# Three-choice problem, the latest research suggests that the universe is a “ball”

A flat sphere with a huge disk, like a super-sized iron cake – a portrait of the Galaxy on which we live. So, what is the shape of the universe? Numerous scientists have speculated about it, and there is no definitive answer to this question. After years of observation and deduction, these assumptions converge on a mainstream view that the universe is an endlessly flat three-dimensional space.

Recently, researchers at the University of Manchester, Eleonora Valentino and others analyzed the Planck satellite’s observational data and suggested that the universe may not be as flat as sheets, but rather a closed three-dimensional sphere that bends like a giant balloon. The study was published in the journal Nature Astronomy.

Two ways of thinking about exploring the mystery of the shape of the universe

Newtonian cosmology based on Newtonian gravity holds that the universe is an infinite three-dimensional European geometric space, that is, the universe is distributed in what we often call three-dimensional geometric space, which is infinite, in which an infinite number of celestial bodies are evenly distributed. However, this assumption does not fully fit with the theory of gravity, but rather some contradictions.

“Later, when people realized the concept of curved space, there was the possibility that the universe was a three-dimensional sphere. Chen Xuelei, a researcher at the National Observatory of the Chinese Academy of Sciences, told Science and Technology Daily that Einstein had constructed a finite static model of the universe, which he believed could be a limited enclosed three-dimensional sphere.

According to general relativity, the existence of matter bends space-time. Near a massive celestial body, light does not “go” in a straight line, but rather “goes” curve. Later, as the understanding of the universe deepened, it was discovered that there were in fact many possibilities for the true shape of the universe.

“The most common are three possibilities, namely straight 3D Euclidean geometry, curved enclosed 3D spheres, and curved 3D bisurfaces. Chen Xuelei said that the curvature of the universe is zero, positive and negative, the universe presents three different forms.

Of these three possible cosmic shapes, only enclosed three-dimensional spheres are limited space. The 3D bisurface is like the shape of a saddle, with an infinite extension along the lower sides of the saddle. The flat three-dimensional Euclidean space is even more endless.

So, which of these three possibilities is the true shape of the universe? In what way do we measure the shape of the universe?

“There are two main ideas, one is to measure by geometric method, and the other is to use density to define. Chen Xuelei introduced.

It is well known that in eunometric geometry in straight space, the sum of the inner corners of any triangle is 180. But if you’re on a spherical surface or on a surface with a positive curvature, the inner angle adds up to more than 180. On a double-surface or a surface with a negative curvature, the inner corners of the triangle add up to less than 180. The principle of the geometric measurement method is that the observer is used as a vertex and then two points are selected in space to form a triangle. If we can measure the edge length of the three edges, we can determine this unique triangle in Euclidean geometry, and the size of its top corner can be calculated. On the other hand, we can also directly observe the size of the top angle we are in, and we can determine whether it is consistent, larger or smaller than the calculated value.

If the observations and calculated values (real values) at this top angle are equal, the universe is a straight three-dimensional Euclidean space, if the observation is greater than the calculated value, the universe is spherical, or the universe is spherical, and if the observation is less than the calculated value, the universe is a double surface of negative curvature.

Another idea depends on the relationship between the overall density and critical density of the expanding universe. The critical density depends on the speed of expansion, and the higher the expansion rate at a given time, the higher the critical density.

According to general relativity, when the overall density of the universe (i.e. the average density) is equal to the critical density, the shape of the universe is infinite, flat three-dimensional Euclidean space; The universe is represented by hyperbolic geometry.

Microwave background radiation sets off cosmic mystery

However, if we follow the geometric measurement sours, on the cosmic scale, we cannot fly far enough to field exploration, because if only measured in the Milky Way or even around the Milky Way, we would get only a partial curvature, not the true curvature of the universe as a whole. It’s like there are mountains and basins on Earth, high and low, but the earth as a whole is still a sphere.

It would be difficult to practice it if we were to study the cosmic density. The reason is that while we have calculated the critical density values associated with the Hubble constant, the overall density of the universe is difficult to measure. There is vast space between galaxies, and the density of space within and between galaxies is very different. What’s more, there are still unobserved, so-called dark matter in the universe, which may be much larger than the current visible matter, which creates great uncertainty for the determination of the overall density.

Cosmic microwave background radiation provides a great boost to the estimation of the average density of the universe. In the millimeter-band balloon observation program in the late 1990s, the ratio of the overall density of the universe to the critical density was measured close to 1 through data collection on cosmic microwave background radiation. “The experiment is error-prone, so based on this, it is believed that the universe has no significant positive or negative curvature, almost flat, smooth spatial structure. Chen Xuelei said this also coincides with the flat universe predicted by the theory of cosmic bulging.

In 2018, the European Space Agency ‘s Planck Survey Program released more accurate observations. “After removing as much of the relevant experimental error as possible, the European Space Agency data suggest that the curvature of the universe may be positive, i.e. the shape of the universe is closed, although this ‘tendency’ is not obvious. Chen Xuelei said.

In this study, Valentino et al. obtained the data base of the “gravitational lensing” degree of cosmic microwave background radiation through Planck satellite observations, and analyzed a large amount of data, using different models to fit the data, the probability of the universe being a closed sphere is about 99%.

The results are more reliable but the debate is far from settled.

Are the results of this study reliable? Has the debate over the shape of the universe settled on this?

“The statistical studies used in this study are not invulnerable, and there are some errors. But if that is the case, it is bound to overturn many traditional perceptions. Chen Xuelei told Science and Technology Daily that researchers may underestimate the statistical error, so the true probability may not be as high as 99%.

“It is worth noting that all parameter deductions are based on a certain model, for example, by time and speed, the distance can be calculated. The relationship between distance, time and speed is a simple model. In this study, we are not sure whether the model itself contains all the physical effects, which is worth further study. Chen Xuelei points out that, for example, not taking into account certain effects, or some unknown effects, can affect our judgment of the true shape of the universe.

“I don’t want to say I believe in a closed universe, ” the researchers said. In his view, the results only show a difference from previous studies, and why this difference exists, the reasons for it should be carefully explored.

Previous studies have pointed out that the shape of the universe is not a flat three-dimensional Eustlidean space. Why is this study of concern to the academic community?

“Previous studies have often judged the shape of the universe based on the thermal spots of cosmic microwave background radiation. Chen Xuelei told reporters that the temperature of cosmic microwave background radiation is uneven. Early in the universe there was sonic oscillations, with the largest heat spots produced by the first oscillation. Previous studies have been equivalent to simply drawing a triangle on the basis of the largest heat spot to measure the curvature of the universe. In fact, if you change some of these parameters, even different models may fit the same curve, so the accuracy is relatively low and the credibility is low.

“The study is equivalent to not only using the triangle of the largest hot spot, but also analyzing the triangles produced by other oscillations, and the result of the universe being closed to the sphere is relatively more credible.” Chen Xuelei said, “The article also mentions that observations other than cosmic microwave background radiation, such as supernovae, are not ideal, indicating that there are some things we have not considered and need further exploration.” “