Cosmological observations before 1998, including visible matter and invisible dark matter inferred from galaxy dynamics, have a total density of about 1/3, which prevents the expansion of space. In this way, the possibility of an infinitely expanded open space is still presented to people.

It is conceivable that many people tried to extend Hawking's quantum theory of the closed universe to the open situation, but it never succeeded. From 65438 to 0998, Hawking and Turuk, a theoretical cosmologist at Cambridge University, only partially realized this wish in their paper "Open Prosperity without False Vacuum". He still uses Euclidean space of four-dimensional sphere. Because the symmetry of the four-dimensional sphere is the highest, he can also get the universe with the open three-dimensional hyperboloid as the space section when he carries out analytical continuation. If this three-dimensional hyperboloid space continues to evolve according to Einstein's equation, the space of the universe will not shrink any more. This evolution is a process from beginning to end. However, this generalization is still unsatisfactory in terms of mathematical self-consistency and experimental observation; And since 1998, physicists have found that 68.5% of the energy components in the universe are cosmological constants or dark energy (the remaining 3 1.5% are ordinary visible matter and invisible cold dark matter); No matter whether the space is closed, flat or open, the space will expand infinitely and accelerate its expansion.

Until 20 12, Chen Zhongyuan, a theoretical physicist at Cambridge University, strictly proved Hawking's borderless conjecture. Unexpectedly, there is no quantum state universe or quantum cosmology, and the classical unbounded condition holds. In this way, the universe has no boundaries, no creation and destruction, is completely self-sufficient, and exists only in the form of a finite four-dimensional sphere. It can be seen that the origin of the universe is indeed that it has no origin, which really solves the first driving problem in physics. Moreover, Chen also found that the finite four-dimensional spherical universe is equivalent to the infinite four-dimensional spherical universe: the whole universe itself is only a four-dimensional sphere with a very small radius of curvature, but in its local reference system, such as everything in the universe, it is an infinite four-dimensional sphere, consisting of all the spaces and things before the Big Bang, past, present, future and infinite time.

At this point, the theoretical physics of the universe can be described completely and consistently, that is, the framework of the borderless cosmology building is basically completed, which is not only mathematically impeccable, but also completely consistent with all solid-state experimental observations. In this system, the quantum field theory of curved spacetime and the cold dark matter model of cosmological constant are no longer approximate effective theories, but strictly established.