Since the Big Bang took place a finite time ago, the Universe would have had to expand at an infinite rate to reach an infinite size. Unless it was already infinite at the time of the Big Bang.
The rubber-sheet model of gravity pictures gravity as the effect of hollows in space-time due to the mass of an object. If the model included bumps in space-time as well, the effect would be to channel all the mass into the valleys between the bumps forming a network of matter across the sheet...