# Can matter leave the cosmic horizon?

Cosmic horizon in the de Sitter space is a sphere, centered at the observer with finite radius where the red shift due to cosmic expansion becomes infinite.

Given that no information can be transmitted from behind the cosmic horizon, I wonder whether any matter can ever pass behind the event horizon, because this will give rise to an information paradox, similar to the black hole information paradox.

The matter approaching the cosmic horizon seems to experience time dilation, so will that time dilation prevent it from crossing the horizon?

To work around the paradox, one have to postulate that the information about outgoing matter should be encoded in the de Sitter radiation.

Everything Thriveth says in his answer is true. However, I can't help feeling it doesn't quite answer the question.

It is indeed correct that no matter can ever pass beyond the cosmic horizon, when considered from the point of view of us, the observers for whom it exists. In this respect it's exactly analogous to a black hole's horizon, in that (again from our point of view), any object attempting to pass it will instead approach it asymptotically, with its emissions becoming rapidly red-shifted to the point where we can't practically detect them.

My general relativity isn't up to showing this in the case of de Sitter spacetime, but it's a property shared by all horizons. It's easiest to see in the case of a Rindler horizon, which is the horizon seen by a continuously accelerated observer. Consider this diagram (from Wikipedia):

The straight lines radiating from the origin are the planes of simultaneity of the accelerated observer. No object reaches the horizon until the observer's $t=\infty$.

Of course, an object passing the horizon will notice nothing special because the horizon only exists for the accelerated observer. The same is true for the cosmic horizon. An observer passing a black hole horizon will also notice nothing special, for the same reason.

• Hmm, you are right. I set up all the pieces for answering the question, but didn't actually answer it. I will try to add a little edit... – Thriveth Jan 15 '14 at 10:55
• "Of course, an object passing the horizon will notice nothing special because the horizon only exists for the accelerated observer." - but the first part of your answerr confirms that nothing will ever pass the horizon in finite time, true? – Anixx Jan 15 '14 at 11:07
• @Anixx, you must remember that time is relative. The event where the object crosses the event horizon will be frozen forever and redshifted to infinity in our rest frame, but to the object we are observing, there is nothing special about the event, and it definitely happens in finite time. And in theory, if you are just a few steps closer to the object than me (discarding the clumpiness of the Universe), the event that will be frozen to infinity for me will be observed in finite time by you. – Thriveth Jan 15 '14 at 12:23
• @Anixx No, that is not true. Because even though there is no point in my time that is the last where I can see you, there will be a point in your time that is the last that I can see, frozen and infinitely redshifted. That event is the "Event" in "Event Horizon". Anything that happens to you after that event will be forever out of my sight. – Thriveth Jan 15 '14 at 12:37
• As for two observers in a bound state: Yes, they will share an event horizon, as they will be co-moving with the same point in Space, which is what defines the event horizon in the first place. – Thriveth Jan 15 '14 at 13:07

There is an important difference between a Schwarzild event horizon and a cosmological event horizon: The latter is unique to each point in Space, just like the Hubble Sphere. From some symmetry considerations it should be fairly clear, that a universe in which no matter could cross any event horizon would have to be a static universe.

From beyond the Black Hole event horizon, no information can ever escape. From beyond the cosmological event horizon no information can ever reach us. That is an important distinction.

When matter falls into a black hole, gravity slows down observed time for any outside observer to asymptotically approach stasis. In the frame of the falling object, however, time will trot on as usual, and the passing of the event horizon will be an event like any other, although it will change the view quite drastically.

In cosmological expansion, as the object moves towards the cosmological event horizon, its light is gradually redshifted towards infinity, which to the observer translates to observed time asymptotically slowing down to a halt. For someone slightly further away from the object, this will have happened at a slightly earlier point in the object's history; for an observer slightly closer, it will happen at a time slightly later in the object's history.
In the object's own frame, however, there is nothing special about the time or the moment at which it crosses OUR unique event horizon. In fact, in an expanding Universe of sufficient size, all objects are crossing event horizons relative to other objects all the time!

In the black hole case, it is true for all observers outside the black hole, that the falling object's observed time is slowing down and grinding to a halt. The object will in its own time frame fall into the black hole, while the entire rest of the universe's history will play out at a accelerating speed approaching infinity.

In the cosmic expansion case, the object's crossing the event horizon is unique to particular observers; to the rest of the Universe, there is nothing special about the event. The object's history goes on in its own local time frame, the only difference being that beyond this time, we will never receive any more information about the object.

To summarize: A given observer will never see an object cross the observer's Event Horizon, very much like an observer will never see an object cross a black hole's event horizon. The difference is that for a black hole, any two observers will agree about which event happens on the Horizon. There is, to the rest of the Universe, one unique event that is the "last" that the Universe will know about the object. This is not the case for a cosmological event horizon, at which the passing event depends on your initial distance from the object. Thus, what we see as the last event ever to happen for this object is just any ordinary event for an observer in the next galaxy over.

• "The later is unique to each point in Space" - can you prove this? Do you and me really have different cosmic horizons? I always thought that all observers who can communicate with each other share the same cosmic horizon. – Anixx Jan 14 '14 at 14:21
• Hmm, I am not an expert on this, but I believe the limiting factor is not whether we can communicate now, but whether we can commmunicate at $t=\infty$. – Thriveth Jan 14 '14 at 15:27
• The Event Horizon is a horizon in time as much as Space, after all. If we have two observers in neighbouring galaxies, and A is slightly closer to the observed object than B, then of course A would be able to observe a slightly later event than B, and if A could then tell B about that event, that would be a paradox. However, A will not observe the limiting event in finite time. And the closer we came to A's limiting event, the farther A would be from B, and thus, the longer it would take for A's story to reach B. – Thriveth Jan 14 '14 at 15:28
• While all this is true, the answer to the question is still that, from our point of view, no matter can ever cross the cosmic horizon. It just approaches it asymptotically and its emissions become red-shifted beyond any reasonable ability to detect them. This is also true in the case of a Rindler horizon for a continuously accelerating observer in flat space. – Nathaniel Jan 15 '14 at 10:41
• You are right @Nathaniel, and I added a summary to clarify this. Thanks for pointing this out. – Thriveth Jan 15 '14 at 12:16

One should be careful not to get confused, because in cosmology we can define two horizons.

The first is called the cosmic event horizon, defined as follows: if a galaxy outside the event horizon emits light today, it will never reach us. That is, we will never observe in the future what that galaxy looks like today (although we might observe today what the galaxy looked like in the past). This also means that once a galaxy is outside our event horizon, it will stay outside: galaxies can never enter our cosmic event horizon. But galaxies can exit the event horizon. In fact, eventually all galaxies outside our local cluster will exit our event horizon.

But you're asking about another horizon, the so-called cosmic particle horizon. This is our observable universe: the region of space from which photons have been emitted that are reaching us today. Galaxies cannot leave our observable universe: once they are inside the horizon, they stay inside (although their redshift goes towards infinity as the universe gets older, so they do become harder to detect). But galaxies currently outside the particle horizon (up to a certain distance) can enter it in the future.

The figures below will illustrate this. The central vertical black line is our world line, the horizontal black line is the current cosmic age; the thick red line is the cosmic event horizon, the thick blue line is the cosmic particle horizon; the yellow lines are light rays, and galaxies move on the dotted black lines.

You can see that light rays inside the event horizon bend towards us, so that we will observe those photons when they cross our worldline. You also see that galaxies can exit the event horizon (but not enter) and galaxies can enter the particle horizon (but not exit), as time goes on.

Our universe is evolving towards a De Sitter space, and which has the property that the distance of the event horizon becomes constant.

We can plot the same figure in co-moving coordinates, i.e. a coordinate system that expands along with the universe. Galaxies have fixed co-moving distances, so their worldlines become vertical dotted lines. And with appropriate scaling of the time axis, light rays move on 45° straight lines.

This figure illustrates the complementary nature of both horizons. In a sense, they are each others mirror image. Note also that the co-moving distance of the particle horizon increases to a finite value at $t=\infty$. Galaxies beyond this maximum distance will never be observable.

For more technical details, see

Can space expand with unlimited speed?

What is the theoretical limit for farthest we can see back in time and distance?

Finally, as others have remarked, these horizons are observer dependent. Every observer in the universe will experience his own event horizon and particle horizon.

• Why did you decide that I was asking about particle horizon? I was asking about event horizon. You say "galaxies can exit event horizon". You even said that there are galaxies which already exited the event horizon. But it is true only if we postulate that the galaxies now have the same proper time as we have. But this contrdicts time dilation. – Anixx Jan 15 '14 at 12:17
• Would you possibly be willing to let me see the code you have used for creating the lower figure? I understand, fo course, if you want to keep it to yourself, but I am curious. – Thriveth Jan 15 '14 at 12:18
• Also you claim that the particle horizon is our observable universe, that light rays reach us today from the particle horizon and not from any further. But this contradicts your graphic: everybody can see that light rays can reach us from behind the blue line, for example, the thick orange line. Conversely, nothing can reach use from behind the event horizon. – Anixx Jan 15 '14 at 12:19
• Pulsar, I think it is important to point out that the Particle Horizon is the distance to the regions from which light emitted has infinite redshift today. The event horizon is the distance to the region, from which light emitted today will be infinitely redshifted before reaching us. – Thriveth Jan 15 '14 at 13:09
• @Anixx: the big bang has infinite redshift due to the scale factor going to zero, but we can't see beyond recombination at $z\approx1100$ anyway; the graphic is correct, but misleading insofar as the redshift/particle horizon overlay is indepent of the lightcone space-time diagram: if you want to relate the overlay to actual events, you need to project the value at a specific time down onto the lightray hitting $d=0$ at that time – Christoph Jan 15 '14 at 20:05

In my understanding, the cosmic horizon is a notion relative to the observer. Let us take two physicists outside of a black hole that they can both observe. They would agree on its horizon. But if the physicists are not at the same place in the universe, they would not agree about the cosmic horizon. Parts of universe will be beyond the cosmic horizon for one of them and not for the others. So nothing prevents matter from going beyond the cosmic horizon of one of them.