<p>The <em>particle horizon</em> marks the region from within which we may have received light. It started out at zero, because light from nowhere had had the time to reach us, and increased as time went by because light from increasingly larger distance reached us. Due to the expansion it will always increase in physical size, but due to the <em>accelerated</em> expansion, there is a limit to the region of the Universe that we will ever be able to receive light from. Today, the particle horizon is 46 Glyr (billion lightyears) away, and the limit — in the far future — is the part that <em>today</em> is 63 Glyr away (but in the far future will be much farther away).</p>

<p>The <em>event horizon</em> can be thought of as sort of the opposite. At any time $t$, it is the distance from which we will be able to receive light. If the Universe contained no dark energy, there would be no limit to how distant a galaxy could be and we would still be able to see it — just wait long enough. However, the accelerated expansion means that an increasingly smaller part of the Universe will be able to emit light toward us with us receiving it, before the expansion carries the photons away faster than they can travel toward us.</p>

<p>At Big Bang, the event horizon consisted of particles that today are 63 Glyr away — that's what I meant by "the opposite of the particle horizon".</p>

<p>The following figure from <a href="https://arxiv.org/abs/astro-ph/0310808" rel="nofollow noreferrer">Davis &amp; Lineweaver (2004)</a> may help explain. It show basically three versions of the same thing, namely how the sizes of various horizons evolve with time. The top panel shows time as a function of physical size, while in the middle panel, the $x$ axis show <em>comoving</em> coordinates, i.e. the coordinates that expand along with the Universe. The lower panel shows not time on the $y$ axis, but conformal time, which can be thought of as the time it would take a photon to travel a distance if we "froze" the Universe.</p>

<p><a href="https://i.sstatic.net/JdoRt.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/JdoRt.png" alt="horizons"></a></p>

CC BY-SA 3.0
2018-05-01T16:55:58.143Z
Are my definitions of the two horizons incorrect?
Benjamin
CC BY-SA 3.0
2018-05-01T16:57:01.113Z
So, basically, at some particular time in the future, the two horizons will cross?
Carl Witthoft
CC BY-SA 3.0
2018-05-01T17:14:57.137Z
@Benjamin No, they're not incorrect, but I think perhaps you're thinking of the horizons in a too "physical" sense. The horizons are not "fixed", neither in physical, nor in comoving coordinates. There isn't a galaxy sitting somewhere on the event horizon that stays at the horizon. They're are simply distances defined how far light can travel between to points in time.
pela
CC BY-SA 3.0
2018-05-01T17:17:03.030Z
@CarlWitthoft They already did that, when the Universe was ~4 Gyr old.
pela
CC BY-SA 4.0
2021-10-14T23:45:02.160Z
Sorry I'm a bit dense, but, re conformal time being "the time it would take a photon to travel if we 'froze' the Universe", what distance might it somehow be travelling, or at what velocity would it be travelling?  (I'd tend to consider a photon a part of the Universe if it would be inboard from our cosmological event horizon, so, if all motion from it would stop, wouldn't the photon stop as well?)  If you mean the distance a photon would travel if we'd stop the expansion of space, are you referring to its travel between a different causal patch, temporal iteration, or local universe & ours?
Edouard
CC BY-SA 4.0
2021-10-15T21:53:05.617Z
@Edouard Yes, by "freezing the Universe" I meant "magically stop the expansion in a way that would still let photons travel through it at the speed of light". I'm unsure what you mean by the last part though?
pela
CC BY-SA 4.0
2021-10-16T03:01:46.677Z
The last part had to do with Brian Greene's discussion (in his 2020 pop-sci book titled "Until the End of Time") of Leonard Susskind's application of Poincare recurrence to the universe surrounding our observable region by interpretation of it as equivalent to a closed container (which Susskind calls a "causal patch"), with complementarity in the explanations of phenomena on opposite sides of a cosmological event horizon:  Greene describes wave and particle descriptions of light as an analogue to the way in which such "horizon complementarity" would work.
Edouard
CC BY-SA 4.0
2021-10-16T08:40:19.157Z
@Edouard Hmm… I'm not sure the Poincaré recurrence applies to our Universe as a whole, but this is beyond my knowledge. What I tried to say is that the conformal time is the distance in Glyr, divided by the speed of light. That means that it's the time it would take a photon to travel that distance, if it wasn't for expansion.
pela
CC BY-SA 4.0
2021-10-16T14:08:05.530Z
Laura Mersini-Houghton has been arguing against cosmological applications of Poincare recurrence since at least 2012, but I believe her last word on the subject saw it (in Section IV of https://www.arxiv-vanity.com/papers/hep-th/0511102/) as a phenomenon that might occur upon the appearance of quantum phenomena.  All of which sounds like a video replay of reality to me, but maybe it is....
Edouard
CC BY-SA 3.0
2018-05-01T16:25:06.727Z
2018-05-01T16:32:06.647Z
2018-05-01T16:32:06.647Z
pela
<p>From what I learned, cosmological event horizon is the horizon that moves away from us at/more than the speed of light. And particle horizon is the horizon that particles inside the horizon can have a causal connection with us. It is the maximum distance from which particles could have traveled to the observer in the age of the universe. This simply indicates a contradiction to me. How is it possible that the cosmological event horizon is closer?</p>

CC BY-SA 3.0
2018-05-01T16:10:46.670Z
What's your source for the claim that cosmo is closer than particle?
Carl Witthoft
CC BY-SA 3.0
2018-05-01T16:14:32.527Z
@CarlWitthoft It's true.
pela
CC BY-SA 3.0
2018-05-01T16:15:27.290Z
@pela why though could you please explain?
Benjamin
CC BY-SA 3.0
2018-05-01T16:15:49.740Z
@CarlWitthoft youtube.com/watch?v=AwwIFcdUFrE It is from a pbs space time video at 3:35. I would really appreciate it if you can take a look.
Benjamin
<cosmological-horizon><event-horizon>
Why is cosmological event horizon closer to us than the particle horizon?
Benjamin
# Why is cosmological event horizon closer to us than the particle horizon?

(Asked by: username_0 on 2018-05-01)

From what I learned, cosmological event horizon is the horizon that moves away from us at/more than the speed of light. And particle horizon is the horizon that particles inside the horizon can have a causal connection with us. It is the maximum distance from which particles could have traveled to the observer in the age of the universe. This simply indicates a contradiction to me. How is it possible that the cosmological event horizon is closer?

**Tags:** cosmological-horizon, event-horizon

> **Comments:**
> **username_1**: What's your source for the claim that cosmo is closer than particle?  
> **username_2**: @username_1 It's true.  
> **username_0**: @username_2 why though could you please explain?  
> **username_0**: @username_1 youtube.com/watch?v=AwwIFcdUFrE It is from a pbs space time video at 3:35. I would really appreciate it if you can take a look.  

---

## 1 answers

### Answer by username_2 on 2018-05-01. Score: 3

The *particle horizon* marks the region from within which we may have received light. It started out at zero, because light from nowhere had had the time to reach us, and increased as time went by because light from increasingly larger distance reached us. Due to the expansion it will always increase in physical size, but due to the *accelerated* expansion, there is a limit to the region of the Universe that we will ever be able to receive light from. Today, the particle horizon is 46 Glyr (billion lightyears) away, and the limit — in the far future — is the part that *today* is 63 Glyr away (but in the far future will be much farther away).

The *event horizon* can be thought of as sort of the opposite. At any time $t$, it is the distance from which we will be able to receive light. If the Universe contained no dark energy, there would be no limit to how distant a galaxy could be and we would still be able to see it — just wait long enough. However, the accelerated expansion means that an increasingly smaller part of the Universe will be able to emit light toward us with us receiving it, before the expansion carries the photons away faster than they can travel toward us.

At Big Bang, the event horizon consisted of particles that today are 63 Glyr away — that's what I meant by "the opposite of the particle horizon".

The following figure from [Davis & Lineweaver (2004)](https://arxiv.org/abs/astro-ph/0310808) may help explain. It show basically three versions of the same thing, namely how the sizes of various horizons evolve with time. The top panel shows time as a function of physical size, while in the middle panel, the $x$ axis show *comoving* coordinates, i.e. the coordinates that expand along with the Universe. The lower panel shows not time on the $y$ axis, but conformal time, which can be thought of as the time it would take a photon to travel a distance if we "froze" the Universe.

[![horizons](https://i.sstatic.net/JdoRt.png)](https://i.sstatic.net/JdoRt.png)

> **Comments:**
> **username_0**: Are my definitions of the two horizons incorrect?  
> **username_1**: So, basically, at some particular time in the future, the two horizons will cross?  
> **username_2**: @username_0 No, they're not incorrect, but I think perhaps you're thinking of the horizons in a too "physical" sense. The horizons are not "fixed", neither in physical, nor in comoving coordinates. There isn't a galaxy sitting somewhere on the event horizon that stays at the horizon. They're are simply distances defined how far light can travel between to points in time.  
> **username_2**: @username_1 They already did that, when the Universe was ~4 Gyr old.  
> **username_3**: Sorry I'm a bit dense, but, re conformal time being "the time it would take a photon to travel if we 'froze' the Universe", what distance might it somehow be travelling, or at what velocity would it be travelling?  (I'd tend to consider a photon a part of the Universe if it would be inboard from our cosmological event horizon, so, if all motion from it would stop, wouldn't the photon stop as well?)  If you mean the distance a photon would travel if we'd stop the expansion of space, are you referring to its travel between a different causal patch, temporal iteration, or local universe & ours?  
> **username_2**: @username_3 Yes, by "freezing the Universe" I meant "magically stop the expansion in a way that would still let photons travel through it at the speed of light". I'm unsure what you mean by the last part though?  
> **username_3**: The last part had to do with Brian Greene's discussion (in his 2020 pop-sci book titled "Until the End of Time") of Leonard Susskind's application of Poincare recurrence to the universe surrounding our observable region by interpretation of it as equivalent to a closed container (which Susskind calls a "causal patch"), with complementarity in the explanations of phenomena on opposite sides of a cosmological event horizon:  Greene describes wave and particle descriptions of light as an analogue to the way in which such "horizon complementarity" would work.  
> **username_2**: @username_3 Hmm… I'm not sure the Poincaré recurrence applies to our Universe as a whole, but this is beyond my knowledge. What I tried to say is that the conformal time is the distance in Glyr, divided by the speed of light. That means that it's the time it would take a photon to travel that distance, if it wasn't for expansion.  
> **username_3**: Laura Mersini-Houghton has been arguing against cosmological applications of Poincare recurrence since at least 2012, but I believe her last word on the subject saw it (in Section IV of https://www.arxiv-vanity.com/papers/hep-th/0511102/) as a phenomenon that might occur upon the appearance of quantum phenomena.  All of which sounds like a video replay of reality to me, but maybe it is....  

---

