Will the Expansion of Space Prevent Overlapping Cosmic Horizons?

[Alektene]

I was reading The Elegant Universe a few days ago, and came upon a passage (p.40) where Brian Green states "Over time the size of the cosmic patches laid out in Figure 2.1b will increase; with more time, light can travel farther and so each of the cosmic patches will grow larger. Ultimately, the cosmic horizons will overlap...".

My question is this: If the expansion of space is generally consistent from one region to the next (let's say between 2 cosmic horizons or "patches" that are not adjacent), then won't the space between them expand at the same rate...thereby relegating them to never overlap?

 

[marcus]

It sounds like you are talking about what is called the "particle horizon". It does expand over time.

Have a look at the top figure here.
http://ned.ipac.caltech.edu/level5/March03/Lineweaver/Figures/figure1.jpg
You see the dashed curve labeled "particle horizon"?
This is like the track of a flash of light that OUR matter released around the start of expansion. It shows how far it can have gotten, helped by expansion.
By the present day it can have gotten 46 Gly (46 billion light years).

The horizontal distance scale in the top figure is called PROPER distance, the closest thing to actual real at-this-moment distance. Imagine stopping expansion and measuring by conventional means e.g. radar or a long string.

The other two figures have a different (but useful) scale called COMOVING distance. Imagine labeling every bit of matter by the proper distance it is today in 2013. Tag it permanently with that. this "distance" number does not change in any way. The matter's comoving "distance" is the same in year 1 and the same in year 100 billion as it is today in year 13.8 billion.

You have this very good intuitive insight that there is matter which a flash of light from our matter will never reach, ever. Even if the flash was emitted in year 1, very early, and has already been traveling 13.8 billion years, and has all the time of the future to travel, it will never get to that matter because of expansion.

Yes, and the critical distance is 63 Gly (63 billion light years). You can see that in the BOTTOM figure on the same page. Matter that is now at a distance of 63 Gly or beyond will never get light from here. And we will never SEE light emitted by that matter, even the light it emitted long ago near start of expansion will never reach us no matter how long we wait.

But our descendants or other Milkyway creatures WILL eventually see light emitted by matter which is, today, less than 63 Gly from here. I don't mean light emitted today (the range of signals sent today is governed by a different horizon called cosmic event horizon or CEH)--I mean light that the matter emitted in early days, which has the most chance of reaching us.
We will eventually get light from stuff that is now nearer than 63 Gly. So it will become part of our observable region. But that is the limit.

Can you see where the particle horizon line hits the comoving distance axis at around 63?

 

[Alektene]

Thanks, marcus - that figure might take a while to assimilate. I'll work on it - but, in the meantime, consider 2 observers sitting on planets whose cosmic horizons don't currently overlap. Depending on how far apart they are, space itself may be expanding faster than the speed of light. Let's assume they are - and it is. In order for their cosmic horizons to overlap, light would have to travel farther for a given unit of time (which Greene says is correct) but it would have to travel fast enough to outpace the expansion of space. Wouldn't it?

 

[Alektene]

@marcus - Give me a bit to read the rest of your message. I posted reply #3 before I was able to read your entire post. My apologies :-)

 

[marcus]

@marcus - Give me a bit to read the rest of your message. I posted reply #3 before I was able to read your entire post. My apologies :-)

Not your fault though :-) I am slow to finish posts.

 

[Alektene]

I understand your response - thanks a bunch!

If I could add another related question (please let me know if this should be another thread): The universe, if taken on a very large scale is essentially homogeneous (isotropic). The distribution of matter/energy is uniform - and I contribute my portion of matter to that distribution. I have read that when cosmologists say "space is expanding", they are referring to "empty" space...not the space between the particles that make up my own body and the planet I reside on. How does "empty space" differ from my space - and why is one expanding and not the other.

 

[marcus]

Thanks, marcus - that figure might take a while to assimilate. I'll work on it - but, in the meantime, consider 2 observers sitting on planets whose cosmic horizons don't currently overlap. Depending on how far apart they are, space itself may be expanding faster than the speed of light. Let's assume they are - and it is. In order for their cosmic horizons to overlap, light would have to travel farther for a given unit of time (which Greene says is correct) but it would have to travel fast enough to outpace the expansion of space. Wouldn't it?

There are an interesting bunch of issues around this. There is a distance called the current HUBBLE RADIUS which is the size of any distance expanding exactly at the speed of light. I have never known astronomers to call that our "cosmic horizon" but maybe it gets called that in popular books.

This distance changes over time. It is currently 14.4 Gly and it is increasing towards a steady size of 17.3 Gly. Basically it is a measure of the rate of expansion. A short Hubble radius means you don't have to look out very far to find things receding at speed c. In the early universe it was much shorter than the 14.4 it is today. A long Hubble radius means overall less percentage growth in distances because you have look out a long way before you see stuff receding at speed c.

It would help me respond to you if you would say what you mean by "cosmic horizon".

Our current Hubble radius = 14.4 Gly
Our current Cosmic Event Horizon = 16.5 Gly
Our current Particle Horizon = 46 Gly

Jorrie's calculator has these figures and some pop-up information about what they mean (mouse the blue dots). Click on this:
http://www.einsteins-theory-of-relativity-4engineers.com/LightCone7/LightCone.html
the Hubble radius column is labeled R
the CEH column is labeled D_hor
the particle horizon column (labeled D_par) has to be selected.

(Easy, open "column definition and selection" menu and check the box for Dpar, then press calculate.)
======================

It's easy to see how a flash of light emitted TODAY in a galaxy out at 16 Gly from us could eventually reach us EVEN THOUGH 16 > 14.4. Even though the distance to the galaxy is receding faster than light!

The light will initially loose ground because its forward progress is canceled by expansion of the distance it has to go to reach us. But it hangs in there and eventually the Hubble radius increases out far enough to take it in. The Hubble radius is scheduled to increase out to 17.3, remember.

You can see the record of Hubble radius increase in Jorrie's table that comes up when you open the calculator. http://www.einsteins-theory-of-relativity-4engineers.com/LightCone7/LightCone.html
The present is denoted by a=1, so you know what row of the table to look at to find current numbers.

 

[marcus]

I understand your response - thanks a bunch!

If I could add another related question (please let me know if this should be another thread): The universe, if taken on a very large scale is essentially homogeneous (isotropic). The distribution of matter/energy is uniform - and I contribute my portion of matter to that distribution. I have read that when cosmologists say "space is expanding", they are referring to "empty" space...not the space between the particles that make up my own body and the planet I reside on. How does "empty space" differ from my space - and why is one expanding and not the other.

Your particles are held together by molecular forces. Bound structures don't expand. Our solar system and our Milkyway galaxy are held together by gravity, so they don't expand.

You are asking "what do cosmologists mean?" when they say space expands. I think what they mean is they have a criterion of cosmic rest. And distances between objects AT REST are increasing at a certain percentage rate. The current rate of increase is 1/144 of one percent per million years.

Eventually this rate will ease off and level out at 1/173 of one percent per million years.

Such a small percentage distance growth rate only has a noticeable effect on very large distances. And it cannot be between objects which are bound together (because then you could not have both ends AT REST).

The criterion of cosmic rest is very interesting, but it is a little bit too much put into popular writing for wide audience, so they just say "space expands" without explaining.

I am exploring the possibility of talking about that at very basic level in this other thread
https://www.physicsforums.com/showthread.php?t=693537

I introduce the idea of a "soup of ancient light" that we are immersed in, and the distances that expand are those between observers who are at rest in this soup.
And actually most galaxies have only rather small speeds thru the soup, so they are comparatively "at rest". So we mostly neglect their individual random motions and just measure the distance expansion as if they were at rest.

I don't know if the wording is successful. Maybe I am trying to condense too much and say too much in a single post. I think point #7 is extra and could be dropped.

 

[Alektene]

Great information, Marcus. Thanks so much for your patience with my armchair cosmology.