I How do we observe the CMB at all?

[Phys12]

TL;DR Summary

If CMB is the oldest light in the universe, then how is it that we potentially can never know something about the universe that emits light.

So, as I understand it, the photons from the microwave background were the result of photon decoupling. Now, if I remember correctly, because of the accelerated expansion of the universe, the diameter of the universe is not about 28 Gyr, but about 90 Gyr, the consequence of which is that there are objects that have accelerated faster than the speed of light and the light that was emitted by those objects will never reach us and so we will never be able to see that light. But how is it possible that we can see the oldest light in the universe (CMB), but never be able to see a younger light (emitted by some object) that was produced after the oldest light. Does my question make sense? If yes, what am I missing?

 

[PeroK]

Summary:: If CMB is the oldest light in the universe, then how is it that we potentially can never know something about the universe that emits light.

So, as I understand it, the photons from the microwave background were the result of photon decoupling. Now, if I remember correctly, because of the accelerated expansion of the universe, the diameter of the universe is not about 28 Gyr, but about 90 Gyr, the consequence of which is that there are objects that have accelerated faster than the speed of light and the light that was emitted by those objects will never reach us and so we will never be able to see that light. But how is it possible that we can see the oldest light in the universe (CMB), but never be able to see a younger light (emitted by some object) that was produced after the oldest light. Does my question make sense? If yes, what am I missing?

You can see the CMB from those parts of the universe that were close enough at photon decoupling. The CMB from a certain distance reached Earth 4 billion years ago. What we are seeing now came from further away.

PS using a model of universe expansion you could do the following calculation:

1) Take a distance from Earth's location at decoupling.

2) Compute the time it takes that light to reach Earth (in an expanding universe).

With the current accelerating model there must be a horizon beyond which we will never see. The light from the horizon itself will take an infinite amount of time to reach Earth. So, what we see is light from closer and closer to that horizon, getting more and more redshifted.

 

[Bandersnatch]

Let's clear up some misconceptions first.

Now, if I remember correctly, because of the accelerated expansion of the universe, the diameter of the universe is not about 28 Gyr, but about 90 Gyr

That the proper distance to the farthest observable object is larger than twice the age of the universe is not a consequence of accelerated expansion, but of expansion, period. This is just due to the emitter receding while the signal is en route to the observer, so that it is farther at reception than we would expect in a static universe.
The only (non-convoluted) way for the diameter of the observable universe to be twice its age times c is for it to be static.

the consequence of which is that there are objects that have accelerated faster than the speed of light and the light that was emitted by those objects will never reach us and so we will never be able to see that light.

One gets faster than light recession in a non-accelerated universe too. In such a universe, this >c recession does not prevent the signal from being observed - regardless of how far it was emitted from = how quickly the emitter was receding. This is the 'ant on a rubber rope' exercise (see Wikipedia).

Accelerated expansion does result in a horizon, as mentioned by PeroK, from beyond which no signal can ever reach the observer. But - in a universe that is not fully dominated by dark energy - this horizon is further back than the Hubble sphere (i.e. distance where recession velocity = c).With those corrections in mind, think of a signal leaving CMB at the dawn of time. It is emitted at a spot that is initially receding from the eventual observer with velocity higher than c, but within the event horizon. It carries a snapshot of the early universe.

Over time, it gradually makes its way through the expanding space. Initially it's carried away by >c expansion, but in time it will start getting closer. At some point in time passes by some already formed galaxy which also emits some light. From then on the two beams travel together, while both emitters keep receding.
It will never be the case that a signal emitted from further behind overtakes one emitted from closer in front. Which is another way of saying that in terms of comoving distance the older signal is always from further away.

After a while, the emitters will have receded to beyond the event horizon, with the farther one (CMB) doing so earlier than the closer one (galaxy). But it doesn't affect the signals already travelling, only signals emitted after passing the event horizon. Which means you can and will observe both, when the two signals arrive simultaneously.
They will be observed in the state they were at emission. CMB will be older, the galaxy will be younger.
You will be able to say that by now, both emitters will have receded sufficiently far away that their signals emitted now will never be observable, but it doesn't stop you from still seeing all the signals they emitted before passing the event horizon.

And since it takes progressively longer for a signal to reach the observer, the closer to the event horizon it was emitted, you will only observe the moment of passing the EH after infinite time. I.e., you will always be able to see CMB, and all the galaxies you see now.

 

[Phys12]

That the proper distance to the farthest observable object is larger than twice the age of the universe is not a consequence of accelerated expansion, but of expansion, period. This is just due to the emitter receding while the signal is en route to the observer

But wouldn't the emitter need to have been moving at the speed of light for it to have reached a distance of twice the distance from the Earth to the point when it first emitted the light that was observed on earth?

The only (non-convoluted) way for the diameter of the observable universe to be twice its age times c is for it to be static.

By non-convoluted, you mean no expansion/contraction, right?

But - in a universe that is not fully dominated by dark energy - this horizon is further back than the Hubble sphere (i.e. distance where recession velocity = c).

To clarify, dark energy here is used only to indicate an accelerated expansion of the universe with recession velocity >c, right? Also, even if a universe is dominated by dark energy, the horizon would still be further back than the Hubble sphere, right?

With those corrections in mind, think of a signal leaving CMB at the dawn of time. It is emitted at a spot that is initially receding from the eventual observer with velocity higher than c, but within the event horizon. It carries a snapshot of the early universe.

Over time, it gradually makes its way through the expanding space. Initially it's carried away by >c expansion, but in time it will start getting closer. At some point in time passes by some already formed galaxy which also emits some light. From then on the two beams travel together, while both emitters keep receding.
It will never be the case that a signal emitted from further behind overtakes one emitted from closer in front. Which is another way of saying that in terms of comoving distance the older signal is always from further away.

After a while, the emitters will have receded to beyond the event horizon, with the farther one (CMB) doing so earlier than the closer one (galaxy). But it doesn't affect the signals already travelling, only signals emitted after passing the event horizon. Which means you can and will observe both, when the two signals arrive simultaneously.
They will be observed in the state they were at emission. CMB will be older, the galaxy will be younger.
You will be able to say that by now, both emitters will have receded sufficiently far away that their signals emitted now will never be observable, but it doesn't stop you from still seeing all the signals they emitted before passing the event horizon.

And since it takes progressively longer for a signal to reach the observer, the closer to the event horizon it was emitted, you will only observe the moment of passing the EH after infinite time. I.e., you will always be able to see CMB, and all the galaxies you see now.

Always? Would it not happen that when I see the photon emitted by the CMB at the EH, that will be the last photon that people on Earth will ever be able to detect?

So we can see light from the CMB, from objects produced after the CMB, but not once they've crossed the EH and not anything that might have been created beyond the EH. Is that accurate?

 

[Bandersnatch]

But wouldn't the emitter need to have been moving at the speed of light for it to have reached a distance of twice the distance from the Earth to the point when it first emitted the light that was observed on earth?

Sure. That's not an issue, though. If you don't see how, check out that 'ant on a rubber rope' article on Wikipedia that was mentioned.
Keep in mind, that the regions from which we're presently receiving CMB have never been receding at velocities lower than c. And yet, we can observe it just fine.

By non-convoluted, you mean no expansion/contraction, right?

By convoluted I meant that one could concoct a model that is in turns expanding and contracting in just the right way to place the emitter exactly where it would be if the universe were static (no expansion/contraction). The non-convoluted one would be just static.

To clarify, dark energy here is used only to indicate an accelerated expansion of the universe with recession velocity >c, right? Also, even if a universe is dominated by dark energy, the horizon would still be further back than the Hubble sphere, right?

With dark energy one gets accelerated expansion, yes. But one doesn't need accelerated expansion to get recession velocities higher than c. A steady, or even decelerated, expansion will produce such recession velocities at sufficiently large distances, as indicated by the Hubble law: $V=H_0 d$. Everything further away than $d_h=c/H_0$ is receding faster than light. $d_h$ is the radius of the Hubble sphere (or just Hubble radius).

Now, in a universe without dark energy, there is no event horizon, but the Hubble radius does exist.
In a universe with dark energy, but also non-negligible other stuff (matter, radiation) in it, the horizon exists and is further away than the Hubble radius.
In a universe with only dark energy in it (de Sitter universe), the event horizon is exactly where the Hubble radius is.
As our universe (assuming the LCDM model) expands, other kinds of energy will keep diluting towards negligible densities, so the horizon will get ever closer to the Hubble radius (but will only reach it asymptotically in infinite future).

Always? Would it not happen that when I see the photon emitted by the CMB at the EH, that will be the last photon that people on Earth will ever be able to detect?

That's right, but this photon will take forever to reach the observer. I.e., a once visible object will disappear from sight only after infinite time has passed. So the object is always visible (disregarding issues with faintness of the signal, etc.).

So we can see light from the CMB, from objects produced after the CMB, but not once they've crossed the EH and not anything that might have been created beyond the EH. Is that accurate?

Yes. By definition, anything beyond EH is forever unobservable. Just as with black holes.

But I have the impression you might still be thinking of those objects as somehow disappearing as they cross the EH. The horizon doesn't 'disappear' objects, it limits how much of the history of the emitter we will be able to see.
It might be better to think of events in space-time, instead of objects. E.g. there are points in space, comoving with the expansion, from which we can observe light as it was emitted over some limited time interval. From the point of view of a distant observer, this limited time interval is stretched to infinity. The points crossing the event horizon means the last moment in the history of this point in space that we may still observe.
So, e.g., taking the CMB. There is a set of points in space, from which the currently-observable CMB was emitted by the gas residing there early in the universe. Later in time, that gas will start to coalesce into proto-galaxies, which some humans in the far future might be able to observe. The formation processes will be seen as increasingly stretched in time, slower and dimmer. But no matter how long they wait, they'll never see a fully formed galaxy in those spots (say, at 5 billion years of age). All they'll ever get is an old image, progressively more and more frozen in time.
Looking at something closer-by, there will be more of its history that will be observable. So a galaxy currently at 20 Gly will eventually be observed as it reaches 5 billion years of age, but the moment it ages to 10 Gy will be forever unobservable.

 

[PeroK]

But wouldn't the emitter need to have been moving at the speed of light for it to have reached a distance of twice the distance from the Earth to the point when it first emitted the light that was observed on earth?

It's not the case that things have been receding at a constant speed since decoupling. The dynamics of expansion (and accelerated expansion) make things more complicated. You could try this Insight:

https://www.physicsforums.com/insights/inflationary-misconceptions-basics-cosmological-horizons/

 

[Phys12]

Sure. That's not an issue, though. If you don't see how, check out that 'ant on a rubber rope' article on Wikipedia that was mentioned.
Keep in mind, that the regions from which we're presently receiving CMB have never been receding at velocities lower than c. And yet, we can observe it just fine.By convoluted I meant that one could concoct a model that is in turns expanding and contracting in just the right way to place the emitter exactly where it would be if the universe were static (no expansion/contraction). The non-convoluted one would be just static.With dark energy one gets accelerated expansion, yes. But one doesn't need accelerated expansion to get recession velocities higher than c. A steady, or even decelerated, expansion will produce such recession velocities at sufficiently large distances, as indicated by the Hubble law: $V=H_0 d$. Everything further away than $d_h=c/H_0$ is receding faster than light. $d_h$ is the radius of the Hubble sphere (or just Hubble radius).

Now, in a universe without dark energy, there is no event horizon, but the Hubble radius does exist.
In a universe with dark energy, but also non-negligible other stuff (matter, radiation) in it, the horizon exists and is further away than the Hubble radius.
In a universe with only dark energy in it (de Sitter universe), the event horizon is exactly where the Hubble radius is.
As our universe (assuming the LCDM model) expands, other kinds of energy will keep diluting towards negligible densities, so the horizon will get ever closer to the Hubble radius (but will only reach it asymptotically in infinite future).That's right, but this photon will take forever to reach the observer. I.e., a once visible object will disappear from sight only after infinite time has passed. So the object is always visible (disregarding issues with faintness of the signal, etc.).Yes. By definition, anything beyond EH is forever unobservable. Just as with black holes.

But I have the impression you might still be thinking of those objects as somehow disappearing as they cross the EH. The horizon doesn't 'disappear' objects, it limits how much of the history of the emitter we will be able to see.
It might be better to think of events in space-time, instead of objects. E.g. there are points in space, comoving with the expansion, from which we can observe light as it was emitted over some limited time interval. From the point of view of a distant observer, this limited time interval is stretched to infinity. The points crossing the event horizon means the last moment in the history of this point in space that we may still observe.
So, e.g., taking the CMB. There is a set of points in space, from which the currently-observable CMB was emitted by the gas residing there early in the universe. Later in time, that gas will start to coalesce into proto-galaxies, which some humans in the far future might be able to observe. The formation processes will be seen as increasingly stretched in time, slower and dimmer. But no matter how long they wait, they'll never see a fully formed galaxy in those spots (say, at 5 billion years of age). All they'll ever get is an old image, progressively more and more frozen in time.
Looking at something closer-by, there will be more of its history that will be observable. So a galaxy currently at 20 Gly will eventually be observed as it reaches 5 billion years of age, but the moment it ages to 10 Gy will be forever unobservable.

Thank you so much for your clear and detailed explanation, I truly appreciate it! :) I understand the entire universe now ;)