<p>First, let me clear up a misunderstanding:</p>
<strong>Particle horizon</strong>
<p>The &quot;edge&quot; of the observable Universe is called the <em>particle horizon</em>, and lies roughly 47 Gly (billion lightyears) away. It is always receding, both because the Universe expands and because light from increasingly large distances eventually reach us. In <em>comoving coordinates</em> (the coordinate system that expands along with the Universe), it asymptotically reaches a finite size (some 63 Gly), but in physical coordinates it increases forever<span class="math-container">$^\dagger$</span>.</p>
<strong>Event horizon</strong>
<p>The <em>event</em> horizon is the boundary between the part of the Universe that contains the galaxies (and other stuff) from which light emitted today will be able to reach us, and the part where it won't. Currently, it is roughly 17 Gly away, but his horizon is always shrinking because the expansion of the Universe accelerates. In other words, stuff outside the event horizon is so far away that the expansion carries it away too fast for the photon amitted today to ever reach us.</p>
<p>Thus, at Big Bang (BB), the event horizon was 63 comoving Gly away, because that was the maximum distance from which we would ever receive information.</p>
<strong>The CMB will always lag behind the particle horizon</strong>
<p>The farther away we look, the more we look back in time. <em>If</em> there were galaxies a second after BB, and <em>if</em> we had the technology to look that far, we would see them right after BB, and they would be 47 Gly away. However, galaxies weren't born until several hundred Myr (million years) after BB. And now to your question: The CMB wasn't emitted <em>at</em> BB, so it doesn't origin from a region that is now 47 Gly away. Instead, it was emitted 380,000 yr after BB, and it was emitted from <em>all</em> of the Universe, in <em>all</em> directions.</p>
<p>This emittance wasn't instantaneous, but almost (took something like 10,000 yr), so let's assume for now that it was. Let's call that time <span class="math-container">$t_\mathrm{CMB}$</span>. In that case, because light travels at <span class="math-container">$c = 300\,000\,\mathrm{km}\,\mathrm{s}^{-1}$</span>, if you were present one second after <span class="math-container">$t_\mathrm{CMB}$</span>, you would see the CMB that came from all regions that were 300,000 km away. That is, the CMB would be the light from a thin shell of radius 300,000 km.</p>
<p>Two seconds after BB, the CMB would be the light from a shell of radius 600,000 km, and so on. However, because the Universe is expanding, it is actually at little more than 600,000 km in radius.
And now, 13.8 Gyr after BB, and hence 13.7996 Gyr after the CMB was emitted, this shell is not almost 14 Gyr away, but in fact 45 Gly away which is almost, but quite, at the particle horizon.</p>
<p>Because of the expansion, the distance to the CMB shell always increases. But so does the distance to the particle horizon, and because the CMB was emitted <em>after</em> BB, the particle horizon will always &quot;be ahead&quot; of the CMB. As the CMB shell recedes, it becomes more and more redshifted, slowly fading into darkness but never disappearing. This is irrespective of whether the Universe is finite or infinite, except in the possible, but rather fantastic, event that the Universe is larger than the ~47 Gly we can see today, but smaller than the 63 comoving Gly that is the maximum size we will ever see.</p>
<strong>Finite or infinite?</strong>
<p>We don't know if the Universe is finite or infinite, but if the un-observable part of it looks like the observable Universe, then it is infinite. What we can say is that, at least in the observable Universe, the CMB was emitted <em>everywhere</em> in space, and there is currently no reason to believe that it was different elsewhere (although it could bee, if it expanded differently in other parts). To the best of our knowledge, space is homogeneous, meaning that (on average) there are as many baryons, photons, dark matter particles, and bicycles in one place as there is in another. In other words, to the best of our knowledge, there is no edge. Even if it's finite, it is difficult to (and most, if not all, astronomers don't) imagine an edge; rather it is thought that it would &quot;curve back on itself&quot;, just as the surface of a ball is finite in area, but doesn't have an edge.</p>
<strong>2D analogy</strong>
<p>As an analogy, imagine living on a flat, inifinite Earth, populated evenly by people with loud voices. At some point in time, everbody yells &quot;CMB&quot;. First you'll hear your neighbors yell, after 1 sec you'll hear those living 340 meters away, after 1 minute those living 20 km away, after a year those 10 million km away, and so on and so on forever.</p>
<p>Now imagine the same on a round Earth. After 16 hours, you would hear the folks living at your antipode, and if I understand correctly, this is when you expect to &quot;hear a hole in the sound&quot;. But now you would start hearing the ones that are <em>closer</em>, but whose sounds have been traveling more than halfway around Earth. After 32 hours, you'd hear your own yell. And so on.</p>
<p>But, our Earth analogy is also expanding. If it were expanding at a steady rate, we <em>would</em> eventually hear our antipode friends. You might think that if it were expanding fast enough, their sound would never reach you, but as explained by the <a href="https://en.wikipedia.org/wiki/Ant_on_a_rubber_rope" rel="nofollow noreferrer">ant-on-a-rubber-band puzzle</a>, that's not the case).</p>
<p>However, our fictional Earth is not only expanding, but in fact this expansion is accelerating. And in <em>that</em> case, there <em>is</em> a limit to how far away you can hear people.</p>
<p>Back to the real Universe, there is a limit to from how distant regions you may receive CMB photons (or any other information).
Moreover, if the Universe were finite, and were not accelerating, you might think that you would eventually see the CMB that was emitted from our own neighborhood and had been traveling around the Universe.
However, it can be shown that, in this case, the Universe will reach a maximum size, start collapsing, and end in a Big Crunch <em>exactly</em> at the time where you expect to see your antipode.</p>
<p>Only in a finite Universe with a rather special mix of gravitating matter and accelerating dark energy might it be possible to delay the collapse or the eternal expansion to a point where we eventually look back at ourselves. But that's sort of fine-tuning.</p>
<hr />
<p><span class="math-container">$^\dagger$</span><sub>Unless the Universe contains a yet unknown substance that is able to halt the acceleration. This is entirely possible, but in this answer I consider only a well-behaving Universe that acts according to current knowledge.</sub></p>

CC BY-SA 3.0
2017-12-09T00:50:48.743Z
I'm confused by the statement that the edge of the observable universe asymptotically reaches a finite size. I don't understand this. Could you enlighten me, please?
Natsfan
CC BY-SA 3.0
2017-12-09T23:59:01.407Z
If I understand, because the expansion of the universe between us and the CMB shell is exponentially increasing and happen so fast that light from the CMB shell can never reach us, we will never have a hole in the CMB, and all we will see is more redshift in the CMB. Thank you for your answer.
user1097111
CC BY-SA 3.0
2017-12-10T13:32:57.070Z
@jmh It's slightly complicated, but hold on: If the Universe were expanding at a steady rate, there would be no limit how far we could see, in principle. We just have to wait long enough for the light to arrive. Even if a galaxy _now_ is receding at twice the speed of light, or $10c$, or a million $c$, eventually the light would reach us. In say "in principle", because in practice the light is redshifted and diluted beyond detection. However, due to the _accelerated_ expansion there is a limit to how far a galaxy can be and still emit light that is able to reach us [cont'd below]
pela
CC BY-SA 3.0
2017-12-10T13:33:27.947Z
[…] The farthest we can see at the moment is (in principle) 47 Gly. In, say, 15 Gyr from now, a point that is _now_ 47 Gyr away will be roughly 90 Gly away, due to expansion. But since light from more distant regions will at that time have had the time to reach us, we can see farther than 90 Gly, in fact roughly 110 Gly. So, all the time points which we see now will get farther away. In _comoving_ coordinates, however, all points lie still (because comoving coordinates are defined to expand along with the Universe). [cont'd below]
pela
CC BY-SA 3.0
2017-12-10T13:33:39.053Z
[…] In comoving coordinates, a point that is now 47 Gly away, will always be 47 Gly away (because comoving coordinates are defined to coincide with today's coordinates). But in 15 Gyr, will will be able to see 55 comoving Gly away. In, say, 30 Gyr, we will be able to see roughly 60 comoving Gly away, which in physical coordinates will at that time be ~250 Gly. In comoving coordinates, you will never be able to see farther away than 63 Gly, but in physical coordinates this so-called particle horizon always gets farther away.
pela
CC BY-SA 3.0
2017-12-10T13:34:50.877Z
All this is much easier to understand in a spacetime diagram, so if you want more details, ask the question "properly", and I can elaborate.
pela
CC BY-SA 3.0
2017-12-10T13:41:02.287Z
@user1097111 Hmm… not exactly. The light from the CMB shell _is_ reaching us right now. But you're right that light emitted _today_ from that region of space will never reach us. But tomorrow, the light that we will call "the CMB" will come from a shell which is slightly farther away, although it was emitted at the same time [cont'd below].
pela
CC BY-SA 3.0
2017-12-10T13:41:06.827Z
In some billion years, the light that we then will call the CMB will come from a shell that today is outside our observable Universe, but it will still have been emitted at the same time as the CMB we see at any other time in history. There will never be a "hole" because there is always a shell outside another shell.
pela
CC BY-SA 3.0
2017-12-11T16:32:07.457Z
@pela thank you for your answer. At the time of the CMB, did the CMB happen "in space"? The universe was about 1/1000 the size which it is now,  but was there an edge to the universe where the baryonic matter phased out? If there was an edge, and as in your comment above, in the future, we [cont'd below]
user1097111
CC BY-SA 3.0
2017-12-11T16:32:14.687Z
will have access to photons from the CMB which are outside our observable universe. Does this mean that CMB we will observe will come from distances further away (when projected back to the time the CMB was emitted). If this is the case, then logically, there should be a time when there is hole in the CMB. A space diagram as you mention might help (assuming I can understand it). Thank you.
user1097111
CC BY-SA 3.0
2017-12-11T22:20:22.770Z
@user1097111 I added two paragraphs. I hope this helps, otherwise let me know; I might be able to make some drawings at some point, but I'm traveling at the moment and don't have much time.
pela
CC BY-SA 3.0
2017-12-12T05:14:58.230Z
@user1097111 According to Big Bang theory, there **never** was any kind of edge to the whole universe where baryonic matter phased out. According to this model, the universe has _always_ been infinite in spatial extent since it started, and (relatively) homogeneous, although it isn't homogeneous at small scales.
PM 2Ring
CC BY-SA 3.0
2017-12-12T18:39:10.017Z
@PM2Ring Correct, except BB doesn't necessarily impose infinity; a finite universe is enirely possible within the framework of BB, but even so, there would be no "midpoint" from where baryons phased out. However, such a universe would be geometrically "closed", and at least the _observable_ Universe doesn't seem to be so (within experimental error). But who knows what's outside…
pela
CC BY-SA 3.0
2017-12-12T18:55:36.387Z
@pela Ah, good point. My previous comment assumes that the global curvature of the universe isn't positive. Which is a little ironic, considering that when I first learned this stuff it was generally assumed that the global curvature _is_ positive. :) Whereas these days the evidence suggests that's quite unlikely: eg, accelerating expansion is hard to reconcile with positive curvature, and it looks like the curvature is either flat or very slightly negative. Of course, we can only make measurements of the observable universe, and maybe we live in a curvature anomaly. ;)
PM 2Ring
CC BY-SA 3.0
2017-12-08T23:17:27.703Z
2017-12-11T22:18:30.253Z
2020-06-17T09:47:40.653Z
pela
<p>If my understanding is correct, the Cosmic Microwave Background always come from our event horizon. By event horizon I mean the edge of the observable universe.</p>

<p>If the universe is finite does it mean that after some time (maybe in billions of years?) there will start being a hole in CMB. As our event horizon let us see CMB from regions further and further away, isn't there a time where it will reach the edge of the universe?</p>

<p>If this is the case, based on the known number of atom and mass of the universe, is it possible to calculate when this will happen?</p>

<universe><cosmic-microwave-background><event-horizon>
Would a future hole in the Cosmic Microwave Background show us the edge of the universe?
user1097111
# Would a future hole in the Cosmic Microwave Background show us the edge of the universe?

(Asked by: username_0 on 2017-12-08)

If my understanding is correct, the Cosmic Microwave Background always come from our event horizon. By event horizon I mean the edge of the observable universe.

If the universe is finite does it mean that after some time (maybe in billions of years?) there will start being a hole in CMB. As our event horizon let us see CMB from regions further and further away, isn't there a time where it will reach the edge of the universe?

If this is the case, based on the known number of atom and mass of the universe, is it possible to calculate when this will happen?

**Tags:** universe, cosmic-microwave-background, event-horizon


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## 1 answers

### Answer by username_1 on 2017-12-08. Score: 10

First, let me clear up a misunderstanding:

**Particle horizon**

The "edge" of the observable Universe is called the *particle horizon*, and lies roughly 47 Gly (billion lightyears) away. It is always receding, both because the Universe expands and because light from increasingly large distances eventually reach us. In *comoving coordinates* (the coordinate system that expands along with the Universe), it asymptotically reaches a finite size (some 63 Gly), but in physical coordinates it increases forever$^\dagger$.

**Event horizon**

The *event* horizon is the boundary between the part of the Universe that contains the galaxies (and other stuff) from which light emitted today will be able to reach us, and the part where it won't. Currently, it is roughly 17 Gly away, but his horizon is always shrinking because the expansion of the Universe accelerates. In other words, stuff outside the event horizon is so far away that the expansion carries it away too fast for the photon amitted today to ever reach us.

Thus, at Big Bang (BB), the event horizon was 63 comoving Gly away, because that was the maximum distance from which we would ever receive information.

**The CMB will always lag behind the particle horizon**

The farther away we look, the more we look back in time. *If* there were galaxies a second after BB, and *if* we had the technology to look that far, we would see them right after BB, and they would be 47 Gly away. However, galaxies weren't born until several hundred Myr (million years) after BB. And now to your question: The CMB wasn't emitted *at* BB, so it doesn't origin from a region that is now 47 Gly away. Instead, it was emitted 380,000 yr after BB, and it was emitted from *all* of the Universe, in *all* directions.

This emittance wasn't instantaneous, but almost (took something like 10,000 yr), so let's assume for now that it was. Let's call that time $t\_\mathrm{CMB}$. In that case, because light travels at $c = 300\,000\,\mathrm{km}\,\mathrm{s}^{-1}$, if you were present one second after $t\_\mathrm{CMB}$, you would see the CMB that came from all regions that were 300,000 km away. That is, the CMB would be the light from a thin shell of radius 300,000 km.

Two seconds after BB, the CMB would be the light from a shell of radius 600,000 km, and so on. However, because the Universe is expanding, it is actually at little more than 600,000 km in radius.
And now, 13.8 Gyr after BB, and hence 13.7996 Gyr after the CMB was emitted, this shell is not almost 14 Gyr away, but in fact 45 Gly away which is almost, but quite, at the particle horizon.

Because of the expansion, the distance to the CMB shell always increases. But so does the distance to the particle horizon, and because the CMB was emitted *after* BB, the particle horizon will always "be ahead" of the CMB. As the CMB shell recedes, it becomes more and more redshifted, slowly fading into darkness but never disappearing. This is irrespective of whether the Universe is finite or infinite, except in the possible, but rather fantastic, event that the Universe is larger than the ~47 Gly we can see today, but smaller than the 63 comoving Gly that is the maximum size we will ever see.

**Finite or infinite?**

We don't know if the Universe is finite or infinite, but if the un-observable part of it looks like the observable Universe, then it is infinite. What we can say is that, at least in the observable Universe, the CMB was emitted *everywhere* in space, and there is currently no reason to believe that it was different elsewhere (although it could bee, if it expanded differently in other parts). To the best of our knowledge, space is homogeneous, meaning that (on average) there are as many baryons, photons, dark matter particles, and bicycles in one place as there is in another. In other words, to the best of our knowledge, there is no edge. Even if it's finite, it is difficult to (and most, if not all, astronomers don't) imagine an edge; rather it is thought that it would "curve back on itself", just as the surface of a ball is finite in area, but doesn't have an edge.

**2D analogy**

As an analogy, imagine living on a flat, inifinite Earth, populated evenly by people with loud voices. At some point in time, everbody yells "CMB". First you'll hear your neighbors yell, after 1 sec you'll hear those living 340 meters away, after 1 minute those living 20 km away, after a year those 10 million km away, and so on and so on forever.

Now imagine the same on a round Earth. After 16 hours, you would hear the folks living at your antipode, and if I understand correctly, this is when you expect to "hear a hole in the sound". But now you would start hearing the ones that are *closer*, but whose sounds have been traveling more than halfway around Earth. After 32 hours, you'd hear your own yell. And so on.

But, our Earth analogy is also expanding. If it were expanding at a steady rate, we *would* eventually hear our antipode friends. You might think that if it were expanding fast enough, their sound would never reach you, but as explained by the [ant-on-a-rubber-band puzzle](https://en.wikipedia.org/wiki/Ant_on_a_rubber_rope), that's not the case).

However, our fictional Earth is not only expanding, but in fact this expansion is accelerating. And in *that* case, there *is* a limit to how far away you can hear people.

Back to the real Universe, there is a limit to from how distant regions you may receive CMB photons (or any other information).
Moreover, if the Universe were finite, and were not accelerating, you might think that you would eventually see the CMB that was emitted from our own neighborhood and had been traveling around the Universe.
However, it can be shown that, in this case, the Universe will reach a maximum size, start collapsing, and end in a Big Crunch *exactly* at the time where you expect to see your antipode.

Only in a finite Universe with a rather special mix of gravitating matter and accelerating dark energy might it be possible to delay the collapse or the eternal expansion to a point where we eventually look back at ourselves. But that's sort of fine-tuning.

---

$^\dagger$Unless the Universe contains a yet unknown substance that is able to halt the acceleration. This is entirely possible, but in this answer I consider only a well-behaving Universe that acts according to current knowledge.

> **Comments:**
> **username_2**: I'm confused by the statement that the edge of the observable universe asymptotically reaches a finite size. I don't understand this. Could you enlighten me, please?  
> **username_0**: If I understand, because the expansion of the universe between us and the CMB shell is exponentially increasing and happen so fast that light from the CMB shell can never reach us, we will never have a hole in the CMB, and all we will see is more redshift in the CMB. Thank you for your answer.  
> **username_1**: @jmh It's slightly complicated, but hold on: If the Universe were expanding at a steady rate, there would be no limit how far we could see, in principle. We just have to wait long enough for the light to arrive. Even if a galaxy _now_ is receding at twice the speed of light, or $10c$, or a million $c$, eventually the light would reach us. In say "in principle", because in practice the light is redshifted and diluted beyond detection. However, due to the _accelerated_ expansion there is a limit to how far a galaxy can be and still emit light that is able to reach us [cont'd below]  
> **username_1**: […] The farthest we can see at the moment is (in principle) 47 Gly. In, say, 15 Gyr from now, a point that is _now_ 47 Gyr away will be roughly 90 Gly away, due to expansion. But since light from more distant regions will at that time have had the time to reach us, we can see farther than 90 Gly, in fact roughly 110 Gly. So, all the time points which we see now will get farther away. In _comoving_ coordinates, however, all points lie still (because comoving coordinates are defined to expand along with the Universe). [cont'd below]  
> **username_1**: […] In comoving coordinates, a point that is now 47 Gly away, will always be 47 Gly away (because comoving coordinates are defined to coincide with today's coordinates). But in 15 Gyr, will will be able to see 55 comoving Gly away. In, say, 30 Gyr, we will be able to see roughly 60 comoving Gly away, which in physical coordinates will at that time be ~250 Gly. In comoving coordinates, you will never be able to see farther away than 63 Gly, but in physical coordinates this so-called particle horizon always gets farther away.  
> **username_1**: All this is much easier to understand in a spacetime diagram, so if you want more details, ask the question "properly", and I can elaborate.  
> **username_1**: @username_0 Hmm… not exactly. The light from the CMB shell _is_ reaching us right now. But you're right that light emitted _today_ from that region of space will never reach us. But tomorrow, the light that we will call "the CMB" will come from a shell which is slightly farther away, although it was emitted at the same time [cont'd below].  
> **username_1**: In some billion years, the light that we then will call the CMB will come from a shell that today is outside our observable Universe, but it will still have been emitted at the same time as the CMB we see at any other time in history. There will never be a "hole" because there is always a shell outside another shell.  
> **username_0**: @username_1 thank you for your answer. At the time of the CMB, did the CMB happen "in space"? The universe was about 1/1000 the size which it is now,  but was there an edge to the universe where the baryonic matter phased out? If there was an edge, and as in your comment above, in the future, we [cont'd below]  
> **username_0**: will have access to photons from the CMB which are outside our observable universe. Does this mean that CMB we will observe will come from distances further away (when projected back to the time the CMB was emitted). If this is the case, then logically, there should be a time when there is hole in the CMB. A space diagram as you mention might help (assuming I can understand it). Thank you.  
> **username_1**: @username_0 I added two paragraphs. I hope this helps, otherwise let me know; I might be able to make some drawings at some point, but I'm traveling at the moment and don't have much time.  
> **username_3**: @username_0 According to Big Bang theory, there **never** was any kind of edge to the whole universe where baryonic matter phased out. According to this model, the universe has _always_ been infinite in spatial extent since it started, and (relatively) homogeneous, although it isn't homogeneous at small scales.  
> **username_1**: @PM2Ring Correct, except BB doesn't necessarily impose infinity; a finite universe is enirely possible within the framework of BB, but even so, there would be no "midpoint" from where baryons phased out. However, such a universe would be geometrically "closed", and at least the _observable_ Universe doesn't seem to be so (within experimental error). But who knows what's outside…  
> **username_3**: @username_1 Ah, good point. My previous comment assumes that the global curvature of the universe isn't positive. Which is a little ironic, considering that when I first learned this stuff it was generally assumed that the global curvature _is_ positive. :) Whereas these days the evidence suggests that's quite unlikely: eg, accelerating expansion is hard to reconcile with positive curvature, and it looks like the curvature is either flat or very slightly negative. Of course, we can only make measurements of the observable universe, and maybe we live in a curvature anomaly. ;)  

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