The Shape of the Universe Isn't What You Think: From Ancient Round Sky to Modern Three-Dimensional Donut

What is the shape of the universe? This is an ancient yet novel question, relevant to our knowledge and understanding of the universe and our place and importance in it.

Ever since humans began to think about their own existence and the environment around them, they have been curious and exploring the shape of the universe. Different civilizations and eras have come up with different answers. In ancient times, people generally believed that the universe was a binary structure consisting of heaven and earth. The sky was a round dome and the earth was a square pedestal. Between them were a number of pillars or peaks for support. These models of the universe can only be considered as human imagination in the mythical era and cannot withstand close scrutiny.

In ancient times, people believed that the sky was a round dome and the Earth was a square pedestal. (Illustration).

With the advancement of science and technology and ever-deepening exploration, we have more clues and evidence about the shape of the universe, but we also have more questions and confusion.

According to Einstein's general theory of relativity, the shape of the universe depends on its density and curvature , and it can be flat, open, or closed. Recent observational data suggest that the density of the universe is very close to the critical density, meaning that the shape of the universe is very close to flat. However, this does not rule out the possibility that the shape of the universe could be different, such as a multi-connected flat space, like a three-dimensional doughnut.

This means that if we keep flying in one direction, we will eventually return to where we started, like on a giant tire. If the universe really is a doughnut, what strange sight would we see?

According to the general theory of relativity, the shape of the universe depends on its density and curvature. (Illustration).

What is the shape of the universe? First we need to understand a concept, which is the flatness of the universe.

The flatness of the universe refers to the geometric properties of the universe, that is, whether the space in the universe is Euclidean space, that is, the flat space we are familiar with.

In Euclidean space , parallel lines never intersect, and the sum of the interior angles of a triangle is 180 degrees. If the universe is flat, it is Euclidean space. If the universe is not flat, it is a non-planar space—a curved space. In a curved space, parallel lines can intersect, and the sum of the interior angles of a triangle can be greater or less than 180 degrees.

So how do we know if the universe is flat? There is a simple way to observe light in space. Light is an electromagnetic wave that travels at a constant speed in a vacuum and always follows the shortest path, a geodesic.

1. If the universe were flat , geodesics would be straight lines and light would always travel in straight lines without bending.
2. If the universe were not flat , then the geodesic would have curves and light would be bent into a space curve. So by observing the bending of light, we can determine the flatness of the universe.

Albert Einstein.

So what kind of light do we use to observe? The best option is the cosmic microwave background, the oldest light left over from the Big Bang. This light permeates almost the entire universe, and is an indicator of the thermodynamic temperature of the universe and a witness to its structure and evolution.

Through precise measurements of the cosmic microwave background radiation, we can obtain some important parameters of the universe, such as the age of the universe, the density of the universe, the composition of the universe, and the flatness of the universe.

According to data scanned by the European Space Agency's Planck satellite in 2018, the universe is generally flat but still has slight tilts and ripples. Generally speaking, within the universe that humans can access, parallel lines still exist. If they do not intersect, the sum of the interior angles of triangles can still be 180 degrees.

This means that the geometry of the universe could be an infinitely extended plane , that is, Euclidean space. But this is not the only possibility, because there is also a special curved space that appears locally flat but is globally closed. A topological space is a space obtained by twisting and gluing space, the properties of which depend not on the size and shape of the space but on the connectivity and number of holes in the space. There are many types of topological spaces, one of which is the familiar doughnut or tire . A doughnut is a hole-filled space that can be obtained by twisting and gluing a flat surface.

There are many types of topological spaces, one of which is the familiar doughnut or tire. (Illustration).

Specifically, glue two opposite faces of a plane to get a cylinder, then glue two circular faces of the cylinder to get a doughnut. In this way, an infinite plane becomes a finite doughnut, but at any point on the doughnut. Therefore, the doughnut is a locally flat but globally closed space.

So is the universe a doughnut? There is no definitive answer to this question, but there are some clues and evidence. The most direct clue is the light from the beginning of the universe, the cosmic microwave background radiation. If the universe were a doughnut, then the light in the universe would be constantly orbiting the doughnut, forming many overlapping images. These images are like fingerprints of the universe, and they can be found in a temperature chart of the cosmic microwave background radiation.

Specifically, look for certain patterns on the temperature distribution map, such as rings, dots, or other symmetries. These patterns are topological features of the universe and they reflect its shape and size.

The observable universe that we can see is just a small piece of the donut. (Illustration).

According to the analysis of some scientists, there are indeed some possible topological features in the temperature distribution map of the cosmic microwave background radiation . For example, there is a method called "ring statistics ", which is to find some similar rings on the temperature distribution map, their radius and temperature are the same, but their positions are different.

Using this method, some estimate the radius of the universe to be around 300-400 billion light years. The observable universe that we can see is only a small part of the doughnut, the rest is limited by the speed of light and belongs to the 'cosmic fog' that astronomers cannot see.

Of course, this estimate is uncertain and contains many errors. Because the temperature distribution map of the cosmic microwave background is not perfect, it is also affected by noise and interference from many factors. For example, dust, galaxies, galaxy clusters and other matter in the universe will have some additional effects on the cosmic microwave background, these effects will make the temperature distribution map of the cosmic microwave background blurry and complicated, thereby obscuring the topology of the universe.

There is still no definitive answer to the question: "Is the universe a doughnut?" (Illustration).

Therefore, more data and analysis are needed to find the doughnut shape of the universe from the temperature distribution map of the cosmic microwave background radiation. So what does the doughnut shape of the universe mean for us?

First , it means that the universe is a limited space, it does not expand infinitely. This brings a limit to the exploration of the universe, we can never see the whole universe and can never know the truth of the universe.

Secondly , it means that the universe is a cyclical space, it is not a one-time event. This creates a cycle of evolution of the universe, the universe can continuously switch between expansion and contraction or it can switch between different donuts. Finally, it means that the universe is a diverse space, it is not unique. This brings up the possibility of the existence of the universe, the universe may not be isolated but connected to other universes to form a multiverse.