B How can the Observable Universe be a closed system?

[Cerenkov]

Thank you Bandersnatch and Halc.

I get it now.

There's just one last item that I'd like some help with please.

Both of you and PeterDonis have been at pains to emphasize that the diagrams employ non-accelerating expansion.

But in 1998 those two supernova teams discovered that the universe's expansion is accelerating.

How would this change things?

Thanks again,

Cerenkov.

 

[PeterDonis]

Both of you and PeterDonis have been at pains to emphasize that the diagrams employ non-accelerating expansion.

Where did we say that? It's not correct. The diagrams @Halc posted are for our actual universe, in which, as you note, the expansion is accelerating (more precisely, it has been accelerating since a few billion years ago).

 

[PeterDonis]

This is a counter-intuitive result of regular expansion. Visit Wikipedia page on 'ant on a rubber rope'. It aims to explain how in (non-accelerating) expanding space the recession velocity is not a barrier to signals, no matter how much it exceeds the signal speed.

Unfortunately, the "ant on a rubber rope" analogy is useless in our actual universe, in which the expansion is accelerating (or, more precisely, has been since a few billion years ago).

Furthermore, that analogy is not necessary to explain why new objects are continually entering our observable universe. The latter does not just happen with non-accelerating expansion. It happens with accelerating expansion as well. The only difference with accelerating expansion is that there is an event horizon, which imposes an upper limit on how many objects will ultimately be inside our OU; but that limit is approached asymptotically, so new objects are always entering our OU, just fewer per unit proper time as we move into the future.

 

[Bandersnatch]

Unfortunately, the "ant on a rubber rope" analogy is useless in our actual universe, in which the expansion is accelerating

It's not meant to be an analogy for our universe. Nobody claimed that. If anything, it's an analogy for a Milne universe (and de Sitter, and Einstein-de Sitter, if we vary the stretching). Much like those simple models, it's a pedagogical tool for helping understand certain properties of expansion. As such, I find it far from useless.

 

[Cerenkov]

Where did we say that? It's not correct. The diagrams @Halc posted are for our actual universe, in which, as you note, the expansion is accelerating (more precisely, it has been accelerating since a few billion years ago).

I'm sorry Peter. My bad. I didn't know that the diagrams factored in accelerating expansion.

 

[Cerenkov]

Unfortunately, the "ant on a rubber rope" analogy is useless in our actual universe, in which the expansion is accelerating (or, more precisely, has been since a few billion years ago).

Furthermore, that analogy is not necessary to explain why new objects are continually entering our observable universe. The latter does not just happen with non-accelerating expansion. It happens with accelerating expansion as well. The only difference with accelerating expansion is that there is an event horizon, which imposes an upper limit on how many objects will ultimately be inside our OU; but that limit is approached asymptotically, so new objects are always entering our OU, just fewer per unit proper time as we move into the future.

Ok, so back to where we were.

I retract what I wrote 54 minutes ago, having misunderstood things.

There is no longer any confusion.

Objects can still enter the light cone of our OU as it's base widens over time.

Therefore, the OU cannot be considered a closed system.

Thank you.

Cerenkov.

 

[Bandersnatch]

the diagrams employ non-accelerating expansion.

The ant on a rubber rope exercise, where the rope is steadily stretched (as on the animation), is what shows non-accelerating expansion.
The lightcone diagrams are for the LCDM model, the best-fit description of our actual universe.

With the ant, if you imagine the end of the rope being stretched at a varying speed, it will change how the ant traverses the rope.
If you gradually slow down the stretching, it's similar to what happens in the matter-dominated expansion phase in our universe: the ant still gets however far it wants, only faster.
If you gradually speed up the stretching, it's similar to the dark energy-dominated phase: the ant still always moves further on the rope, always passing more marks (i.e. the emitted light passes by more comoving galaxies, i.e. particle horizon grows, i.e. the observable universe grows), but now there will be a distance which it can never reach (the cosmological event horizon).

 

[Cerenkov]

The ant on a rubber rope exercise, where the rope is steadily stretched (as on the animation), is what shows non-accelerating expansion.
The lightcone diagrams are for the LCDM model, the best-fit description of our actual universe.

With the ant, if you imagine the end of the rope being stretched at a varying speed, it will change how the ant traverses the rope.
If you gradually slow down the stretching, it's similar to what happens in the matter-dominated expansion phase in our universe: the ant still gets however far it wants, only faster.
If you gradually speed up the stretching, it's similar to the dark energy-dominated phase: the ant still always moves further on the rope, always passing more marks (i.e. the emitted light passes by more comoving galaxies, i.e. particle horizon grows, i.e. the observable universe grows), but now there will be a distance which it can never reach (the cosmological event horizon).

Thank Bandersnatch.

That's useful. Knowing the the light cone diagrams are configured for the LCDM model, I mean.

All the best,

Cerenkov.