I was reading The Hidden Reality by Brian Greene and came across his description of the "quilted universe." In it he states that if the universe is infinite with a homogenous mixture of matter, then there must mathematically be a place for every conceivable configuration of matter as there are only so many possible combinations and infinity would allow for all of them. Further, there would be an infinite number of these configurations infinitely repeating. My problem is that this would require infinite matter, and infinite matter would mean infinite mass and wouldn't the universe collapse back in on itself if that were the case?
If we assume the cosmological principle where we have the same average density everywhere an infinite universe would of course contain an infinite amount of matter. But since the infinite matter is distributed over an infinite volume instead of one point there is no need for a collapse since the gravitational force of each particle still falls of with the distance squared. Also there would be no prefered direction or center onto which the matter could collapse.
For the calculations see Alan Guth's lecture on the subject: Can a uniform infinite distribution of mass be stable?