What is meant by the size of the early observable universe?

[Grinkle]

As a reference I will make the vague statement that others have posted the below on these forums:

As one rolls back the clock, the size of the observable universe becomes smaller than it is today.

Does this mean that all of what we observe today was more densely packed yesterday than it is today? If so, I understand that.

Does this mean that we couldn't see as far away yesterday as we can today? If so, I don't understand that (and would be asking for help in understanding).

 

[Chalnoth]

It's a relative statement rather than a statement about the overall size, since the overall size is not observed.

What it means specifically is that objects in our universe that we observe today were much closer together.

 

[Bandersnatch]

Does this mean that all of what we observe today was more densely packed yesterday than it is today? If so, I understand that.

Does this mean that we couldn't see as far away yesterday as we can today? If so, I don't understand that (and would be asking for help in understanding).

Both statements are true.
Since the latter seems to be the problem - consider a hypothetical, static universe of finite age. Due to its finite age and the finite speed of light, it is trivially true that in such a universe what you see today is smaller than what you'll see tomorrow. After all, tomorrow you can see light that had one day more to travel to your eyes from whence it was emitted.
The same effect is still at work if the universe is expanding. The thing that differs is how much 'extra distance' out one can see every day, as the light has to travel through expanding space.

So what you see today is both less densely packed than yesterday, as well as spanning further out than yesterday.

 

[Grinkle]

Both statements are true.
Since the latter seems to be the problem - consider a hypothetical, static universe of finite age. Due to its finite age and the finite speed of light, it is trivially true that in such a universe what you see today is smaller than what you'll see tomorrow. After all, tomorrow you can see light that had one day more to travel to your eyes from whence it was emitted.
The same effect is still at work if the universe is expanding. The thing that differs is how much 'extra distance' out one can see every day, as the light has to travel through expanding space.

So what you see today is both less densely packed than yesterday, as well as spanning further out than yesterday.

The part about that which I find confusing is that it seems to assume a finite number of particles in the universe. If the universe is infinitely large and very dense, then for as far away as I care to imagine and for as long ago as I care to imagine (after photons start to exist at least) there will be photons emitted towards me. The only thing bounding how far away I can see is my ability to detect the photons. There should be no boundary beyond which there are no longer emitting sources existing. I can understand that the sources which I am able to detect keep moving farther away, but if I turn back the clock, other sources which are now beyond my ability to detect should come into view, and the size of what I can observe should not change, it should just be getting less dense as time moves forward and more dense as time moves backwards.

 

[Drakkith]

The part about that which I find confusing is that it seems to assume a finite number of particles in the universe. If the universe is infinitely large and very dense, then for as far away as I care to imagine and for as long ago as I care to imagine (after photons start to exist at least) there will be photons emitted towards me. The only thing bounding how far away I can see is my ability to detect the photons. There should be no boundary beyond which there are no longer emitting sources existing.

But there is a 'boundary'. Two in fact. The first has to do with the CMB. The CMB is the oldest light in the universe. It was emitted a few hundred thousand years after the big bang at the time of recombination. Prior to this, the universe was so hot and dense that the matter within it existed as a plasma that absorbed light shortly after it was emitted (by other parts of the plasma). In other words, the mean free path of each photon was very short. After recombination, the universe turned transparent to most EM radiation. The CMB is the final burst of thermal radiation from the hot plasma and was now capable of traveling essentially an infinite distance (specifically, I think this means that the mean free path of a photon became much, much larger than the observable universe).

This means that no light from prior to recombination exists and we can never see further away than something known as the surface of last scattering. The surface of last scattering represents a thin spherical shell of plasma where the currently observed CMB was emitted from in the past. This surface is constantly expanding away from us because, as time passes, light from shells further away from us has had enough time to reach us and light from closer shells has already reached us and either been observed or passed us by. See here: https://ned.ipac.caltech.edu/level5/Glossary/Essay_lss.html

The 2nd 'boundary' is below.

I can understand that the sources which I am able to detect keep moving farther away, but if I turn back the clock, other sources which are now beyond my ability to detect should come into view, and the size of what I can observe should not change, it should just be getting less dense as time moves forward and more dense as time moves backwards.

Turning back the clock means that the further back we go, the less time light has had travel from its origin to you, so your observable universe is limited by light travel time. Objects which are observable now would move out of view, not come into view.

Expansion slightly complicates all of this, but I believe this holds true for at least the entire period from recombination to the current time.

 

[kimbyd]

Sort of. But those boundaries have more in common with the horizon than they do with a wall. A horizon is just a limit to how far you can see and is relative to where you are standing, while a wall is a physical object.

 

[nikkkom]

The only thing bounding how far away I can see is my ability to detect the photons.

This is wrong. You are also limited by the fact that you can only see photons which had time to reach you from the moment of their emission, which can't be earlier than recombination epoch.

Even if the entire universe is infinite, photons only from a *finite* volume of space have that property. That's what we call "Observable universe".

 

[Grinkle]

You are also limited by the fact that you can only see photons which had time to reach you from the moment of their emission

This means that no light from prior to recombination exists and we can never see further away than something known as the surface of last scattering.

Thanks - that makes sense. Can we see as far back as the moment of last scattering, or is there thought to be some zone where with better technology we could see shells that are further out?

 

[nikkkom]

Cosmic neutrino background is from a much earlier time - it decoupled only ~1 second after BB.
But observing CNB promises to be very, very difficult. Even "just" detecting these low-energy neutrinos is hard; creating an "image" with meager ~one degree resolution would be still harder.

 

[Grinkle]

I suppose if the CMB hum ever stops, then the size of the universe would be known to be finite and more or less calculateable?

edit:

If we were unfortunate enough that the universe is finite and the last of the CMB passed by the Earth ~200 years ago or so, would we potentially be debating whether absence of the CMB implied that expansion is incorrect? Is there other observable evidence that supports expansion in as direct a manner as CMB for a finite-size universe?

 

[PeterDonis]

I suppose if the CMB hum ever stops, then the size of the universe would be known to be finite and more or less calculateable?

If the universe is finite, i.e., if it has the spatial geometry of a 3-sphere, the CMB will never stop. Eventually we'll just see CMB photons that have circumnavigated the universe and are passing us a second time.

 

[rootone]

If the universe is finite, i.e., if it has the spatial geometry of a 3-sphere, the CMB will never stop. Eventually we'll just see CMB photons that have circumnavigated the universe and are passing us a second time.

Then ultimately they must pass by 'us' an infinite amount of times?

 

[PeterDonis]

Then ultimately they must pass by 'us' an infinite amount of times?

If the universe expands forever, yes. (Note that this requires a nonzero cosmological constant, which is consistent with our best current knowledge, but it's still worth pointing out. A closed universe with zero cosmological constant will recollapse to a Big Crunch before any photons have a chance to circumnavigate it.)