Fate of Universe: Is c/H an Asymptotic Singularity?

[Ranku]

Eventually the universe will approach an asymptotic value of the Hubble constant. Is it true that when H = asymptotic value, light from anything further than c/H will never reach us? Can we therefore define the volume within c/H being akin to being enveloped by a singularity?

 

[marcus]

It sounds like you are describing a feature of the standard cosmology model called the "cosmic event horizon" CEH.

The current distance to CEH is estimated to be 15.7 billion lightyears.
It is somewhat analogous to a black hole event horizon.
Any light that is emitted today by material farther than 15.7 will never reach us.

The asymptotic value of H(t) is estimated to be about 61 km/s per Mpc.
As t goes to infinity, c/H(t) will approach 16.4 billion light years.
That is the asymptotic distance to the CEH.

It is somewhat like being surrounded by a black hole event horizon, where everything OUTSIDE the horizon is what is in the black hole.
But there are differences.
One thing is that what I said applies to light emitted today. We still continue to receive light that was emitted in the past by material which is farther away.

There are a lot of galaxies which, even though they are outside the CEH, the light that they emitted in the past is already safely inside the CEH (headed toward us) and so it WILL eventually reach us. So we can expect to continue seeing these galaxies as they were in the past for a long time still.

So the CEH is not quite like an inverted black hole horizon. But it's quite interesting. I think a good article to read about it is one by Lineweaver and Egan posted in 2008. I'll get the link.
http://arxiv.org/pdf/0909.3983
They give those estimates of 15.7 and 16.4 billion lightyears. See equations (47) and (50).

Those distances are given in what they call proper distance. The proper distance to something (at a given time t) is what you would get if you could freeze the expansion process, and then measure by radar or by timing a light signal. It is the distance at that moment.

You can see in their Figure 1 how the proper distance to the horizon is now 15.7 and is converging to 16.4. It has been a smaller distance in the past, and it is now nearly what it is going to be long term. They draw the picture.

 

[Ich]

So the CEH is not quite like an inverted black hole horizon.

It is the same in almost every relevant aspect. FRW coordinates are free fall coordinates, not like static Schwarzschild coordinates. In free fall coordinates, things pass the horizon at a certain time t, but keep being visible to outside (in the FRW case: inside) observers.
The only difference is that, in the Black Hole case, radially infalling observers will eventually see the horizon change. You'd have to place the observer far away enough or give it a little angular momentum to circumvent that.

 

[Ranku]

Thank you both. :)

 

[Ranku]

Thank you both. :)

Well, needed to clarify something. How will an observer outside CEH view time inside CEH, and how will an observer inside CEH view time outside CEH?

 

[Chronos]

There are no observers outside the CEH, and no observer inside the CEH can measure time external to the CEH. Sort of like asking how infinity looks to infinity +1, or vice versa. The question lacks logical context.

 

[Ranku]

There are no observers outside the CEH, and no observer inside the CEH can measure time external to the CEH. Sort of like asking how infinity looks to infinity +1, or vice versa. The question lacks logical context.

Give me the 'in principle' answer, as you did for an observer inside the CEH. Imagine an observer outside CEH, would it be able to discern time inside CEH?

 

[magnusrobot12]

i really want to follow along, but the language is difficult for me right now. I will get better.

But for now, the fate of the universe will eventually become a "big freeze". the universe will expand until space reaches absolute zero or 1 electron in 1,000,000,000,000 cubic light years of space. That will probably never happen, but that is what is predicted if expansion continued forever. True?

 

[Ranku]

It is the same in almost every relevant aspect. FRW coordinates are free fall coordinates, not like static Schwarzschild coordinates. In free fall coordinates, things pass the horizon at a certain time t, but keep being visible to outside (in the FRW case: inside) observers.
The only difference is that, in the Black Hole case, radially infalling observers will eventually see the horizon change. You'd have to place the observer far away enough or give it a little angular momentum to circumvent that.

How will an observer outside CEH view time inside CEH, and how will an observer inside CEH view time outside CEH?

 

[Ich]

The answer is conceptually extremely difficult. I'll try anyway.
How we split spacetime into space and time depends on the coordinates we choose. I'll give two quite different descriptions of the same thing. You don't have - in fact, shouldn't - choose between them. Both are true, just different aspects.

Chronos' short version:
In static coordinates, it takes infinitely long for something to reach the horizon. It that sense, one might argue that there is nothing outside the EH.
OTOH, "infinitely long" just means that we get causally disconnected. You can't reach something that's right now quite "frozen" at the horizon. It's already our of reach; as its time virutally comes to a halt from our perspective, we can't follow its further fate. This relation is reciprocal, the same thing happens to us in their point of view.
So, we can see the other object up to a certain proper time of theirs, and no longer.

...Now for free falling (FRW) coordinates...

The object "crosses the horizon" at exactly this proper time. There is no horizon there from their point of view, and they don't mind that this happens in our future infinity. The horizon hides their future being from us (that's why we call it horizon), and it does so by shifting it to our our eternity. Which simply means that we never will see what happens to them.
Right now, we're crossing somebody else's horizon. She will never see that happen. He crosses our horizon as well - after an eternity for us.

This must be more confusing than helpful. I warned you.

Maybe it's a bit easier with spacetime diagrams, in FRW proper distance -proper time coordinates (sorry, didn't find some in the web). There are whole regions behind the horizon (in fact, most of the universe is there), and everyone except us goes there sooner or later, so that we can't see what happens to them after that.
That's accomplished, in our static coordinates, by transferring that whole region to our future infinity. For us, they'll never cross the horizon. But they don't mind, and go on and on...
just like we do.

 

[Ranku]

The answer is conceptually extremely difficult. I'll try anyway.
How we split spacetime into space and time depends on the coordinates we choose. I'll give two quite different descriptions of the same thing. You don't have - in fact, shouldn't - choose between them. Both are true, just different aspects.

Chronos' short version:
In static coordinates, it takes infinitely long for something to reach the horizon. It that sense, one might argue that there is nothing outside the EH.
OTOH, "infinitely long" just means that we get causally disconnected. You can't reach something that's right now quite "frozen" at the horizon. It's already our of reach; as its time virutally comes to a halt from our perspective, we can't follow its further fate. This relation is reciprocal, the same thing happens to us in their point of view.
So, we can see the other object up to a certain proper time of theirs, and no longer.

...Now for free falling (FRW) coordinates...

The object "crosses the horizon" at exactly this proper time. There is no horizon there from their point of view, and they don't mind that this happens in our future infinity. The horizon hides their future being from us (that's why we call it horizon), and it does so by shifting it to our our eternity. Which simply means that we never will see what happens to them.
Right now, we're crossing somebody else's horizon. She will never see that happen. He crosses our horizon as well - after an eternity for us.

This must be more confusing than helpful. I warned you.

Maybe it's a bit easier with spacetime diagrams, in FRW proper distance -proper time coordinates (sorry, didn't find some in the web). There are whole regions behind the horizon (in fact, most of the universe is there), and everyone except us goes there sooner or later, so that we can't see what happens to them after that.
That's accomplished, in our static coordinates, by transferring that whole region to our future infinity. For us, they'll never cross the horizon. But they don't mind, and go on and on...
just like we do.

Ok, let me clarify the essence of it. Does the concept of causal disconnection in static coordinates between either side of the CEH also apply to FRW coordinates?

 

[Ich]

Yes, causal disconnection is independent of coordinates. In one set of coordinates, the object freezes at the horizon, in the other it simply crosses it, but the result is the same in both cases: disconnection.

 

[Ranku]

Yes, causal disconnection is independent of coordinates. In one set of coordinates, the object freezes at the horizon, in the other it simply crosses it, but the result is the same in both cases: disconnection.

Cool. Thanks.

 

[qwe]

Yes, causal disconnection is independent of coordinates. In one set of coordinates, the object freezes at the horizon, in the other it simply crosses it, but the result is the same in both cases: disconnection.

is this related to the black hole's event horizon, where the object appears redshifted and slower, and goes slower and slower and eventually appears frozen at the event horizon?

 

[Chronos]

is this related to the black hole's event horizon, where the object appears redshifted and slower, and goes slower and slower and eventually appears frozen at the event horizon?

We are certain event horizons can form, but, it is less certain whether true singularities exist in this universe. That may seem like splitting hairs, but, it is an issue in cosmology.

 

[Ich]

is this related to the black hole's event horizon, where the object appears redshifted and slower, and goes slower and slower and eventually appears frozen at the event horizon?

It's the same "effect".