I What does "expansion of the universe" mean?

[Dale]

A congruence does not describe the universe.

I disagree, it describes the universe every bit as much as the co-rotating congruence describes the disk.

In any case, when we say "the universe is expanding" we are directly referring to this congruence.

 

[Dale]

You are wrong, and I am sorry but it is pretty basic GR.

What exactly is wrong with the statement. So far all you have said is that the expansion tensor is not a tensor, which is wrong (with the minor mathematical caveat above), and then simply asserted that it is misleading without giving any explanation. If this is basic GR then there should be lots of references to show what is wrong.

 

[Dale]

Is still everybody but I fully agreeing with the statement that in general relativity the universe is expanding and that this is a coordinate independent fact?

Yes or no?

Yes! When we make the statement that the universe is expanding in GR we are directly referencing the fact that the commoving congruence is expanding. That is what this statement means.

@PeterDonis objection is a fine point about whether or not the commoving congruence describes the universe or is just a convention and @RockyMarciano objection is a fine point about whether we use the usual GR term "tensor" or the more correct mathematical term "pseudotensor". But neither of these fine points changes the answer to you which is that when scientists say "the universe is expanding" what they mean is "the trace of the expansion tensor of the commoving congruence is positive" and that statement does not depend on which observer is stating/testing it.

 

[PeterDonis]

I disagree, it describes the universe every bit as much as the co-rotating congruence describes the disk.

The disk is not spacetime; it's a family of worldlines in spacetime. The universe is spacetime. You can't describe spacetime with a congruence. You can only describe a family of worldlines in spacetime. A family of worldlines is not spacetime.

As I've already said, I agree that "the expansion of the universe" is an invariant, coordinate-independent fact when that term is defined appropriately. But that doesn't mean we can describe spacetime itself with a congruence. It only means that there is a particular congruence that matches up with a key symmetry of the spacetime of the universe, so there is a good reason to call the expansion of that congruence "the expansion of the universe" as a convention of terminology.

 

[MeJennifer]

As I've already said, I agree that "the expansion of the universe" is an invariant, coordinate-independent fact when that term is defined appropriately.

But it wasn't!

[Moderator's note: Edited to delete comment on which forum this discussion was taking place in; discussion has now been moved to Cosmology.]

 

[PeterDonis]

But it wasn't!

I have no idea what you mean. "The expansion of the universe" is standardly defined, in cosmology, to mean "the expansion of the congruence of worldlines of comoving observers".

[Moderator's note: Edited to delete comment on which forum this discussion was taking place in; discussion has now been moved to Cosmology.]

 

[Dale]

The disk is not spacetime; it's a family of worldlines in spacetime. The universe is spacetime.

Ah, I see the difference. I am thinking about the "dust" as defining the universe, and you are thinking about the spacetime. I agree that the spacetime does not single out any specific congruence, but the dust does.

 

[PeterDonis]

I agree that the spacetime does not single out any specific congruence, but the dust does.

Exactly.