When this mysterious number changes from 5.7 to 6, our conjecture about the shape of the universe changes

Schematic diagram of cosmic space shape (picture source: quantamagazine)

This overturns the mainstream view in recent years that the universe is an infinite flat three-dimensional space. This new conclusion involves a key figure that determines the shape of the universe: the critical density of the universe.

Three possibilities of space

What is the shape of the universe? Is there a boundary in the universe? For the outline of the universe, human beings had many fantasies. But after Einstein applied the cosmological principles to the study of cosmology, the shape of the universe was strictly limited. The principle of cosmology requires that every point in the universe is equal, so it is impossible for the universe to have a very strange topological structure - for example, the universe cannot grow into a bicycle tube, because the points on the outer side of the tube are obviously different from those on the inner side.

Therefore, considering the limitations of cosmological principles, then there are only three possibilities left in the shape of a single connected universe: if space has positive curvature, then it is a closed three-dimensional sphere; if the curvature of space is zero, then it is a boundless flat three-dimensional space; if space has negative curvature, then it is also boundless and is a three-dimensional saddle surface.

So, in this sense, the shape of space is determined by curvature. According to Einstein's general relativity, the curvature of the universe depends on the distribution of the matter field in the universe. Therefore, as long as the distribution of the material field in the universe is measured accurately, the shape of the universe can be inferred.

Now, Planck satellite provides a new basis for the solution of this problem. In a new paper published in Natural Astronomy, Eliona Valentino (Eleonora Di valentino), of the University of Manchester, Alessandro Melchio (Alessandro Melchiorri of the University of Sapinza, Italy, and Joseph Alessandro (Joseph Silk), of Oxford University calculate the curvature of space as positive based on the magnitude of the gravitational lens in the satellite's cosmic microwave background radiation power spectrum. In other words, space is a closed three-dimensional sphere.

Critical density is the key

So how do physicists judge the shape of space?

For space, there is a boundary that determines its shape, which is the critical density of the universe.

In theory, we can define a critical density. This critical density is related to the Hubble constant, and its physical meaning is the average density of all matter and energy in the universe, including dark matter and dark energy. At this average density, space is flat.

According to the calculation of Hubble constant, the critical density is equal to about 5.7 protons per cubic meter.

As a contrast, we know that in the solar system, only dark matter has a density of 30,000 protons per cubic meter. So the density of the solar system is much higher than the critical density of the universe. But because the material distribution in other parts of the universe, such as interstellar space, is thin, the average critical density is certainly not as high as in the solar system. It is important to note that, although the density of the substance in the solar system is high, it is certainly not a flat space in the local sense; however, in the cosmological scale, we do not have to take into account the size of the solar system, and in the cosmology, the Milky Way is a particle. The discussion of whether the space is flat is considered from the cosmological dimension.

Therefore, once the measured total density of the universe is equal to the critical density, then the universe is a flat three-dimensional Euclidean space; if the measured density is greater than or less than the critical density, then the universe will be a curved closed three-dimensional sphere or a three-dimensional saddle surface, respectively.

In the above three cases, only the closed three-dimensional sphere indicates that the universe space is limited, and in the other two cases, the whole universe space is infinite.

Planck satellite gives a new conclusion

The most important experimental method is the observation of cosmic microwave background radiation. The research on cosmic microwave background radiation has won the Nobel Prize in physics for three times in 1978, 2006 and 2019. However, this field is still in its infancy. For human beings, the study of cosmic microwave background is an important means to understand the universe.

Valentino et al.'s recent paper analyzes data from Planck satellites that observe cosmic microwave background radiation. Planck's telescopes measured the extent of the "gravitational lens" of cosmic microwave background radiation over the past 13.8 billion years to measure the average density of the universe. Specifically, they study these cosmic microwave background radiation photons. The more matter these photons encounter as they fly to Earth, the less their direction clearly reflects their starting point in the early universe. In satellite observation data, such a phenomenon presents a vague effect. According to their analysis of the data, the average density of the universe may be 5% higher than previously estimated critical density. In other words, there are an average of six protons per cubic meter in the universe, instead of 5.7.

Cosmic microwave background radiation

According to this study, space may be a closed three-dimensional sphere. Prior to this, physicists established a standard cosmological model called LAMDA-CDM based on WMAP satellite observations of cosmic microwave background radiation and the first batch of data from Planck satellite in 2013. In that model, the universe is flat. Therefore, we can say that the conclusions of the latest study are subversive.

The so-called three-dimensional sphere can also be associated with the well-known Poincare conjecture, and the Poincare conjecture is that the unbounded three-dimensional geometry in a single communication is only one, and the only possibility is a three-dimensional sphere. So if Elena Valentino's paper is right, then we can hook the Bombay's guess with the shape of the space, which has a theoretical beauty.

Of course, we must distinguish the observable universe from the whole universe. The observable universe is only a space area in the whole universe. At present, we define it as an ideal sphere with the earth as the observation center and a radius of about 46 billion light-years.

In the latest paper, the researchers discuss the shape of the whole space, and they think that more than 99% of the probability of the whole universe is a closed three-dimensional sphere.

Despite the latest results of the study, the debate about the shape of the universe has yet to settle. One important reason is that the calculation of the critical density of the universe depends on the measurement of the Hubble constant. But at present, it seems that the Hubble constant is still uncertain: Although Planck satellite gives a Hubble constant, it has obvious differences with the Hubble constant measured by other methods. Since the Hubble constant is not accurate, so the average density of the universe is not accurate, so the boundary line is fuzzy. Therefore, it is too early to say that space must be closed.

The Simmons observatory, which is currently being built in Chile, and the Ali cosmic microwave background radiation polarization detector in Tibet, China, will provide more accurate measurements. Perhaps over the next five years, we will be able to re-understand this space from the observation data of these devices.