(untitled) (European Journal of Formal Sciences and Engineering, 2017)
The main pillar of the Big Bang paradigm is the expansion of the Universe predicted by the cosmological redshift. Singularity is inevitable in the Big Bang model. The Universe is hyperbolic as we did prove mathematically; where the cosmological redshift is no longer a distance indicator. After all, in the hyperbolic spacetime a group of objects would grow apart even when not moving as their worldlines would be divergent. We show the manifold of the hyperbolic Universe is complete with no singular points. While the distance horizon in the Big Bang flat spacetime is finite, the distance horizon is infinite in the hyperbolic universe. The pillars of the big Bang and its consequences had been refuted and disproved or reinterpreted.