The Boundary of the Observable Universe

[Jaime Rudas]

TL;DR Summary

Is the particle horizon the boundary of the observable universe? Can some objects leave the observable universe? Can objects outside the observable universe influence the characteristics of objects we can observe?

In a recent discussion on the Cosmological Redshift in Simulated Universe thread, I claimed that the boundary of the observable universe is the particle horizon, that objects could enter the observable universe but could not leave it, and that objects outside the observable universe could not influence the characteristics of objects we can observe. @PeterDonis called these claims false or wrong.

In this regard, the Davis & Lineweaver 2003 paper (which has been referenced in plenty of PF threads) states:

"The particle horizon is the distance light can have travelled from t = 0 to a given time t" [Page 2]

"Currently observable light that has been travelling towards us since the beginning of the universe, was emitted from comoving positions that are now 46 Glyr from us." [Page 3]

"The particle horizon marks the size of our observable universe. It is the distance to the most distant object we can see at any particular time." [Page 4]

"[The] photons we receive that have infinite redshift were emitted by objects on our particle horizon." [Page 4]

"The particle horizon [...] marks the size of our observable universe because we cannot have received light from, or sent light to, anything beyond the particle horizon." [Page 9]

Given the above, is it false to claim that the boundary of the observable universe is the particle horizon? Is it wrong to claim that objects can enter the observable universe but can't leave it? Is it wrong to say that objects outside the observable universe can't influence the characteristics of objects we can observe?

 

[PeterDonis]

Given the above, is it false to claim that the boundary of the observable universe is the particle horizon?

Yes, if we adopt the interpretation that boundary means boundary in spacetime, which is the interpretation I will use in this post. The particle horizon line in the diagram in Figure 1 of Davis & Lineweaver is not the boundary in spacetime of the observable universe. The boundary in spacetime of the observable universe "now", i.e., all the events which we at distance "0" can observe "now", is the past light cone. The boundary in spacetime of the region containing all the events that will ever be observed by an observer at distance "0" is the event horizon.

"The particle horizon marks the size of our observable universe. It is the distance to the most distant object we can see at any particular time."

Yes, but this does not mean the particle horizon line in the diagram is the boundary of the observable universe in spacetime. What it means is that the comoving distance at which the particle horizon line crosses the "now" surface is the same as the comoving distance at which the boundary of the past light cone crosses the "initial singularity" surface.

Is it wrong to claim that objects can enter the observable universe

Yes. If you look at the diagram in Figure 1, it should be obvious that no worldline ever enters the region of spacetime bounded by the past light cone.

but can't leave it?

Yes. The worldlines of objects can obviously leave the past light cone region of spacetime, and the event horizon region of spacetime, so that all we can see of the history of those objects, and all we will ever see of that history, is some initial segment.

Is it wrong to say that objects outside the observable universe can't influence the characteristics of objects we can observe?

Yes, because portions of their worldlines in the past can still be within our past light cone, even if their worldlines "now" are not.

 

[Ibix]

The intersection between the particle horizon and the constant time surface "now" is the boundary of the region currently containing co-moving objects that have been in our past lightcone, yes. So objects can only enter it, not leave it, because the particle horizon is an outgoing null surface.

But it's worth remembering that the context of that thread was about a very much non-co-moving object (the OP's black hole). With its enormous peculiar velocity, it may (oddly) be observable without being in the observable universe. That is easiest to see on the bottom graph in Davis and Lineweaver's figure 1 - pick any point on the bottom of the graph inside our past lightcone and draw a line sloping away from us at 44.99...9°. It can be seen (light from it is a 45° slope in the other direction), but is not in the observable universe.

I think you are correct in what you are saying, but the other thread's topic is odd-ball enough that I think you both may have been talking past each other there. Unfortunately I only skimmed what was said in the other thread and it's now deleted, but that would be my guess.

 

[PeterDonis]

"The particle horizon marks the size of our observable universe. It is the distance to the most distant object we can see at any particular time."

Note that this statement (very unfortunately in a paper which tries to correct misunderstandings) does invite a misunderstanding: that if we take an object whose worldline is just crossing the particle horizon "now", meaning that it is at a comoving distance that is just within our observable universe "now", we see that object as it is "now". Of course that is false: we see the object as it was just after the "initial singularity" surface in the diagram, since that is the portion of its worldline where the light we are seeing from it now was emitted.

In other words, the statement quoted above invites the interpretation that our "observable universe" is a region of space, instead of a region of spacetime. But when we focus on what we can actually see, on the light that is actually reaching us from distant objects, which in turn determines what can affect us causally, it should be obvious that in practice, the region of spacetime that contains events within our past light cone is the region that is actually relevant. I do find it unfortunate that this point is not made clearly in the otherwise very useful paper by Davis & Lineweaver.

 

[PeterDonis]

the boundary of the region containing co-moving objects that have been in our past lightcone, yes. So objects can only enter it, not leave it, because the particle horizon is an outgoing null surface.

To put this another way: the set of comoving objects whose worldlines have some portion within our past light cone always gets larger, not smaller. So it is possible, if we use the term "observable universe" to mean something like "the set of comoving objects whose worldlines we can see some portion of", to say that objects can only enter our observable universe, not leave it.

However, as I said in previous posts, I think this interpretation invites other misunderstandings, which is unfortunate in a paper that is trying to correct misunderstandings.

 

[PeterDonis]

the context of that thread was about a very much non-co-moving object (the OP's black hole).

I don't think the OP of the other thread intended their black hole to be non-comoving. If anything, I think they intended their "cloud", receding from the hole at ultrarelativistic speed, to be non-comoving. But either way, I agree that one can't apply reasoning based on any common concept of "observable universe" in such a scenario, since the common concepts of "observable universe" all deal only with comoving objects.

 

[PeterDonis]

I think you both may have been talking past each other there.

That's quite possible if we were interpreting the term "observable universe" to mean different things.

 

[Ibix]

I don't think the OP of the other thread intended their black hole to be non-comoving. If anything, I think they intended their "cloud", receding from the hole at ultrarelativistic speed, to be non-comoving. But either way, I agree that one can't apply reasoning based on any common concept of "observable universe" in such a scenario, since the common concepts of "observable universe" all deal only with comoving objects.

I think, to be honest, if we're talking about a universe containing a black hole with a mass several orders of magnitude larger than the dust cloud that we can see, and which is empty enough that said dust cloud can travel at ultra-relativistic speeds without being obliterated, we aren't in Kansas any more and we shouldn't really be talking about co-moving or otherwise. At best we're talking about something like an out-going Vaidya metric with high speed timelike dust instead of null.

 

[PeterDonis]

pick any point on the bottom of the graph inside our past lightcone and draw a line sloping away from us at 44.99...9°. It can be seen (light from it is a 45° slope in the other direction), but is not in the observable universe.

Note that this illustrates a key issue with interpreting "observable universe" to mean "the set of objects whose comoving distance from us now is less than the particle horizon distance now". The object in question has a portion of its worldline within our past light cone--so it is in the region of spacetime that we can observe, hence it, or at least a portion of its history, is within our observable universe by the definition I have been using. And hence that portion of its history can affect us causally, even though a comoving object whose comoving distance from us "now" was the same (i.e., beyond our particle horizon distance "now") would have a worldline that was entirely outside our past light cone "now" and hence would not have any portion of its history able to affect us causally "now".

In other words, the "region of spacetime" interpretation generalizes easily to any object, whatever its state of motion. Just look at the object's worldline and our past light cone and see if they intersect. Whereas the "region of space" interpretation only works if all the objects involved are always comoving for their entire history.

 

[PeterDonis]

if we're talking about a universe containing a black hole with a mass several orders of magnitude larger than the dust cloud that we can see, and which is empty enough that said dust cloud can travel at ultra-relativistic speeds without being obliterated

That could happen in our actual universe as far as the relative sizes are concerned. The only part that is highly unlikely in our actual universe is the dust cloud having ultrarelativistic velocity relative to the hole--though even that might not be so unlikely if we look at jets emitted by rotating black holes in distant galaxies, at least some of which do have velocities relative to the emitting holes that are close to the speed of light. But there is no issue at all with embedding the scenario that was described in an overall universe whose global structure is similar to ours.

 

[Ibix]

That could happen in our actual universe as far as the relative sizes are concerned

Can it? The black hole was supposed to be 4,600 Gly radius, so something like 100 times the mass of the observable universe. That would mean it's swept up all the matter in a sphere about $\sqrt[3]{100}\approx 4.6$ times the diameter of the observable universe (assuming near flat space), which it doesn't have time to do unless the universe is, at absolute minimum, 4.6 times older than we think (and that's an absolute minimum). And something about our region meant we didn't get drawn in too, which I think implies our entire observable universe is also an enormous over-dense region that somehow hasn't collapsed on a timescale that allowed a much larger region to completely collapse.

I know you can perturb FLRW solutions to get more realistic models that form stars and galaxies. I'm just wondering about the power spectrum of perturbations that allows a more-or-less FLRW universe on our observable universe's length scale, but also allows fluctuations on much larger scales.

 

[Jaime Rudas]

Yes, if we adopt the interpretation that boundary means boundary in spacetime, which is the interpretation I will use in this post.

So you call my statement false because you interpreted it completely wrong?

The particle horizon line in the diagram in Figure 1 of Davis & Lineweaver is not the boundary in spacetime of the observable universe. The boundary in spacetime of the observable universe "now", i.e., all the events which we at distance "0" can observe "now", is the past light cone.

False. The limit of the observable universe "now" is a sphere of radius 46 Gly centered on the observer and, in cosmology, this limit is called the (current) particle horizon.

If you look at the diagram in Figure 1, it should be obvious that no worldline ever enters the region of spacetime bounded by the past light cone.

Yes, that is obvious, but what I am referring to is the observable universe that you insist on confusing with "the region of spacetime bounded by the past light cone".

 

[PeterDonis]

The black hole was supposed to be 4,600 Gly radius

Yes, but remember our best current model of our universe is spatially infinite. Just consider a similar model far enough in the future for the size of the observable universe to approach the size of the event horizon, and with a small enough cosmological constant (and hence a large enough event horizon) that the area "swept clean" by the hole is small compared to the spatial extent of the region within the event horizon. The relevant qualitative features will still be similar enough.

So yes, I did misspeak slightly when I said it could happen in our actual universe--I had forgotten about the 4,600 Gly part. But it could happen in a universe similar enough to ours in the relevant qualitative features.

 

[PeterDonis]

False.

No, my statement was not false. It was just referring to something different than what you are referring to.

a sphere of radius 46 Gly centered on the observer and, in cosmology, this limit is called the (current) particle horizon.

And this is not a boundary in spacetime. It is a boundary in space in the spacelike hypersurface labeled "now" in the diagram. The boundary in spacetime of the spacetime region containing events that we can observe is what I stated.

 

[PeterDonis]

So you call my statement false because you interpreted it completely wrong?

I have already agreed (in response to @Ibix, not you) that we were talking past each other in the previous thread. I apologize for the confusion on my part.

(Please note that you did not receive any penalty for your posts in the other thread; both your posts and mine in that subthread were simply deleted. I was going to PM you to suggest that you start a new thread addressing the topic, when I saw that you already had. The topic itself is a perfectly legitimate question and this thread is the right place to discuss it.)

 

[Jaime Rudas]

In other words, the statement quoted above invites the interpretation that our "observable universe" is a region of space, instead of a region of spacetime.

Can you provide some reference that indicates that the observable universe isn't a region of space, but a region of spacetime?

 

[Jaime Rudas]

(Please note that you did not receive any penalty for your posts in the other thread; both your posts and mine in that subthread were simply deleted. I was going to PM you to suggest that you start a new thread addressing the topic, when I saw that you already had. The topic itself is a perfectly legitimate question and this thread is the right place to discuss it.)

I am very grateful that I was not penalized for the post that showed that the original post in the other thread presented an impossible scenario, a post that was deleted without warning and without any explanation.

 

[PeterDonis]

Can you provide some reference that indicates that the observable universe isn't a region of space, but a region of spacetime?

See, for example, this paper:

https://arxiv.org/pdf/2207.05765

The paper never actually defines what it means by the term "observable universe" (which, aside from the title, is used in only a few places in the paper); but the content of the paper makes it clear that it is talking about what we actually observe, i.e., what is in our past light cone. The basic idea of the paper is to address the question of whether our observations are consistent with the cosmological principle (i.e., homogeneity and isotropy).

 

[PeterDonis]

this statement (very unfortunately in a paper which tries to correct misunderstandings) does invite a misunderstanding: that if we take an object whose worldline is just crossing the particle horizon "now", meaning that it is at a comoving distance that is just within our observable universe "now", we see that object as it is "now".

For an example along these lines, consider this paper:

https://arxiv.org/abs/1908.07533

It talks about how much of the "volume of the observable universe" can be probed using various methods, and it defines "volume" as spatial volume "now"--in other words, it is basically talking about what fraction of all comoving objects in the spatial observable universe can actually be observed by these methods.

But what it does not talk about is that the spacetime volume we can actually observe--which is what is relevant if we are trying to assess how much evidence we have in favor of our best current cosmological models--is a much smaller fraction than 80% of the total spacetime volume in our past light cone. In other words, the actual evidence we have is much weaker than this paper leads one to believe.

For example, consider this statement from the abstract: "large-scale structure must be mapped over a wide range in frequency to trace its time evolution over a reasonable fraction of the volume of the observable Universe"

But that's not what's being traced. We cannot trace the time evolution of a comoving object billions of light years away over any substantial fraction of its history. The best we can do is to take what we see of different comoving objects, at very different distances from us, which we are seeing tiny snapshots of at very different stages of their history, and infer something about the time evolution of individual objects from that data. Which is, of course, much weaker support for any proposed model of such time evolution, than actually being able to observe billions of years' worth of time evolution of particular objects would be. The terminology used in the paper invites the misunderstanding that the latter is the kind of evidence being collected, when in fact it's only the former.

 

[Ibix]

Can you provide some reference that indicates that the observable universe isn't a region of space, but a region of spacetime?

Tong's notes define (p16)$$d_H=ca(t)\int_0^t\frac{dt'}{a(t')}$$This is clearly an increasing quantity in an expanding universe, and this is immediately followed by "[t]his is the size of the observable universe". That is consistent with your interpretation of "observable universe" and Davis & Lineweaver. However, Tong goes on to say (p17, literally the next paragraph) that "[t]he distance $d_H$ is sometimes referred to as the particle horizon" and then adds that "nothing outside the particle horizon can influence us today". Coupled with figure 8 (p18), it looks like Tong is here regarding the particle horizon as what Davis & Lineweaver's figure 1 labels the light cone - and this is consistent with Peter's interpretation of "observable universe".

So, unless I'm very much misreading Tong, even reputable sources can get in a contradictory mess with terminology in two consecutive paragraphs. So I would advise a cautious and flexible reading of anything on this topic.

 

[Ibix]

On a personal note, reflecting on this discussion, I'd say it does seem odd to name a spatial volume, some of which will never be observable to us, "the observable universe". The surface or interior of the light cone does seem a much more reasonable thing to name "observable universe". In that interpretation, $d_H$ is the distance today to the furthest co-moving object that we could (in principle) be affected by today, and hence "the size of the observable universe", while not actually being a direct measure of the observable universe (!).

 

[PeterDonis]

@Devin-M I have moved your post to your original thread and reopened it so that discussion of the scenario you proposed can continue there. This thread is for discussion of the other topic raised by @Jaime Rudas.

 

[Jaime Rudas]

Tong's notes define (p16)$$d_H=ca(t)\int_0^t\frac{dt'}{a(t')}$$This is clearly an increasing quantity in an expanding universe, and this is immediately followed by "[t]his is the size of the observable universe". That is consistent with your interpretation of "observable universe" and Davis & Lineweaver. However, Tong goes on to say (p17, literally the next paragraph) that "[t]he distance $d_H$ is sometimes referred to as the particle horizon" and then adds that "nothing outside the particle horizon can influence us today". Coupled with figure 8 (p18), it looks like Tong is here regarding the particle horizon as what Davis & Lineweaver's figure 1 labels the light cone - and this is consistent with Peter's interpretation of "observable universe".

So, unless I'm very much misreading Tong, .

I think you are misinterpreting Tong. What Tong's figure 8 shows does not contradict what the bottom panel of Davis & Lineweaver's figure 1 shows. Perhaps the only difference is that Tong does not show how the particle horizon evolves over time, but only shows the distance to it at present.

 

[Ibix]

Perhaps the only difference is that Tong does not show how the particle horizon evolves over time, but only shows the distance to it at present.

But Tong says "nothing outside the particle horizon can influence us today". That's a description of our past light cone.

To be fair, the statement is also true of events now that are outside what you and Davis and Lineweaver call the observable universe. But it is also true of events now that are inside it - so on your reading Tong's statement is vacuous.

 

[Jaime Rudas]

But Tong says "nothing outside the particle horizon can influence us today". That's a description of our past light cone.

To be fair, the statement is also true of events now that are outside what you and Davis and Lineweaver call the observable universe. But it is also true of events now that are inside it - so on your reading Tong's statement is vacuous.

I think you are misunderstanding Tong again. He is not referring to whether current events within the particle horizon can influence us now, but rather whether objects that are or are not within the particle horizon today can or cannot influence us now. That is, the possibility that past events of those objects can influence us now.

 

[Jaime Rudas]

No, my statement was not false. It was just referring to something different than what you are referring to.

And this is not a boundary in spacetime. It is a boundary in space in the spacelike hypersurface labeled "now" in the diagram. The boundary in spacetime of the spacetime region containing events that we can observe is what I stated.

No, it is not true that we were referring to different things. You stated that it was false that the particle horizon was the boundary of the observable universe. You also stated that the observable universe is not a region in space, but a region in spacetime whose boundary is the past light cone. I consider that statement false, among other things, because if the observable universe is not a region in space, it cannot be 93 Gly wide, as you stated it was in another post.

 

[Jaime Rudas]

Coupled with figure 8 (p18), it looks like Tong is here regarding the particle horizon as what Davis & Lineweaver's figure 1 labels the light cone - and this is consistent with Peter's interpretation of "observable universe".

So, unless I'm very much misreading Tong,

As a complement to my post #23, I note that Davis & Lineweaver in 3.4 and figure 3 (lower panel) carry out a detailed analysis of the drawbacks of representing the particle horizon as the dashed vertical line in Tong's figure 8.

 

[PeterDonis]

it is not true that we were referring to different things.

Yes, we were. I was using the term "observable universe" to refer to a region in spacetime. You were using it to refer to a region in space. As I've pointed out once already, I have agreed that we were talking past each other in the other thread. I have also apologized for the confusion on my part as to what we were each using the term "observable universe" to refer to. Given all that, I would appreciate it if you would stop arguing over this point.

All that said, "observable universe" is just words. Words are not physics. As far as I can see, we have no disagreement about the actual physics--what can causally affect what, what things we can actually observe or not. But if you do still have questions about the physics which you think have not been resolved, that is what I think we should focus on.

 

[Dale]

A few posts discussing moderation actions have been deleted.

This forum is for technical content only. Please post comments about moderation actions (including complaints) in the feedback forum. That forum is provided explicitly to provide a place where such things may be discussed without detracting from the technical content.

(And yes, I recognize the irony inherent in this post)

 

[Jaime Rudas]

The intersection between the particle horizon and the constant time surface "now" is the boundary of the region currently containing co-moving objects that have been in our past lightcone, yes. So objects can only enter it, not leave it, because the particle horizon is an outgoing null surface.

Yes this is true, but it is important to note that, since the particle horizon recedes at the local speed of light, it contains not only comoving objects, but all objects that have been in our past lightcone, regardless of their own peculiar velocity.

But it's worth remembering that the context of that thread was about a very much non-co-moving object (the OP's black hole). With its enormous peculiar velocity, it may (oddly) be observable without being in the observable universe. That is easiest to see on the bottom graph in Davis and Lineweaver's figure 1 - pick any point on the bottom of the graph inside our past lightcone and draw a line sloping away from us at 44.99...9°. It can be seen (light from it is a 45° slope in the other direction), but is not in the observable universe.

I don't think I understand the figure you propose, but the highlighted part seems contradictory to me because any point I choose within our past lightcone will necessarily be within our observable universe. On the other hand, if something is outside our observable universe, the photons it emitted even at the beginning of the universe would not have had time to reach us, that is, it is not possible to see them. Keep in mind that whether we see something or not does not depend on the object's peculiar velocity.

 

[PeterDonis]

if something is outside our observable universe, the photons it emitted even at the beginning of the universe would not have had time to reach us

Only if it is a comoving object. That is @Ibix's point. If the object is not comoving, this statement you are making is no longer always true. It is possible for a non-comoving object to be outside our particle horizon now, but to have a portion of its worldline in our past light cone now.

 

[Jaime Rudas]

Only if it is a comoving object. That is @Ibix's point. If the object is not comoving, this statement you are making is no longer always true. It is possible for a non-comoving object to be outside our particle horizon now, but to have a portion of its worldline in our past light cone now.

Could you provide a concrete numerical example of this?

 

[PeterDonis]

Could you provide a concrete numerical example of this?

Consider an object that, at the "now" surface of the bottom diagram of Fig. 1 in Davis & Lineweaver 2003 (the one that uses conformal time), is at a comoving distance of 50 Gly. That puts it outside the particle horizon.

Now draw a worldline from that point that goes down and inward, decreasing in comoving distance, so that, at the initial moment of time (the bottom line of the diagram), it is at a comoving distance of 20 Gly. That is a timelike worldline (because its slope is closer to vertical than 45 degrees, and on a conformal diagram, that is timelike), and it has a substantial segment that is within our past light cone "now", so we will be able to see that portion of its history.

 

[Bandersnatch]

And that works to at most twice the distance of the particle horizon, as beyond that distance not even an object moving away at arbitrarily close to light speed could ever have been inside our past light cone.
Since I've never heard of this distance be called anything, I call dibs on naming rights. From now on it will be known as the particlest horizon :P

 

[Orodruin]

From now on it will be known as the particlest horizon

If there is a particle horizon and a particlest horizon there must be a particler horizon …