# Does the boundary of the causal universe function as an event horizon?

1. Mar 25, 2013

### benlittle

The universe is expanding as described by Hubble's law, which means that at a certain distance from an observer, expansion exceeds the speed of light, so all waves become infinitely red-shifted. In other words, if an goes beyond this point, no information about it can ever come back to the observer.

My question is this: Does that mean that every observer has a sort of event horizon at that distance? If so, shouldn't that even horizon emit Hawking radiation?

2. Mar 25, 2013

### phinds

Every single point in the entire universe including the tip of your nose is exactly at the edge of the "observable universe" for some other point. Do you reckon the tip of your nose is going to start emitting Hawking radiation just because there is some other point in the universe from which it is at the edge of that point's observable universe?

3. Mar 25, 2013

### benlittle

No, because the virtual particles annihilate in my frame, yielding no net radiation.

4. Mar 26, 2013

### Chronos

5. Mar 26, 2013

### bapowell

Your last sentence does not necessarily follow from the previous -- just because something is infinitely redshifted (relative to us) today, doesn't mean it will be so tomorrow. In non-accelerating spacetimes, the Hubble distance grows faster than the expansion, so that points on the Hubble sphere today will be inside the horizon tomorrow. Now, during inflation (accelerated expansion), things are very different. Here the expansion overtakes the Hubble distance and objects are pulled outside the horizon, never to return (so long as the accelerated expansion continues). So inflating spacetimes have event horizons. Where is it? Only when the accelerated expansion is exponential do you find that the Hubble sphere coincides with the event horizon; otherwise it lies further out.

6. Mar 27, 2013

### marcus

Ben, you have gotten clear correct answers from several people. I will add a bit of concrete detail. If it helps, good, otherwise ignore.
You are talking about the Hubble distance--the distance that is increasing at speed c. And any distance larger than that of course increases faster than c.
The Hubble distance is currently 14.56 billion (latest Planck estimate, I'm neglecting to round off and to give uncertainties). See the row labeled S=1 of the table.
That is not a "causal horizon" however, as Brian Powell just pointed out. Galaxies at that distance can still send us light today that will eventually get here, events today at that distance can still eventually affect us. There is something called "cosmic event horizon" (CEH) which is somewhat more distant, 16.73 Gly. You may be thinking of that as the "causal horizon."

If, today, a galaxy at the Hubble distance (14.56 Gly) sends us a photon or a flash of light, that photon will AT FIRST not make any headway. It will stay at the same distance, because its forward motion just cancels the expansion of the distance it still has to cross. But eventually it will make it to us.

Looking again at the present-day numbers, the S=1 row, you can see that the distance to the CEH is 16.73 Gly. A galaxy that is today farther than that, if it sends us a message today that message will never reach us no matter how long we wait.

However most of the galaxies we can see today are NOW farther away than 16.73 Gly. We are getting light from them that they emitted earlier. We will not suddenly STOP seeing them, the light we get from them will just gradually get more and more wave-stretched.

$${\begin{array}{|r|r|r|r|r|r|r|} \hline S=z+1&a=1/S&T (Gy)&T_{Hub}(Gy)&D (Gly)&D_{then}(Gly)&D_{hor}(Gly)&D_{par}(Gly)\\ \hline45.000&0.022&0.056&0.085&39.362&0.875&1.247&0.153\\ \hline37.201&0.027&0.075&0.114&38.595&1.037&1.488&0.206\\ \hline30.753&0.033&0.100&0.151&37.750&1.228&1.772&0.277\\ \hline25.423&0.039&0.133&0.201&36.821&1.448&2.107&0.372\\ \hline21.017&0.048&0.178&0.268&35.798&1.703&2.500&0.498\\ \hline17.374&0.058&0.237&0.357&34.672&1.996&2.959&0.667\\ \hline14.363&0.070&0.316&0.475&33.434&2.328&3.494&0.893\\ \hline11.874&0.084&0.420&0.632&32.071&2.701&4.111&1.196\\ \hline9.816&0.102&0.559&0.841&30.573&3.115&4.821&1.599\\ \hline8.115&0.123&0.745&1.118&28.926&3.565&5.628&2.137\\ \hline6.708&0.149&0.991&1.485&27.115&4.042&6.538&2.855\\ \hline5.546&0.180&1.317&1.971&25.129&4.531&7.551&3.812\\ \hline4.584&0.218&1.751&2.610&22.951&5.006&8.659&5.086\\ \hline3.790&0.264&2.323&3.443&20.571&5.428&9.846&6.780\\ \hline3.133&0.319&3.076&4.516&17.982&5.740&11.084&9.028\\ \hline2.590&0.386&4.060&5.861&15.189&5.865&12.330&11.999\\ \hline2.141&0.467&5.325&7.485&12.215&5.705&13.526&15.903\\ \hline1.770&0.565&6.923&9.331&9.111&5.148&14.608&20.991\\ \hline1.463&0.683&8.883&11.256&5.963&4.075&15.518&27.544\\ \hline1.210&0.827&11.200&13.059&2.882&2.382&16.225&35.865\\ \hline1.000&1.000&13.834&14.560&0.000&0.000&16.730&46.281\\ \hline0.851&1.175&16.259&15.529&-2.253&-2.646&17.023&56.991\\ \hline0.725&1.380&18.819&16.232&-4.264&-5.883&17.220&69.718\\ \hline0.617&1.621&21.473&16.718&-6.040&-9.789&17.348&84.771\\ \hline0.525&1.904&24.191&17.040&-7.589&-14.446&17.429&102.522\\ \hline0.447&2.236&26.951&17.248&-8.928&-19.964&17.478&123.419\\ \hline0.381&2.627&29.739&17.380&-10.079&-26.473&17.507&147.994\\ \hline0.324&3.085&32.543&17.463&-11.065&-34.139&17.521&176.879\\ \hline0.276&3.624&35.358&17.515&-11.908&-43.154&17.526&210.819\\ \hline0.235&4.257&38.180&17.548&-12.627&-53.751&17.548&250.694\\ \hline0.200&5.000&41.006&17.568&-13.241&-66.203&17.568&297.535\\ \hline0.170&5.873&43.834&17.580&-13.763&-80.832&17.580&352.560\\ \hline0.145&6.899&46.664&17.588&-14.208&-98.017&17.588&417.194\\ \hline0.123&8.103&49.495&17.592&-14.587&-118.205&17.592&493.115\\ \hline0.105&9.518&52.327&17.595&-14.910&-141.917&17.595&582.294\\ \hline0.089&11.180&55.159&17.597&-15.185&-169.772&17.597&687.047\\ \hline0.076&13.133&57.991&17.598&-15.419&-202.490&17.598&810.091\\ \hline0.065&15.426&60.823&17.599&-15.618&-240.921&17.599&954.621\\ \hline0.055&18.119&63.656&17.599&-15.788&-286.064&17.599&1124.389\\ \hline0.047&21.283&66.488&17.600&-15.932&-339.089&17.600&1323.801\\ \hline0.040&25.000&69.321&17.600&-16.055&-401.373&17.600&1558.036\\ \hline\end{array}}$$
Time now (at S=1) or present age in billion years:13.834
'T' in billion years (Gy) and 'D' in billion light years (Gly)
http://www.einsteins-theory-of-relativity-4engineers.com/TabCosmo7.html
To specify the dimensions of the table, I set
upper=45
lower=0.04
steps=20
and checked the "S = exactly 1" box.
This means the table goes back in past well before stars existed, when distances were 1/45 what they are today, and it goes out into future when distances are 25 times what they are today.
I also set all the columns to have 3-place precision. The often useful 6-place precision was not needed in this case.

Last edited: Mar 27, 2013
7. Mar 27, 2013

### Mordred

See atachments I included an article on Unruh radiation, which is is describes cosmological horizons as observer dependant. Unruh radiation is a form of Hawking radiation used to describe Hawking radation in terms of cosmological horizons.

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8. Mar 27, 2013

### marcus

The reason that light sent today, from a galaxy at the Hubble distance (14.56 Gly), will eventually reach us, is, to repeat a point Brian made, the expansion speed at a FIXED DISTANCE is not accelerating.

The recession speed at any given fixed distance is actually declining. You can see that in the table.
You see the Hubble distance is constantly increasing throughout history (although mores slowly in later universe). Therefore its reciprocal, the percentage growth rate, is declining.

But if one considers a fixed distance, like 15 billion LY, the percentage growth rate is proportional to the SPEED of expansion. Therefore the speed is declining.

So as I said, if a galaxy at 14.56 Gly sends us a photon or a flash of light today, that photon will AT FIRST not make any headway. It will stay at the same distance, because its forward motion just cancels the expansion of the distance it still has to cross. But eventually the recession speed at that distance will decline and the photon will begin to advance towards us. Eventually it will make it to us.

Then the question is, since obviously the percentage growth rate of separations between stationary observers (and the expansion speed at any fixed distance) is declining, why do people talk about ACCELERATION?

Well what accelerates is the expansion speed of a given separation between two given observers.
You have to choose two galaxies, say, and watch their separation. Then as that grows, you will see the speed increase, even though the percentage growth rate gradually declines.

It's like you deposit money in a bank which is very slowly reducing the percentage interest it is paying on your savings account. The amount of dollars your account grows each year might increase (because the principal is growing) even though the percentage interest is coming down.
It just has to fall slowly enough and you will still see "acceleration" in the dollar amount.

9. Mar 27, 2013

### bapowell

I'm a little confused by that description because a comoving (non-accelerating) observer in de Sitter space certainly sees radiation which is not Unruh (which is seen by accelerating observers and is the result of an observer-dependent horizon.) The cosmological event horizon is a property of the spacetime is therefore not observer-dependent.

While the spacetime is accelerating during de Sitter (or otherwise inflationary) expansion, Unruh radiation is observed by accelerating observers.

10. Mar 27, 2013

### Mordred

Trust me I read that article dozens of times along with the one I meant to post which I will attach now and I am still confused by it lol. The OP asked for an observer dependant model, Unruh is one such model. There was an earlier thread on this I'll try to find it and attach.

the subject came up in this thread.

https://www.physicsforums.com/showthread.php?t=663719& starts around page 2 or 3

I

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11. Mar 27, 2013

### Mordred

12. Mar 27, 2013

### kevinferreira

Not all "expanding universe" cosmological models admit a event horizon, it is not as straightforward as it may seem. The existence or not of an event horizon depends on the constituents of the universe, i.e. radiation, baryonic and dark matter, dark energy and the curvature.
You may have different densities of these constituents, and as each constituent behaves differently under the expansion the existence or not of an event horizon at any given time in the universe is dependent on these densities.
It turns out the modern model to the universe, called $\Lambda CDM$, admits such an event horizon.

13. Mar 27, 2013

### Mordred

A couple of key points here. The articles I posted describe Unruh-Hawking radiation in a variety of observer dependant situations. Their is several forms of radiation similar to Unruh-Hawkings. Parker radiation, Casimir effect, There is also one for electromagnetic sources but can't recall the name.

One of the qualifiers of which type is the source of perturbations and the types of vacuum.
The Arxiv paper mentions that their is similarity to Parker radiation however the type of vacuum is different. This is in the conclusions of that paper.

However my knowledge of QM is very poor, so this may be misinterpretations on my part

14. Mar 27, 2013

### bapowell

Right. What you're calling Parker radiation is the same formalism as that which generates the primordial perturbations during inflation. My point is simply that this type of particle creation is a result of the changing metric -- it is a gravitational phenomenon related to the spacetime -- not the observer. On the other hand, Unruh radiation is the thermal background observed by Rindler (or accelerating) observers and is not a result of any gravitational dynamics -- this is fundamentally different from the above-mentioned mechanisms of particle creation. I was just pointing this out. Thanks for digging up all the links.

15. Mar 27, 2013

### Mordred

Thanks for the claification. I was having trouble distinguishing Parker radiation. Sounds like a
model that best describes Guth's false vacuum?

16. Mar 27, 2013

### bapowell

Sure. Guth's false vacuum is as good as any other!

More seriously, whenever you have vacuum-dominated expansion there is an event horizon and thus gravitational particle creation (or in more modern parlance, fluctuations).

17. Mar 27, 2013

### Mordred

Thanks again. That definetely will help me understand Parker easier. As I've already studied Guth's model. I was holding off till I finish a couple QM text books I bought and am still going through.

18. Mar 27, 2013

### benlittle

Thanks for the relevant info and papers so far. I think the title may have contaminated the original impetus for the question, however. Let me try to clarify my question with a scenario:

A particle pair is created at the boundary of the causal universe of an observer. One particle is inside, the other is out. Information about the particle outside can never reach us, therefore the observer gets the inside particle "for free" as any energy taken from the area outside the causal universe can never be measured.

This leads me to three possible conclusions:
1. The above is correct and there should be (theoretically) measurable radiation from the boundary of the universe. If so, have we measured it?
2. The particle outside can be detected, therefore the two particles simply cancel and the field returns to its ground state. If so, how can we detect it?
3. I am misinterpreting the mechanism behind Hawking radiation. If so, what is the mechanism?

19. Mar 27, 2013

### bapowell

Theoretically, yes, there is a temperature associated with the event horizon of an accelerating spacetime. You can call it a "Hawking" (although see caveat below) or "de Sitter" temperature. Since one observer's position -- say yours -- is at the event horizon of some other observer, you will measure this temperature at your location; and likewise he'll measure radiation at your event horizon. Extending this construction across the isotropic universe results in the conclusion that the spacetime is uniformly bathed in thermal background of radiation. The temperature associated with this radiation is proportional to the Hubble scale (i.e. the horizon size) and so is very much lower than the CMB temperature. Hence, it is currently undetectable.

As I mentioned, you might hear the above kind of radiation as being referred to as the "Hawking temperature of the horizon" or some such similar combination of terms. But it's not to be confused with *the* Hawking effect associated with the horizon of a black hole, which has some key differences. In both cases, however, one should be cautious to attempt an interpretation in terms of virtual particles for several reasons: 1) virtual particles are likely only a mathematical artifact 2) Hawking's calculation says nothing about virtual particle pairs -- in fact it says nothing about what's happening within the vicinity of the event horizon. Nowhere in Hawking's calculation are virtual particle pairs being forever separated on account of one falling into the black hole. Similarly for the cosmological horizon: the popular picture is that a virtual pair pops out of the vacuum and the two particles are whisked away from each other due to the exponentially rapid expansion of space, never to meet again. But this is just a cartoon of what's happening and it's difficult to connect that kind of a picture with the underlying mathematics. At least I've never seen it. (I will mention, however, that the temperature associated with the cosmological horizon is twice that of the black hole...could it be because there are 2 particles instead of 1? Tantalizing, but for the reasons mentioned above, my bet is no.)