Exploring Alternatives to Dark Energy: Carroll & Turner, Jacobson & Mattingly

[marcus]

Two new October papers.
the first is notable because of the reputation of some of the authors. Sean Carroll and Michael Turner are among a handful of the most prominent mainstream cosmologists.
here they are trying to see if one can avoid the need for dark energy by a modification of the Einstein-Hilbert action.
A slight modification of the law of gravity in General Relativity which is only noticeable over very long distances.

Sean M. Carroll, Antonio De Felice, Vikram Duvvuri, Damien A. Easson, Mark Trodden, Michael S. Turner
The Cosmology of Generalized Modified Gravity Models
27 pages, 7 figures
http://arxiv.org/abs/astro-ph/0410031

"We consider general curvature-invariant modifications of the Einstein-Hilbert action that become important only in regions of extremely low space-time curvature. We investigate the far future evolution of the universe in such models, examining the possibilities for cosmic acceleration and other ultimate destinies. The models generically possesses de Sitter space as an unstable solution and exhibit an interesting set of attractor solutions which, in some cases, provide alternatives to dark energy models."


The next paper, though not about obviating dark energy is similarly off-beat. It is noteworthy partly because it is by Ted Jacobson and David Mattingly, both prominent in testing quantum gravity---it was their paper on Crab Nebula synchrotron radiation that effectively disposed of "preferred-frame" approaches. Or so we thought. Here they are probing what looks like yet another possible avenue to violate or distort Lorentz symmetry.

C. Eling, T. Jacobson, D. Mattingly
Einstein-Aether Theory
17 pages, to appear in the Deserfest proceedings (World Scientific)
http://arxiv.org/abs/gr-qc/0410001

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[Mike2]

Just a moment... Perhaps I'm on the fringe, but has anyone stopped to consider that: if there is an event horizon, then it is the same for all point in the universe. And as matter disappears behind the event horizon of each point, that point has less gravitational potential energy. Since it no longer feel the force of gravity from the galaxies disappearing behind the event horizon, this is equal to an increase in a repulsive force that is added to gravity. If matter only disappear behind the event horizon, then there is alway an increase in this repulsive addition. And this means that the potential derived from this added repulsive force is and has always been positive. OK, isn't this the same as adding a cosmological constant to Einstein's field equations? It seems to me that this would be a cosmological constant that is very small at first, since little mass escapes behind the event horizon. But it would grow as mass is lost in ever greater emounts but would never get larger than the energy-momentum term and would eventually lead to a zero source solution.

 

[meteor]

The paper were Einstein-Aether theory was first proposed is this:
"Einstein-aether waves"
http://arxiv.org/abs/gr-qc/0402005
Wow, an aether theory that adds the name of Einstein to its name. Albert must be turning in his tomb

 

[Mike2]

Just a moment... Perhaps I'm on the fringe, but has anyone stopped to consider that: if there is an event horizon, then it is the same for all point in the universe. And as matter disappears behind the event horizon of each point, that point has less gravitational potential energy. Since it no longer feel the force of gravity from the galaxies disappearing behind the event horizon, this is equal to an increase in a repulsive force that is added to gravity. If matter only disappear behind the event horizon, then there is always an increase in this repulsive addition. And this means that the potential derived from this added repulsive force is and has always been positive. OK, isn't this the same as adding a cosmological constant to Einstein's field equations?

Or is it the Hubble sphere beyond which galaxies are disappearing from our present view?

In any event, if the disappearance of mass behind the horizon which causes the loss of negative gravitational potential (on average), is equal to an increase of a positive potential at each point, then does this increase in potential energy (=mass?) at each point cause particle creation in otherwise empty space? Does the information lost behind the horizon return to us in particle creation throughout the rest of space?

When we talk about black holes, is it not supposed (correct me if I'm wrong) that the information lost behind that horizon is gained by the retention of some virtual particles near the horizon? If so, then since every point in space has a cosmological horizon, then perhaps the info lost behind the cosmological horizon is returned by the retention of some virtual particles at all points in space?

Thanks.

 

[Mike2]

Or is it the Hubble sphere beyond which galaxies are disappearing from our present view?

In any event, if the disappearance of mass behind the horizon which causes the loss of negative gravitational potential (on average), is equal to an increase of a positive potential at each point, then does this increase in potential energy (=mass?) at each point cause particle creation in otherwise empty space? Does the information lost behind the horizon return to us in particle creation throughout the rest of space?
Thanks.

So, continuing to think along these lines, then during inflation, much more potential energy is disappearing behind the horizon as the universe expanse much more rapidly than now. Does this account for a very much faster increase in potential energy which corresponds to most of the matter in the universe being created at that time? I suppose it does not matter which came first. Might it have been just as easily stated that expansion is caused by the great amount of matter that was being created at that time?

 

[Chronos]

I am uncomfortable with an event horizon that allows physical structures to exit or enter. I know of no theory that proposes/allows that to happen. A simplified version is a black hole. No observer on either side of the event horizon can see what happens on the other side.

 

[anti_crank]

I am uncomfortable with an event horizon that allows physical structures to exit or enter. I know of no theory that proposes/allows that to happen. A simplified version is a black hole. No observer on either side of the event horizon can see what happens on the other side.

Interesting. It is my understanding that concerning a standard (Schwarzschild) black hole, someone within the horizon can still see what happens outside the hole, as there is nothing preventing light from outside to reach him. It is only the outside that cannot know what goes on inside. There is a good chance I am mistaken, however, seeing as I am not an expert in GR.

 

[Mike2]

I am uncomfortable with an event horizon that allows physical structures to exit or enter. I know of no theory that proposes/allows that to happen. A simplified version is a black hole. No observer on either side of the event horizon can see what happens on the other side.

If there was an "inflationary" phase of expansion, then at one time some portions of the universe were traveling faster than light with respect to other portions of the universe so that light sent from one portion was not visible to other portions of the universe. So at least during inflation there was a horizon for each point beyond which there was no communication.

 

[meteor]

I am uncomfortable with an event horizon that allows physical structures to exit or enter

But our cosmological event horizon is at a redshift of z=1'8 (comoving radial distance of 16 Gly) and actually there are galaxies crossing it. when they'll cross it, whatever pass to them will be never observed by us

 

[Mike2]

But our cosmological event horizon is at a redshift of z=1'8 (comoving radial distance of 16 Gly) and actually there are galaxies crossing it. when they'll cross it, whatever pass to them will be never observed by us

And what horizon is it that when they cross, they are not visible to us, not to imply that they may never be seen again, but only that we do not now see them? Thanks.

 

[Mike2]

In any event, if the disappearance of mass behind the horizon which causes the loss of negative gravitational potential (on average), is equal to an increase of a positive potential at each point, then does this increase in potential energy (=mass?) at each point cause particle creation in otherwise empty space? Does the information lost behind the horizon return to us in particle creation throughout the rest of space?

I just heard that the cosmological constant is a coupling constant is some purterbative expansion of some QFT and can be interpreted as a mass? Is this true? Where can I learn more about this? Thanks.

Wouldn't that be interesting? That would mean that the GR effect of expansion may be responsible (or may be an equivalent expression for) QFT, right?

 

[ray b]

will the central mass of a BH be effected by the mass outside the BH
will two BHs orbit each other outside the event horizons of both
it sure looks like gravity can pass thru an event horizon

so "IF" our big bang was a local event, and other big bangs happen outside our univerce why couldnot their gravity pass thru our big bangs event horizon to
power the observed expansions in our univerce esp if curved space is not limited to lightspeed time limits

so maybe we are seeing effects of things beyond the limits of our event horizon
but calling them dark energy rather then what they truly are, gravity

 

[Chronos]

Interesting. It is my understanding that concerning a standard (Schwarzschild) black hole, someone within the horizon can still see what happens outside the hole, as there is nothing preventing light from outside to reach him. It is only the outside that cannot know what goes on inside. There is a good chance I am mistaken, however, seeing as I am not an expert in GR.

You are correct. I was careless in making my point. In the case of the observable universe, the equivalent of an event horizon exists at z ~ 1100. With the exception of relic neutrinos [courtesy of Nereid], there is nothing left to see beyond that point. And since that barrier has and will always recede faster than less distant objects, nothing will ever cross that barrier. While objects we currently see may someday become too distant and faint to be seen, they will never exit the observable universe.

 

[Mike2]

You are correct. I was careless in making my point. In the case of the observable universe, the equivalent of an event horizon exists at z ~ 1100. With the exception of relic neutrinos [courtesy of Nereid], there is nothing left to see beyond that point. And since that barrier has and will always recede faster than less distant objects, nothing will ever cross that barrier. While objects we currently see may someday become too distant and faint to be seen, they will never exit the observable universe.

According to the Robertson-Walker metric of the universe, the Hubble sphere is the distance from us that is receding faster than the speed of light. Any light emitted at that distance will never reach us.

I would be curious to know... given the distance to the event horizon (or is it the Hubble sphere), and the density of all matter in the universe (or at least baryonic matter), and the Hubble constant of the expansion rate, is it possible that a conservation law applicable only within the horizon require that the amount of mass and/or energy leaving the horizon must be equal to the mass/energy associated with the cosmological constant? Maybe someone intimate with the numbers involved can do the calculation. Thanks.

 

[Chronos]

According to the Robertson-Walker metric of the universe, the Hubble sphere is the distance from us that is receding faster than the speed of light. Any light emitted at that distance will never reach us.

I disagree with that interpretation.

I would be curious to know... given the distance to the event horizon (or is it the Hubble sphere), and the density of all matter in the universe (or at least baryonic matter), and the Hubble constant of the expansion rate, is it possible that a conservation law applicable only within the horizon require that the amount of mass and/or energy leaving the horizon must be equal to the mass/energy associated with the cosmological constant? Maybe someone intimate with the numbers involved can do the calculation. Thanks.

It is not an event horizon if structures are free to depart.

 

[turbo]

You are correct. I was careless in making my point. In the case of the observable universe, the equivalent of an event horizon exists at z ~ 1100. With the exception of relic neutrinos [courtesy of Nereid], there is nothing left to see beyond that point. And since that barrier has and will always recede faster than less distant objects, nothing will ever cross that barrier. While objects we currently see may someday become too distant and faint to be seen, they will never exit the observable universe.

Current LCDM models (flat, infinite U w/ accelerating expansion) have what is called a "future event horizon". If you do some Google searching, you will find some descriptions and diagrams that will explain the concept better than I can. According to these models, after some arbitrarily long time, the only galaxies visible from our viewpoint will be those of our local group. Here is a non-technical explanation of Abraham Loeb's work.

http://cfa-www.harvard.edu/newtop/previous/122001.html

I personally do not subscribe to the LCDM matter model, but you defend it quite vigorously, so I'm surprised that you do not embrace the concept of the future event horizon. If you do not accept the concept of the future event horizon, you might have to modify standard cosmology by modeling the universe as closed like this author does:

http://adsabs.harvard.edu/cgi-bin/nph-bib_query?2001astro.ph.10193Z

 

[Mike2]

I disagree with that interpretation.It is not an event horizon if structures are free to depart.

I thought it was defined as an horizon only if matter did disappear behind it.

But I understand your question. Since we can see the CMBR which is the farthest thing from us and thus the fastest moving thing away from us, then we should be able to see anything less distant, namely everything. But I also wonder if the CMBR is not instead the radiation from every point in space near and far. As I understand it, light was first able to travel across the entire universe when things cooled down enough for nuclei to capture electrons to form stable atoms. Since the temperature of the universe was pretty much the same everywhere, this recombination happened everywhere pretty much at the same time and photons started to travel across the universe from every point in space in all directions. So the photons were evenly distributed throughout all of space at recombination. Then as the universe expanded, the photon soup remained evenly distributed throughout, but the density of photons decreased with expansion until now they represent only about 3 degrees Kelvin. So the CMBR does not represent the farthest object that we can see. They represent a "background" that exists everywhere amongst which stars and galaxies are placed. Others are welcome to correct me if I'm wrong.

 

[Garth]

I thought it was defined as an horizon only if matter did disappear behind it.

It is a horizon if we cannot see behind it. If we cannot see objects today they are behind our particle horizon, if we will never be to see objects ever they are behind our event horizon.

So the CMBR does not represent the farthest object that we can see. They represent a "background" that exists everywhere amongst which stars and galaxies are placed. Others are welcome to correct me if I'm wrong.

I'm not correcting you only clarifying what you have said. The CMB consists of a "background" of photons emitted at the surface of last scattering, the glowing fog of ionised hydrogen before the electrons and protons combined; in the foreground of which are placed the galaxies etc.
Garth

 

[Mike2]

It is a horizon if we cannot see behind it. If we cannot see objects today they are behind our particle horizon, if we will never be to see objects ever they are behind our event horizon.

The graphs I've seen (available on line) show the particle horizon presently at about 45 Billion light years away whereas the event horizon is only about 15Gly away and the Hubble sphere is about 13.5Gly away. If at the time of the BB (about 13.5Gyrs ago) there were objects that emitted photons at the particle horizon some 45Gly away we would be able to see their light. However, there were no objects that far away at that time, so we do not see them.

I'm not correcting you only clarifying what you have said. The CMB consists of a "background" of photons emitted at the surface of last scattering, the glowing fog of ionised hydrogen before the electrons and protons combined; in the foreground of which are placed the galaxies etc.
Garth

Can we see any kind of lensing effect on the "background" of the CMBR caused by a "foreground" of distant galaxies? I've never heard of such a thing.

 

[Chronos]

Current LCDM models (flat, infinite U w/ accelerating expansion) have what is called a "future event horizon". If you do some Google searching, you will find some descriptions and diagrams that will explain the concept better than I can. According to these models, after some arbitrarily long time, the only galaxies visible from our viewpoint will be those of our local group. Here is a non-technical explanation of Abraham Loeb's work.
http://cfa-www.harvard.edu/newtop/previous/122001.html

I think this may be as much a matter of semantics as substance. The cfa paper is saying exactly what I thought I was saying [in an apparently bumbling way]. There is no horizon that objects we presently see will some day cross and suddenly disappear from view. There is, and always has been an observer horizon, but that horizon continuosly recedes and is forever beyond the reach of any object inside of it.

Bear in mind that not only are distant galaxies increasingly red shifted, they are increasingly time dilated. We are watching them in slow motion. Cosmologists routinely factor this in when plotting the light curves of distant type Ia supernova [they do not fade as quickly as relatively nearby ones]. Enormously red shifted galaxies, whether now or in the future, are / will be so severely time dilated, they will appear to be virtually frozen in time. Ultimately, they will simply fade from view as they become to faint to be seen, not suddenly vanish as if they crossed some arbitrary horizon.

What I am saying is we can already see everything that will ever be possible for us to see [but only as it looks in our current particle horizon]. Since the CMBR photons have already made it here, and it is probably safe to say there was no large scale structure prior to recombination, it seems reasonable to conclude that photons emitted from structures that subsequently formed have also had time to reach us. Will new galaxies come into view in the future? Of course. But they will not suddenly pop into view fully formed as if they crossed some arbitrary horizon. We will watch them coalesce out of primordial gas clouds already visible to us and light up star by star.

...but the density of photons decreased with expansion until now they represent only about 3 degrees Kelvin.

Density is not the issue, CMBR photons are redshifted to 3k due to expansion. Read this and see what you think.
http://cobi.gsfc.nasa.gov/msam-ripples.html

 

[Mike2]

You seem to be repeating my argument at one time: how could the CMB indicate the beginning of large scale structure if it does not occur prior to the formation of galaxies, which would have to mean that it is older and farther away? And as you say, this means that if we can see the CMB, then we can see everything else in between, namely everything. And this denies the existence of any horizons to disappear behind.

Could it be that if the CMB being a measure of the background of every point in space near and far. Such a background would still have slightly higher densities where galaxies clusters would latter form?

The redshift of the CMB is due to the wavelength of the original light being stretched out along with the expansion and not because of the speed of recession of some distant backdrop, right?

 

[Chronos]

I pretty much agree with everything you just said [perhaps a few technical difficulties, but, no big deal]. CMBR anisotropy is very consistent with observed distributions of mass in the universe.

 

[Mike2]

I just heard that the cosmological constant is a coupling constant is some purterbative expansion of some QFT and can be interpreted as a mass? Is this true? Where can I learn more about this? Thanks.

Wouldn't that be interesting? That would mean that the GR effect of expansion may be responsible (or may be an equivalent expression for) QFT, right?

IIRC, there is now two ways to look at mass - as the coupling constant in QFT and as the mass matrix that is the metric that transforms between configuration space and phase space (Frankel's The Geometry of Physics, page 55). Since the coupling constant is solved for using the integrals of a perturbation expansion, is it possible to equate the coupling constant, which is a mass, to the metric, or its determinate, and equate this to the integral of the perturbation expansion, which also involves the metric in the integrand. Wouldn't this turn the metric into a dynamical entity to be solved for in the process? Or has this already been attempted?

 

[Garth]

And as you say, this means that if we can see the CMB, then we can see everything else in between, namely everything. And this denies the existence of any horizons to disappear behind.

The look back time to the surface of last scattering is not infinite. Therefore in an infinite universe there would be objects that we cannot see at a greater distance than the distance to our CMB; they are behind our particle and possibly our event horizons.

Consider our past light cone expanding outwards the further back you look. It is not in fact a cone because of the space-like expansion of space-time. Looking backwards in time space-time contracts in space, so the reverse expansion of the cone is modified by the space-like contraction of past space-time. Depending on the Friedmann model it will eventually begin to converge, maybe even to a point.
Somewhere along this light cone you encounter the surface of last scattering beyond which the universe goes foggy and you cannot see any further. Although you see this surface as the CMB in whatever direction you look, the footprint you observe on that surface of last scattering is finite. Yet in an infinite universe the total surface of last scattering is also infinite. You can therefore only see a part of that surface, in the surface outside of our footprint are our horizons.

Could it be that if the CMB being a measure of the background of every point in space near and far. Such a background would still have slightly higher densities where galaxies clusters would latter form?

These are the fluctuations mapped with great precision by WMAP.

The redshift of the CMB is due to the wavelength of the original light being stretched out along with the expansion and not because of the speed of recession of some distant backdrop, right?

Hmmm - if you define particle mass as invariant and therefore rulers are fixed (they don't shrink/expand) then the stretching out of the photons' wavelength is interpreted as a Doppler velocity of recession. But the red shift can be also interpreted as a gravitational time dilation effect.
Garth

 

[Mike2]

The look back time to the surface of last scattering is not infinite. Therefore in an infinite universe there would be objects that we cannot see at a greater distance than the distance to our CMB; they are behind our particle and possibly our event horizons.

So are you saying that the CMB itself IS our particle horizon?

The particle horizon is the distance a photon would travel away from us adding the expansion rate for that farthest photon. It's about 45Gly away, how many parsecs is that? I would think that photons headed away from us from the beginning (the particle horizon) will never reach us.

The Hubble Sphere is where the distance that is receding faster than light. We cannot see things now that were outside the Hubble sphere at the time they were emitted.

The event horizon is the distance at which we will never receive the light from an object. Shouldn't the particle horizon aways be farther than the event horizon or the Hubble Sphere?

We will eventually see the light from objects that are between the event horizon and the Hubble sphere. Light emitted between the event horizon and the Hubble sphere is initially heading away from us but at a slower rate than the Hubble sphere is growing. So eventually, the Hubble sphere will catch up with that photon and it will start heading towards us.

What I don't get is how can the particle horizon be inside the event horizon? How can a photon traveling away from us at the farthest distance eventually catch up with us. I ask this because some figures show this. And I assume that the CMB is the intersection of our past light cone with the past particle horizon that was then inside the event horizon, right?

 

[Chronos]

The Hubble sphere is not a 'center' of the universe. Each point has its own Hubble sphere. The Hubble sphere defines that portion of the universe which is observable from the specified point at a specified time

 

[Garth]

So are you saying that the CMB itself IS our particle horizon?

No, I thought I had explained that the CMB is only an horizon in the sense that there the universe becomes opaque. Photons do still reach us from beyond it, however they have to fight their way through the fog, being scattered/absorbed/emitted many times before they become free of the ionised hydrogen. (The hydrogen plasma becomes atomic at the CMB) The fact that the red shift at the CMB is 'only' about 1000 indicates that it is not the particle horizon, which lies much further away. [It would become significant in an infinite universe that is infinitely old, the present day red shift of an object at the particle horizon would be infinite, the red shift of an object on the event horizon would always be infinite, whenever it was 'observed'.]

What I don't get is how can the particle horizon be inside the event horizon? How can a photon traveling away from us at the farthest distance eventually catch up with us. I ask this because some figures show this.

Imagine a wave front of light from a distant super nova expanding towards us in an expanding universe. In an accelerating universe we may accelerate away from the S/N and the light never catch up with us. In a decelerating universe the reverse could be true. It depends on the dynamics of the Hubble expansion.

And I assume that the CMB is the intersection of our past light cone with the past particle horizon that was then inside the event horizon, right?

Wrong actually! The CMB is well within our particle and event horizons, which is why we can observe it. See above.
Garth

 

[Mike2]

No, I thought I had explained that the CMB is only an horizon in the sense that there the universe becomes opaque. Photons do still reach us from beyond it, however they have to fight their way through the fog, being scattered/absorbed/emitted many times before they become free of the ionised hydrogen.

Wouldn't redshift be shifted to infinity where it disappears and isn't this the event horizon?

We cannot see everything all the way back to t=0 because inflation expanded the universe faster than our past light cone expanded. It takes time for space-like event at the end of inflation to catch up with us. I suppose that not all events at the end of inflation have caught up with us yet. So we still have to wait to learn more about what happened then.

Imagine a wave front of light from a distant super nova expanding towards us in an expanding universe. In an accelerating universe we may accelerate away from the S/N and the light never catch up with us. In a decelerating universe the reverse could be true. It depends on the dynamics of the Hubble expansion.

I don't see how the universe could fail to accelerate. If the expansion of space is proportional to the distance, then as space expands, it will expand faster. And I don't see how space could fail to expand proportionately with distance. For if there is no preferred place in the universe, then every point of space expands the same. And so the farther away a point is the faster it expands. And the more space there is, the faster it grows, right?

Wrong actually! The CMB is well within our particle and event horizons, which is why we can observe it. See above.
Garth

So are you saying that our particle horizon is t=0? Some of the graphs I see (don't have the link, sorry) show our past light cone intersecting with the particle horizon at t not equal to zero.

Do you know of a book or on-line video that explains these thing clearly in detail. It seems as though these professionals never explain things clearly - it's always incomplete - they never make definitive statements, they never draw clear distinctions. It's almost as if their works are little more than cheat sheets with just enough information to define the variable, if you're lucky. Sorry for the frustration, but I know they can do a lot better if they would just stop competing with each other and start cooperating to make things clear.

 

[Chronos]

Do you know of a book or on-line video that explains these thing clearly in detail. It seems as though these professionals never explain things clearly - it's always incomplete - they never make definitive statements, they never draw clear distinctions. It's almost as if their works are little more than cheat sheets with just enough information to define the variable, if you're lucky. Sorry for the frustration, but I know they can do a lot better if they would just stop competing with each other and start cooperating to make things clear.

Try here
http://adsabs.harvard.edu/cgi-bin/bib_query?1956MNRAS.116..662R

 

[Garth]

Wouldn't redshift be shifted to infinity where it disappears and isn't this the event horizon?

No that would be our particle horizon beyond which events cannot be seen by us today; the event horizon lies beyond and it is that barrier beyond which events will never be seen by us.

I don't see how the universe could fail to accelerate.

Are you confusing acceleration with expansion? Normally in GR the universe is said to decelerate because of the mutual gravitational attraction of all the matter within it. However recent observations of distant Type 1a Supernovae have been interpreted as evidence that the universe has accelerated, at least for a time, and this has to be explained by some sort of 'anti-gravity' effect normally attributed to Dark Energy.

So are you saying that our particle horizon is t=0? Some of the graphs I see (don't have the link, sorry) show our past light cone intersecting with the particle horizon at t not equal to zero.

Red shift -> infinity at the particle horizon, where this happens depends on the actual dynamics of the universe. If acceleration as well as deceleration is allowed it could be anywhere! (Well not anywhere!)

 

[Mike2]

Try here
http://adsabs.harvard.edu/cgi-bin/bib_query?1956MNRAS.116..662R

I was not able to get the info from that site. Does this require a subscription or special on-line reader program?

 

[Chronos]

The PDF file appears to be broke. The GIF download work.

 

[Mike2]

In any event, if the disappearance of mass behind the horizon which causes the loss of negative gravitational potential (on average), is equal to an increase of a positive potential at each point, then does this increase in potential energy (=mass?) at each point cause particle creation in otherwise empty space? Does the information lost behind the horizon return to us in particle creation throughout the rest of space?

I wonder if the big Freeze of galaxies that leave our horizon so we can no longer see them... what effect would that have on information content of the visible universe? Is that saying that information cannot leave our visible universe? The entropy, S=Q/T. If everything freezes at the horizon, then Q tends to zero, but also T tends to zero. Would Q include the rest mass which is energy?

 

[Chronos]

Mike2, you may also find this of interest with regard to cosmological horizons
http://arxiv.org/abs/astro-ph/0406099

 

[turbo]

In a universe dominated by a small cosmological constant or by eternal dark energy with equation of state w < -1/3, observers are surrounded by event horizons. The horizons limit how much of the universe the observers can ever access.

Interesting paper. The authors note that if the U continues to expand, the CMB will eventually be redshifted into the noise of the Hawking radiation at the event horizon and the information in the CMB will be lost to us.