# Does an infinite universe imply infinite mass?

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?

• I'm guessing you're thinking about the Big Bang as if it happened at a point but it didn't happen at a point. – John Rennie Dec 6 '16 at 17:09
• Possible duplicate of Total energy of the Universe – user4552 Dec 7 '16 at 5:57
• @BenCrowell I think it has more common with JohnRennie's link. In my opinion, if the question could be a dupe of multiple, signifantly different questions, then it is not really a dupe. – peterh Dec 7 '16 at 6:35

## 1 Answer

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?

• Good answer. I'd just add that our observations have shown a uniform (at cosmological scales) distribution of matter, not a principle but a generalization of observations. When talking about size of the universe it's also worth pointing out that if the universe is open or flat it would be infinite if it has a trivial topology, but otherwise it could be bounded and finite – Bob Bee Dec 7 '16 at 6:06
• For the benefit of whatever persons reading this good answer might be confused by our inability (so far) to arrive at a theory of quantum gravity, I'd like to point out the fact that, in a cosmological context, "particle" can mean such large objects as planets, stars, etc. – Edouard Jan 30 at 10:42