Can the universe be both infinite AND expanding

[Silvers931]

I was researching the inflationary model of the universe and came across the idea that the universe may be both infinite and expanding; and that there isn't a contradiction. As time goes by, the amount of matter in any given area will become less dense due to the metric expansion of space itself. If It was infinite a billion years ago, it is still infinite now, but our finite neighborhood takes up more space in that infinite universe.

This would explain why ALL measurements yield a universe with flat curvature; because since the universe has an infinite volume any arbitrary measurement will yield a 0 curvature. My question is this; Can the topology of the universe be infinite in size, flat locally, and have a curvature globally such that the "infinite" universe is simply stretching and not necessary growing in total size.

 

[bapowell]

This would explain why ALL measurements yield a universe with flat curvature; because since the universe has an infinite volume any arbitrary measurement will yield a 0 curvature.

Why? There are infinite negatively curved spaces.

My question is this; Can the topology of the universe be infinite in size, flat locally, and have a curvature globally such that the "infinite" universe is simply stretching and not necessary growing in total size.

If the universe is infinite, then it is not growing in size.

 

[marcus]

... My question is this; Can ... the universe be infinite in size, flat locally, and ...such that the "infinite" universe is simply stretching and not necessary growing in total size.

I think the short answer to that question is YES. For the reason that Brian Powell gave:

...If the universe is infinite, then it is not growing in size.

If I understand the core of your question, you put it concisely in the title: Can the universe be both infinite AND expanding?

It certainly can be! as far as we know. There is no clear evidence that it is finite. So we have to allow that it might be infinite. And it certainly is expanding!

By expanding I simply mean what you called "stretching", percentage growth of distances between widely separated objects.
If the U is spatially infinite then space doesn't have any definite size, so we can't talk about the size of the universe increasing. But distances between objects can be growing at a regular percentage rate (as long as the objects are not part of the same cluster held together by its own gravity, they have to be separated enough to participate in the pattern of distance expansion).

What would be evidence of spatial finiteness? Some pattern in the deep sky which repeats? Some pattern that is the same coming from two opposing directions? A very accurate measurement of angles showing that with a big enough triangle they add up to more than 180 degrees? (Like on the surface of the Earth large geodesic triangles can add up to more. E.g. a segment of the equator for base, and vertex at the north pole.) Someday humanity may discover evidence of spatial finiteness, but for now we have to accept the possibility that expanding space might be infinite in volume and have no definite size.