Apparent Accelerated Expansion of the Three-Dimensional Spherical Universe Observed during Its Contraction Phase

In recent years, it has been thought that the expansion of the universe has begun to accelerate. However, there are other views against this. Here we propose a new theory based on the three-dimensional spherical (S3) universe wherein the same observations as the present universe can also be found by the accelerated contraction of the universe. According to our theory, the expansion velocity of the S3 universe slowed down after the Big Bang, and all the kinetic energy was converted into potential energy to reach the great sphere. After that, accelerated contraction begins, and the universe finally converges to an original single point. In the S3 universe, the passage of time (referred to as “proper time”) changes depending on its expansion velocity. The frequency of light emitted from celestial bodies is determined by their proper time on emission, and when the light is observed by observers having different proper time, a redshift or blueshift is observed. Observers in the expansion phase observe redshifts, because the proper time of the observer progresses faster than that of emitted light, but observers in the contraction phase observe an accelerated delay of the proper time, so the progress of the proper time is reversed based upon its order from nearby celestial bodies, a blueshift is observed, and its range of observable distance increases. The results of this early contraction phase are consistent with the observations of the current universe. In conclusion, the S3 universe may be able to explain the geometrical structure of the current universe.