I Why do we still see the CMB today?

[Pyter]

The universe is either infinite in extent or a closed spherical geometry

By "universe" do you mean the energy/matter present in the universe, or the empty space?
I thought that there was also a model contemplating a finite amount of matter expanding in a flat, infinite 3D Euclidean space.

 

[Ibix]

By "universe" do you mean the energy/matter present in the universe, or the empty space?

The universe is filled with matter everywhere, so I don't understand the distinction you're trying to make.

I thought that there was also a model contemplating a finite amount of matter expanding in a flat, infinite 3D Euclidean space.

No. The flat and negative curvature space models are both infinite in extent and filled with matter everywhere.

 

[Pyter]

The flat space model is infinite in extent and filled with matter everywhere.

In that model, that for me is easier to visualize than the others, what is it that "expands" after the BB?

 

[Ibix]

In that model, that for me is easier to visualize than the others, what is it that "expands" after the BB?

Everything. Pick any pair of particles. Measure the distance between them. Wait a while then measure it again and the distance will have increased.

In an ideal model, this works for literally any pair of particles. In the real universe most things have a bit of random motion and local interaction on top of that, and that can make them move together or orbit or whatever, so you only see the pure systematic expansion when you measure distances between galaxies that are separated enough that they are not gravitationally bound to each other.

 

[PeterDonis]

did the outer layers cool first, then the inner ones, up to the the core?

By "universe" do you mean the energy/matter present in the universe, or the empty space?

Remember that the matter in the universe at the time of the CMB formation was very, very different from what it is today. It was not stars and galaxies separated by empty space. It was plasma which turned into ordinary gas as atoms formed from electrons and ions at recombination: that was what formed the CMB. The plasma/gas was uniform to about one part in 100,000 (i.e., the density only varied on that very small scale) at that time. How do we know? Because that's the degree to which the CMB itself is uniform. So there were no "outer layers", "inner layers", or "core", and there was no empty space. It was all uniform plasma/gas everywhere.

 

[Hornbein]

This is one of those cases where "seems" isn't good enough. We need to actually look at the math. If you look at the Penrose diagram of de Sitter spacetime, as shown, for example, in Fig. 2 of this paper, you will see that the best a photon can do during the infinite history of the universe from $I^-$ to $I^+$ is to just make it from the "North Pole" to the "South Pole" (i.e., halfway around the 3-sphere of the universe).

The link to this paper fails on my smart phone.

 

[Ibix]

The link to this paper fails on my smart phone.

Works for me. Try a different device?

 

[Ibix]

If you only want to see the picture Peter references it's a square with dotted lines across the diagonals. The top and bottom edges are labelled $\mathcal{I}^+$ and $\mathcal{I}^-$ respectively, and the sides are labelled north and south pole.

I note that it's one of the most stunningly dull diagrams I have ever seen, considering the subject matter.

 

[Pyter]

Everything. Pick any pair of particles. Measure the distance between them. Wait a while then measure it again and the distance will have increased.

In an ideal model, this works for literally any pair of particles. In the real universe most things have a bit of random motion and local interaction on top of that, and that can make them move together or orbit or whatever, so you only see the pure systematic expansion when you measure distances between galaxies that are separated enough that they are not gravitationally bound to each other.

So right after the BB, let's say one Planck time interval after, there already was infinite matter spanning infinite 3D Euclidean space (assuming the flat space model holds)?

 

[Ibix]

So right after the BB, let's say one Planck time interval after, there already was infinite matter spanning infinite 3D Euclidean space (assuming the flat space model holds)?

If the universe is infinite in extent now then it always was, yes. Something finite cannot grow into something infinite in finite time.

 

[Pyter]

If the universe is infinite in extent now then it always was, yes. Something finite cannot grow into something infinite in finite time.

In that case the accepted CMB explanation starts to make sense to me.

But this "infinite matter" model is at odd with other cosmology notions I've gleaned, namely the enigma of the prevalence of matter over antimatter.
As you surely know, it is argued that at the beginning they should've been present in equal quantity and thus annihilate each another, except that for some unknown reason the matter was slightly more than the antimatter, and our current universe is made of the matter that survived the annihilation.

I've always thought that these considerations implied that the matter in our universe was finite from the beginning. Unless the initial matter was a "double infinite", the antimatter a "single infinite", and thus the difference stays infinite, or something to that effect.

 

[Ibix]

I've always thought that these considerations implied that the matter in our universe was finite from the beginning. Unless the initial matter was a "double infinite", the antimatter a "single infinite", and thus the difference stays infinite, or something to that effect.

The best way to describe it is "different densities".

 

[PeterDonis]

this "infinite matter" model is at odd with other cosmology notions I've gleaned, namely the enigma of the prevalence of matter over antimatter.

No, it isn't. "Infinite matter" as you use the term here actually means "a spatially infinite universe with uniform average density of stress-energy everywhere". It does not require the stress-energy to have any particular form. It could all be radiation. It could all be matter. It could all be antimatter. It could be any mixture of any of those things. It could include dark energy. There is no contradiction in any of this.

it is argued that at the beginning they should've been present in equal quantity and thus annihilate each another, except that for some unknown reason the matter was slightly more than the antimatter, and our current universe is made of the matter that survived the annihilation.

I've always thought that these considerations implied that the matter in our universe was finite from the beginning.

Then you thought wrong. They imply no such thing.

Unless the initial matter was a "double infinite", the antimatter a "single infinite", and thus the difference stays infinite, or something to that effect.

This is word salad.

 

[Hornbein]

I've always thought that these considerations implied that the matter in our universe was finite from the beginning. Unless the initial matter was a "double infinite", the antimatter a "single infinite", and thus the difference stays infinite, or something to that effect.

We are taught in mathematics it makes no sense to subtract one infinity from another. But the infinite ton gorilla does as it pleases.

 

[Hornbein]

If the universe is infinite in extent now then it always was, yes. Something finite cannot grow into something infinite in finite time.

Actually it can if it grows infinitely quickly. But this is even harder to imagine actually happening.

The trick is double in size in y time, then again in y/2 time, again in y/4 time, y/8, and so forth.

 

[PeterDonis]

We are taught in mathematics it makes no sense to subtract one infinity from another

No such subtraction has to take place anywhere in the actual mathematical account of matter-antimatter annihilation in the early universe.

 

[Hornbein]

No such subtraction has to take place anywhere in the actual mathematical account of matter-antimatter annihilation in the early universe.

Correct.

 

[Pyter]

We are taught in mathematics it makes no sense to subtract one infinity from another. But the infinite ton gorilla does as it pleases.

In maths this is legal: $2\delta(x) - \delta(x) = \delta(x)$ . Perhaps also in physics, in branches other than cosmology apparently.

So there's currently no cosmological model based on finite matter/energy, at least no one able to explain the CMB convincingly?

 

[Ibix]

So there's currently no cosmological model based on finite matter/energy, at least no one able to explain the CMB convincingly?

A closed universe is boundaryless but finite.

 

[Pyter]

A closed universe is boundaryless but finite.

With that model, has it been said in the previous posts that the observed CMB should stop at one time, since there's no infinite matter from which it might come from?

 

[Jaime Rudas]

With that model, has it been said in the previous posts that the observed CMB should stop at one time, since there's no infinite matter from which it might come from?

In which posts is this said?

 

[Jaime Rudas]

So there's currently no cosmological model based on finite matter/energy, at least no one able to explain the CMB convincingly?

The cosmological model most accepted by the scientific community today is the ΛCDM model, which explains the CMB in a finite universe quite convincingly.

 

[Ibix]

With that model, has it been said in the previous posts that the observed CMB should stop at one time, since there's no infinite matter from which it might come from?

No. In a naive matter-dominated closed universe model the universe ends before light can circumnavigate it. In a dark-energy dominated model, which lives longer, you start to receive photons that have circumnavigated the universe once, then twice, and so on. There is a finite energy in the CMB in this case, though, so it's possible to imagine it all being absorbed, but it would take a very, very, very long time.

 

[Ibix]

In which posts is this said?

#4. Wrongly, as pointed out by you and Peter. I had forgotten we were in that thread...

 

[Jaime Rudas]

In a dark-energy dominated model, which lives longer, you start to receive photons that have circumnavigated the universe once, then twice, and so on.

In fact, in a realistic dark-energy dominated model, photons can't circumnavigate the universe.

 

[PeterDonis]

there's currently no cosmological model based on finite matter/energy, at least no one able to explain the CMB convincingly?

Yes, there is, a spatially closed, spatially finite universe. This is one of the basic FRW models.

With that model, has it been said in the previous posts that the observed CMB should stop at one time, since there's no infinite matter from which it might come from?

This is wrong. The CMB does not require "infinite matter" (i.e., infinite spatial extent) in order to continue traveling around the universe. @Ibix explained why in post #83.

There is a finite energy in the CMB in this case, though, so it's possible to imagine it all being absorbed

No, it isn't, because it would just be re-emitted again, since whatever absorbed it would then be at a slightly higher temperature than the CMB.

 

[PeterDonis]

in a realistic dark-energy dominated model, photons can't circumnavigate the universe.

What is your basis for this statement?

 

[Jaime Rudas]

What is your basis for this statement?

As I hinted in post #17, in a realistic dark-energy dominated model there is a cosmological event horizon that is smaller than the particle horizon (i.e., the boundary of the observable universe) which, in turn, is smaller than the entire universe.

 

[PeterDonis]

As I hinted in post #17, in a realistic dark-energy dominated model there is a cosmological event horizon that is smaller than the particle horizon (i.e., the boundary of the observable universe) which, in turn, is smaller than the entire universe.

This is not a sufficient basis for the claim you are making now. It is true that there exist dark energy dominated models with the property you describe. But that does not support the claim you are making, that all "realistic" dark energy dominated models have the property you describe.

 

[Jaime Rudas]

This is not a sufficient basis for the claim you are making now. It is true that there exist dark energy dominated models with the property you describe. But that does not support the claim you are making, that all "realistic" dark energy dominated models have the property you describe.

What I assume by "realistic" are those models that can reasonably well describe the observations we make of the real universe.

On the other hand, I notice that you changed your mind from what you stated in post #18