studies of the cosmic microwave background indicated that the universe is not homogeneous in all directions. An unusual topological universe, like the aforementioned 3-torus variant, could explain this. Starkman also stated that the asymmetry of the universe is “one of the latest mysteries of the universe that has yet to be resolved.”
