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The Universe is globally hyperbolic as we did prove mathematically. The false flat universe paradigm needs mysterious ingredients: dark energy, dark matter and inflation to bridge the gap between theory and observations. In testing the validity of any scientific paradigm, the key criterion is whether measurements agree with what is expected given the paradigm. We modify the laws of gravity through the new hyperbolic spacetime paradigm. Such a modification explains the accelerating expansion of the Universe without need for dark energy and inflation. and also explains the flat rotation curve without need for dark matter. The hyperbolic time evolution equation of the universe fits the observed data and successfully predicts the Planck length at micro-cosmos scale as well as it predicts the current observed large structure at macro-cosmos scale, thus connecting both General elativity and Quantum Theory. We did prove mathematically that the Big Bang point and the center of the Black hole are nonsingular. The Information Loss Paradox does no longer exist in the nonsingular hyperbolic spacetime.