Proposal of a Model of a Three-Dimensional Spherical Universe

Abstract

Despite the existence of several exact solutions to the general theory of relativity, it is still difficult to explain the entire structure of the universe. In this paper, we propose a novel three-dimensional spherical (S3) universe model. According to this model, the universe had a powerful gravity source at its origin, and a part of the gravitational source formed a bubble of spacetime in which the universe was born. The universe expanded explosively immediately after the Big Bang. The energy obtained from the gravity source at the birth of the universe is constant, that is, it remains constant from the birth of the universe to the end. The expansion and contraction of the universe is determined by the passage of coordinate time. The S3 universe observed from outside can be considered to be a two-dimensional spherical surface by projecting it onto a three-dimensional space. On the other hand, the visible universe viewed from inside is observed as a three-dimensional sphere with an arbitrary observation point. The origin of the S3 universe can be seen to be evenly spread in the outer shell of the visible universe. We define visible longitude as the difference between an observation point and its farthest light source. At an initial phase of the expansion of the universe, few stars can be seen, because the visible longitude is small. However, when the expansion of the universe progresses, the number of visible stars also increases, since visible longitude increases. In our S3 universe model, the redshifts observed and reported so far in literature appear to indicate that the expansion of the universe is accelerating. Our S3 universe model can thus lead to a novel exact solution to general relativity.