Transcript: One of the very difficult things to explain in standard cosmology is the flatness of space. Remember that the early universe was small and dense, and space-time was actually curved and knotted in the quantum era so the current flatness of space is an unusual condition. In standard cosmologies with no vacuum energy, flat space corresponds to a critical energy density, and in the expansion dynamics of the universe it’s an equal amount of energy in kinetic energy of the expansion and in the potential energy of all the gravity in the universe. The best analogy for this strange situation is to imagine throwing something up into the air. If you give it some particular random speed it’s likely to fall back down to your feet, but if you give it the very special velocity of the escape velocity, the object will just leave the gravity of the Earth. If you give it much larger than the escape velocity, the object will sail off into space and travel forever. The universe itself is poised between re-collapse and endless expansion. The flat space condition is a very particular condition corresponding to equal amounts of potential and kinetic energy. It’s as if the odds of throwing something up into the air and having it at exactly the escape velocity were very small. The fine tuning of the universe is the closeness of the space-time shape to being flat. The fact that space-time is this close to being flat now means that the initial parameters of the big bang expansion must have been very finely tuned early in the universe.