We present a Quantum Space Model (QSM) of cosmic evolution based on the theory that space consists of energy quanta from which our universe came about. We used the Friedmann equations to trace its history and predict its ultimate fate. Results provide further support to our recent proposal that the accelerating expansion of the universe is due to a scalar space field which has become known as Dark Energy. In our model, the universe started from high energy space quanta which were triggered by quantum fluctuations that caused the Big Bang. It then expanded and cooled undergoing phase transitions to radiation, fundamental particles, and matter. Matter agglomerated and grew into stars, galaxies, etc. and was eventually consolidated by gravity into Black Holes, which finally ended in a Big Crunch in a state of deep freeze inside the Black hole at 1.380 trillion years. Fluctuations, quantum tunneling, or some other mechanisms caused a new Bang to start another cycle in its life. Our results are in good agreement with the theoretical predictions of a cyclic universe by Steinhardt and his associates, and by Penrose. Space and energy are equivalent as embodied in the Planck energy equation. They give rise to the two principal long range forces in the universe: the gravitational force and the space force. The latter may be the fifth force in the universe. The two forces could provide the clockwork mechanism operating our cyclic universe. If the Law of Conservation of Energy is universal, then the cosmos is eternal.