As to the expansion or inflation of the early universe, Alan Guth, a theoretical physicist and cosmologist, was the first to clearly develop a model of the inflationary universe at an earlly stage around ten to the minus 34 seconds or so, the size of the universe inflated many billions of times it's intial, nearly infinitely small size.
However, if we considered the universe a crystal lattice and you were at one of the host sites or intersects, you would see everybody moving away from you at "many orders of magnitude" greater than the speed of light. But no one would feel the slightest acceleration since it wasn't mass that was expanding, it was the space that was growing so rapidly.
In this inflationary time gravity was effectively "repulsive". This kind of expansion was necessary to overcome the speed of light limitation for the calibrating of pariticles separted by large distances in order to maintain a perfect state of equilibrium while the universe achieved the minimum size to ensure continued inflation
If the unverse weren't perfectly uniform for some critical, but finite time the expansion would have failed and the universe would collapsed back on itself.
As it was, the estimation o many cosmologists is that at least 10 additional dimensions existed at that critical moment of inflation butdid fold back on themselves and only the four (width, length, height and time) formed...