<p>It is a common misconception that galaxies receding faster than light cannot be observed. There are two versions of this misconception:</p>
<ol>
<li>Galaxies that are <em>now</em> receding faster than light cannot be seen.</li>
<li>If we observe a galaxy <em>today</em>, it may recede faster than light <em>now</em>, but when it emitted the light we see now, it did not.</li>
</ol>
<p>Both are incorrect.</p>
<h4><strong>Intuitive explanation</strong></h4>
<p>This is most easily seen in a spacetime diagram. But before showing that, a somewhat intuitive way of understanding this apparent paradox is to consider the journey of the photon from the reference frame of the emitting galaxy: In this frame, the photon leaves the emitter with a velocity <span class="math-container">$v=c$</span> (as it should), but as it increases its distance from the source, there's more and more space that can expand. That means that its distance increases faster and faster, i.e. that its velocity increases without bounds. This is not a proof, but may help to show that &quot;light may travel faster the the speed of light&quot;.</p>
<h4><strong>Spacetime diagram</strong></h4>
<p>Now to the spacetime diagram. My favorite version is from the classic paper by <a href="https://arxiv.org/abs/astro-ph/0310808" rel="nofollow noreferrer">Davis &amp; Lineweaver (2004)</a>, but I actually like better this version from <a href="https://physics.stackexchange.com/a/63780/70207">Pulsar's excellent (!) post</a>:</p>
<p><a href="https://i.sstatic.net/SR9EP.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/SR9EP.png" alt="spacetime" /></a></p>
<h4><strong>Real example of a galaxy that has always been, and always will be, receding with superluminal velocity</strong></h4>
<p>Such a diagram shows age (or, equivalently, size) of the Universe, as a function of the corresponding comoving distance<span class="math-container">$^1$</span> of events. A lot of things are going on in this diagram, and I'll refer to Pulsar's answer for an interesting discussion of all this. For our purposes, consider the only thing the I have added to the figure: the world line — i.e. the &quot;path&quot; taken through spacetime of some object — of the galaxy <a href="https://en.wikipedia.org/wiki/GN-z11" rel="nofollow noreferrer">GN-z11</a>, seen as a vertical dashed line at a comoving distance <span class="math-container">$d_C \simeq 32.2\,\mathrm{Gly}$</span>. It is vertical, because it doesn't move in comoving coordinates. We observe it at a redshift of <span class="math-container">$z=11.09$</span>, which means that the light we see (moving at 45º toward <em>our</em> worldline which is at <span class="math-container">$d_C=0$</span>) was emitted when the Universe was roughly 400 Myr old. At that time, GN-z11 was receding at a velocity <span class="math-container">$v\simeq4c$</span>!</p>
<h4><strong>Hubble sphere and event horizon</strong></h4>
<p>The innermost green bubble (labeled &quot;<span class="math-container">$v_\mathrm{rec}=c$</span>&quot;) is the <em>Hubble sphere</em>, defined such that at any point in time, everything outside recedes faster than <span class="math-container">$c$</span>. Meanwhile, the red line shows the <em>event horizon</em>, which defines the boundary between everything that <em>can</em> eventually be observed (light red region), and everything that cannot. A subset of this is out <em>past lightcone</em> (orange region) which is stuff that we have already observed (or at least have had the chance to).</p>
<p>Everything lying in between the Hubble sphere and the event horizon consists of events that we have been, or will eventually be, able to see, but which recede faster than the speed of light when it emits the light we see.</p>
<p>As you can see the region becomes narrower with time<span class="math-container">$^2$</span>, meaning that the accelerated expansion of the Universe makes it harder and harder for photons emitted far away to reach us. We will never be able to see galaxies that today are farther away than roughly 17 Gly. But galaxies that are nearer <em>will</em> be seen (if we look), and a subset of these — namely the ones with <span class="math-container">$14\,\mathrm{Gly} \lesssim d_C \lesssim 17\,\mathrm{Gly}$</span> — are currently receding faster than the speed of light.</p>
<h4><strong>The size of the observable Universe always increases</strong></h4>
<p>The observable Universe is defined as the region within which light has had the time to reach us. The &quot;edge&quot; of this is called the <em>particle horizon</em>, and as seen from the blue line, it always increases its distance from us (in comoving coordinates, and thus even more so in physical coordinates). In comoving coodinates, it reach a maximum size of roughly 63 Gly. That means that more and more galaxies will enter our observable Universe, but as time goes they will do so at an ever-decreasing pace, asymptotically reaching a finite value (of 5 trillion galaxies, more or less). Once inside the particle horizon, a galaxy will never leave. It will, however, keep increasing its distance from us in physical coordinates, as well as its speed, and thus redshift without bounds and fade to black.</p>
<hr />
<p><span class="math-container">$^1$</span><sub>Comoving coordinates are defined so that they &quot;expand with the expansion of the Universe&quot;. That means that in these coordinates, galaxies lie approximately still wrt. each other. To get the <em>physical</em> coordinates — i.e. what you would measure if you froze the Universe and laid out measuring rods — multiply the comoving coordinates by the scale factor <span class="math-container">$a$</span> seen on the right <span class="math-container">$y$</span> axis. Since today <span class="math-container">$a\equiv1$</span>, comoving and physical coordinates coincide today.</sub></p>
<p><span class="math-container">$^2$</span><sub>The fact that the diagram is in comoving coordinates makes it a bit hard to see, but this is still the case in physical coordinates.</sub></p>

CC BY-SA 3.0
2017-01-31T23:17:46.087Z
nice answer! 2 questions: can you elaborate more what the event horizon is? I've read on wikipedia, it's the lower limit for the radius of an object with mass. Below this radius, it would become a blackhole. I can understand that, but what then is the event horizon drawn into that diagram? Is is the radius corresponding to the total mass of the universe? Does this even make sense?
2. How is this diagram derived?
rtime
CC BY-SA 3.0
2017-02-01T00:31:00.580Z
@t.rathjen: 1. An "event horizon" is a boundary that separates spacetime event that cannot influence each other. What you are referring to is the event horizon of a black hole. I am talking about the _cosmic_ event horizon which is related, but different, thing. It is the boundary between what in the Universe may, and what may not, influence us. Its size is dictated by the expansion rate of the Universe, not by its total mass.
pela
CC BY-SA 3.0
2017-02-01T00:34:22.107Z
2. The diagram is created using the various relations between redshift/scale factor and comoving distance, age of the Universe, expansion rate etc. Most of these quantities require integrating numerically the Friedman equation, which can be done using e.g. the Python module "cosmolopy.distance".
pela
CC BY-SA 3.0
2017-02-01T10:17:50.590Z
Now I start getting it... Light we receive from GN-z11 has ~traveled far more than 11Gly before reaching us... so it looks like light traveled quicker. I think I got my misconception from books where they were exploring theory where universe dominated by [phantom energy](https://en.wikipedia.org/wiki/Phantom_energy)(with an equation of state with $w$ < -1...
J. Chomel
CC BY-SA 3.0
2017-02-01T11:03:30.290Z
@pela, what does this spacetime diagram would look like with $w$ < -1?
J. Chomel
CC BY-SA 3.0
2017-02-01T11:12:26.113Z
@J.Chomel: Well, the distance to GN-z11 _today_ is 32.2 Gly (or 10 Gpc). The distance when the light that we see today was _emitted_ was 32.2 Gly / (1+z) = 2.7 Gly. Although the distance to GN-z11 has thus increased by (32.2-2.7) Gly = 29.5 Gly during its journey, part of this is not due to light propagating, but due to expansion. The total path that the light "by itself" has traveled is given by the time it took, divided by the speed of light, i.e. 13.4 Gyr / c = 13.4 Gly.
pela
CC BY-SA 3.0
2017-02-01T11:17:57.117Z
Regarding a w < -1 plot, I can make one at some point, but I don't have the time now. I'm not used to thinking about w < -1 so I would have to think, but I suppose since the plot is in comoving coordinates, the 45º lines would still be 45º, but the dashed purple lines would be more skewed toward to upper corners. Hmm… don't take this too seriously, I'm not quite sure right now…
pela
CC BY-SA 3.0
2017-02-01T12:35:47.210Z
^
 
Now I start getting it... Light we receive from GN-z11 has ~traveled far more before reaching us than the distance it was from us at the time that light was emitted (2.7Gly) ... so it looks like light traveled quicker.
J. Chomel
CC BY-SA 3.0
2017-02-01T13:38:32.743Z
@J.Chomel Yes, exactly!
pela
CC BY-SA 4.0
2017-01-31T16:55:51.953Z
2024-12-21T22:43:35.693Z
2024-12-21T22:43:35.693Z
pela
<p>Does the fact that universe is currently expanding at an accelerating rate means that far far away objects (<em>FAO</em>) might start disappearing with time, set aside the &quot;red shift&quot;?</p>
<p>I'm saying this because from what I understand until now:</p>
<ul>
<li>we receive photons from <em>FAO</em> that were emitted long long ago</li>
<li>due to space expansion, some of those objects will be moving away at speed greater than the speed of light.</li>
</ul>
<p>So there must be a point in time at which these far away objects disappear from view. How is this concept called?, or is it only a mistake I'm doing in my thinking?</p>
<p>Here's a simple drawing to illustrate:</p>
<ul>
<li>at t=-11 billion years(By), photons are emitted in a slow expanding universe, and today we can view the object as it was</li>
<li>at t=-2 By, the object moves faster than speed of light, so photon emitted at that time will never reach us, even if we wait the 9 by + &quot;expansion correction&quot; needed...</li>
</ul>
<p><a href="https://i.sstatic.net/VEZjt.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/VEZjt.png" alt="light from fast receding objects will never reach us" /></a></p>
<p>I couldn't be convinced by the answer I found <a href="https://astronomy.stackexchange.com/a/14338/11264">here</a>, saying nothing disappears out of horizon. I don't see how it complies with <a href="https://astronomy.stackexchange.com/a/6035/11264">that answer</a> were event horizon approaches us.</p>

CC BY-SA 3.0
2017-01-31T16:05:23.447Z
Phil Plait says yes.  There's an entry on this topic somewhere in the slate.com/badastronomy column.
Carl Witthoft
CC BY-SA 3.0
2017-01-31T16:33:02.960Z
I think this was also discussed in [this question](http://astronomy.stackexchange.com/questions/19896/what-fraction-of-galaxies-in-the-observable-universe-have-we-actually-observed) yesterday.
Dean
CC BY-SA 4.0
2024-12-28T23:34:11.203Z
This question has an excellent answer which carefully and directly addresses the OP's question. Closing as duplicate directs readers away from the ideal answer, which in my opinion does more damage than good. The two questions are now linked, but there is no reason to shut this page down. **voting to reopen open**
uhoh
CC BY-SA 4.0
2024-12-29T13:49:33.083Z
I wouldn't suggest reopening is good, however merging is a good option where there are good answers on two questions that are duplicates.
Rory Alsop
<universe><expansion><fate-of-universe>
Will we start seeing galaxies disappear due to the newly discovered acceleration of the expansion of the universe?
J. Chomel
# Will we start seeing galaxies disappear due to the newly discovered acceleration of the expansion of the universe?

(Asked by: username_0 on 2017-01-31)

Does the fact that universe is currently expanding at an accelerating rate means that far far away objects (*FAO*) might start disappearing with time, set aside the "red shift"?

I'm saying this because from what I understand until now:

* we receive photons from *FAO* that were emitted long long ago
* due to space expansion, some of those objects will be moving away at speed greater than the speed of light.

So there must be a point in time at which these far away objects disappear from view. How is this concept called?, or is it only a mistake I'm doing in my thinking?

Here's a simple drawing to illustrate:

* at t=-11 billion years(By), photons are emitted in a slow expanding universe, and today we can view the object as it was
* at t=-2 By, the object moves faster than speed of light, so photon emitted at that time will never reach us, even if we wait the 9 by + "expansion correction" needed...

[![light from fast receding objects will never reach us](https://i.sstatic.net/VEZjt.png)](https://i.sstatic.net/VEZjt.png)

I couldn't be convinced by the answer I found [here](https://astronomy.stackexchange.com/a/14338/11264), saying nothing disappears out of horizon. I don't see how it complies with [that answer](https://astronomy.stackexchange.com/a/6035/11264) were event horizon approaches us.

**Tags:** universe, expansion, fate-of-universe
> **Comments:**
> **username_1**: Phil Plait says yes.  There's an entry on this topic somewhere in the slate.com/badastronomy column.  
> **username_2**: I think this was also discussed in [this question](http://astronomy.stackexchange.com/questions/19896/what-fraction-of-galaxies-in-the-observable-universe-have-we-actually-observed) yesterday.  
> **username_3**: This question has an excellent answer which carefully and directly addresses the OP's question. Closing as duplicate directs readers away from the ideal answer, which in my opinion does more damage than good. The two questions are now linked, but there is no reason to shut this page down. **voting to reopen open**  
> **username_4**: I wouldn't suggest reopening is good, however merging is a good option where there are good answers on two questions that are duplicates.  

---

## 1 answers

### Answer by username_5 on 2017-01-31. Score: 26 | Accepted answer

It is a common misconception that galaxies receding faster than light cannot be observed. There are two versions of this misconception:

1. Galaxies that are *now* receding faster than light cannot be seen.
2. If we observe a galaxy *today*, it may recede faster than light *now*, but when it emitted the light we see now, it did not.

Both are incorrect.

#### **Intuitive explanation**

This is most easily seen in a spacetime diagram. But before showing that, a somewhat intuitive way of understanding this apparent paradox is to consider the journey of the photon from the reference frame of the emitting galaxy: In this frame, the photon leaves the emitter with a velocity $v=c$ (as it should), but as it increases its distance from the source, there's more and more space that can expand. That means that its distance increases faster and faster, i.e. that its velocity increases without bounds. This is not a proof, but may help to show that "light may travel faster the the speed of light".

#### **Spacetime diagram**

Now to the spacetime diagram. My favorite version is from the classic paper by [Davis & Lineweaver (2004)](https://arxiv.org/abs/astro-ph/0310808), but I actually like better this version from [Pulsar's excellent (!) post](https://physics.stackexchange.com/a/63780/70207):

[![spacetime](https://i.sstatic.net/SR9EP.png)](https://i.sstatic.net/SR9EP.png)

#### **Real example of a galaxy that has always been, and always will be, receding with superluminal velocity**

Such a diagram shows age (or, equivalently, size) of the Universe, as a function of the corresponding comoving distance$^1$ of events. A lot of things are going on in this diagram, and I'll refer to Pulsar's answer for an interesting discussion of all this. For our purposes, consider the only thing the I have added to the figure: the world line — i.e. the "path" taken through spacetime of some object — of the galaxy [GN-z11](https://en.wikipedia.org/wiki/GN-z11), seen as a vertical dashed line at a comoving distance $d\_C \simeq 32.2\,\mathrm{Gly}$. It is vertical, because it doesn't move in comoving coordinates. We observe it at a redshift of $z=11.09$, which means that the light we see (moving at 45º toward *our* worldline which is at $d\_C=0$) was emitted when the Universe was roughly 400 Myr old. At that time, GN-z11 was receding at a velocity $v\simeq4c$!

#### **Hubble sphere and event horizon**

The innermost green bubble (labeled "$v\_\mathrm{rec}=c$") is the *Hubble sphere*, defined such that at any point in time, everything outside recedes faster than $c$. Meanwhile, the red line shows the *event horizon*, which defines the boundary between everything that *can* eventually be observed (light red region), and everything that cannot. A subset of this is out *past lightcone* (orange region) which is stuff that we have already observed (or at least have had the chance to).

Everything lying in between the Hubble sphere and the event horizon consists of events that we have been, or will eventually be, able to see, but which recede faster than the speed of light when it emits the light we see.

As you can see the region becomes narrower with time$^2$, meaning that the accelerated expansion of the Universe makes it harder and harder for photons emitted far away to reach us. We will never be able to see galaxies that today are farther away than roughly 17 Gly. But galaxies that are nearer *will* be seen (if we look), and a subset of these — namely the ones with $14\,\mathrm{Gly} \lesssim d\_C \lesssim 17\,\mathrm{Gly}$ — are currently receding faster than the speed of light.

#### **The size of the observable Universe always increases**

The observable Universe is defined as the region within which light has had the time to reach us. The "edge" of this is called the *particle horizon*, and as seen from the blue line, it always increases its distance from us (in comoving coordinates, and thus even more so in physical coordinates). In comoving coodinates, it reach a maximum size of roughly 63 Gly. That means that more and more galaxies will enter our observable Universe, but as time goes they will do so at an ever-decreasing pace, asymptotically reaching a finite value (of 5 trillion galaxies, more or less). Once inside the particle horizon, a galaxy will never leave. It will, however, keep increasing its distance from us in physical coordinates, as well as its speed, and thus redshift without bounds and fade to black.

---

$^1$Comoving coordinates are defined so that they "expand with the expansion of the Universe". That means that in these coordinates, galaxies lie approximately still wrt. each other. To get the *physical* coordinates — i.e. what you would measure if you froze the Universe and laid out measuring rods — multiply the comoving coordinates by the scale factor $a$ seen on the right $y$ axis. Since today $a\equiv1$, comoving and physical coordinates coincide today.

$^2$The fact that the diagram is in comoving coordinates makes it a bit hard to see, but this is still the case in physical coordinates.

> **Comments:**
> **username_6**: nice answer! 2 questions: can you elaborate more what the event horizon is? I've read on wikipedia, it's the lower limit for the radius of an object with mass. Below this radius, it would become a blackhole. I can understand that, but what then is the event horizon drawn into that diagram? Is is the radius corresponding to the total mass of the universe? Does this even make sense? 2. How is this diagram derived?  
> **username_5**: @t.rathjen: 1. An "event horizon" is a boundary that separates spacetime event that cannot influence each other. What you are referring to is the event horizon of a black hole. I am talking about the _cosmic_ event horizon which is related, but different, thing. It is the boundary between what in the Universe may, and what may not, influence us. Its size is dictated by the expansion rate of the Universe, not by its total mass.  
> **username_5**: 2. The diagram is created using the various relations between redshift/scale factor and comoving distance, age of the Universe, expansion rate etc. Most of these quantities require integrating numerically the Friedman equation, which can be done using e.g. the Python module "cosmolopy.distance".  
> **username_0**: Now I start getting it... Light we receive from GN-z11 has ~traveled far more than 11Gly before reaching us... so it looks like light traveled quicker. I think I got my misconception from books where they were exploring theory where universe dominated by [phantom energy](https://en.wikipedia.org/wiki/Phantom_energy)(with an equation of state with $w$ < -1...  
> **username_0**: @pela, what does this spacetime diagram would look like with $w$ < -1?  
> **username_5**: @J.Chomel: Well, the distance to GN-z11 _today_ is 32.2 Gly (or 10 Gpc). The distance when the light that we see today was _emitted_ was 32.2 Gly / (1+z) = 2.7 Gly. Although the distance to GN-z11 has thus increased by (32.2-2.7) Gly = 29.5 Gly during its journey, part of this is not due to light propagating, but due to expansion. The total path that the light "by itself" has traveled is given by the time it took, divided by the speed of light, i.e. 13.4 Gyr / c = 13.4 Gly.  
> **username_5**: Regarding a w < -1 plot, I can make one at some point, but I don't have the time now. I'm not used to thinking about w < -1 so I would have to think, but I suppose since the plot is in comoving coordinates, the 45º lines would still be 45º, but the dashed purple lines would be more skewed toward to upper corners. Hmm… don't take this too seriously, I'm not quite sure right now…  
> **username_0**: ^   Now I start getting it... Light we receive from GN-z11 has ~traveled far more before reaching us than the distance it was from us at the time that light was emitted (2.7Gly) ... so it looks like light traveled quicker.  
> **username_5**: @J.Chomel Yes, exactly!  

---

