# Questions about expansion

1. Jan 14, 2010

### Skolon

1. As time past, the accelerated expansion of Universe will make to see less and less galaxies, or because we can see further, we will see more and more galaxies?

2. Considering a constant expansion (not accelerated) at today value (70.8 (km/s)/Mpc), how far is the most distant galaxy to witch we can send a radio message? How far it will be that galaxy when the message will arrive?

Thank you for any answer.
I will appreciate if somebody will show me the equations used to calculate the values for second question.

2. Jan 14, 2010

### marcus

Skolon, when people talk about the expansion rate (and its increase) they are talking about the time derivative of the scalefactor a(t).
This is what plugs into the metric, the distance function used in the standard cosmo model.

Expansion means a'(t) is positive. Acceleration means a'(t) is increasing, in other words a''(t) is positive.

This doesn't translate directly into facts about the Hubble rate H(t).

In fact the Hubble rate H(t) is currently decreasing. And is projected to continue decreasing indefinitely.
The Hubble rate is defined to be H(t) = a'(t)/a(t) and the denominator a(t) is increasing so rapidly that it makes H(t) decrease.

If we had a constant expansion H(t) would continue to decrease.

So if you want to ask about what if expansion were constant then you should specify that the time derivative of the scale factor is constant.
That is, you should require that a'(t) = constant.
And in other words a''(t) = 0.

Then one can answer your question, the question that I think you intend to ask. In the zero acceleration case there is no galaxy that we cannot send a light-signal to.
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Incidentally, if one took what you said literally, about H(t)= constant, that would correspond to exponential expansion. There would have to be rapid acceleration in order to achieve constant H(t). We would have a definite horizon beyond which we could not send messages. Galaxies more than some 13.8 billion lightyears would not be reachable.
The formula is just the formula for the Hubble distance c/H, since H in this case would be constant.

Last edited: Jan 14, 2010
3. Jan 14, 2010

### Skolon

I know and I understand that facts. But what is that related to my (first) question?

4. Jan 14, 2010

### marcus

Good, glad you understand. The answer to your first question is that we see less and less.

Because of accelerated expansion, eventually we will only be able to see our own local group of galaxies (andromeda and few others)

And our local group (of on the order of 10 galaxies, mostly small) will gradually merge into one big galaxy.

And all we will see is that one big galaxy.

And the CMB microwave will gradually redshift and redshift until it is so weak that we cannot detect it. The images of other galaxies will gradually fade away as they cross the horizon.

The estimated distance to the horizon is around 15-16 billion lightyears.

(I am using the "freeze-expansion" type of distance. A galaxy is 15 billion lightyears from us, by this measure, if you imagine freezing the expansion process and then it takes 16 billion years for a signal to reach.)

But in fact because of accelerated expansion if a galaxy is, today, 15-16 billion lightyears away, a light signal that we send today could never reach it even with unlimited time.

Lawrence Krauss has a good 2007 article about the future, according to the standard model.
You can go to arxiv.org and look up L Krauss.
You will find this:
http://arxiv.org/abs/0704.0221
It is free to download.
This article will give details I can't include in this post.

Last edited: Jan 14, 2010
5. Jan 15, 2010

### Chalnoth

Well, sort of. We'll still see all of the same objects we can see today. Those objects will just become more and more redshifted as time goes on, eventually to the point that their light will be undetectable.

6. Jan 15, 2010

### marcus

Good description. What I meant by gradually fading but didn't say it so clearly and explicitly.
Analogous to the red-out fading images on a BH event horizon, of things that have fallen thru, which an outside observer sees.

I've been using 15-16 billion lightyears as the current distance to the cosmological event horizon, do you have a more exact figure that you prefer. It's an interesting visual concept, the cosmo EH, maybe we should discuss it more.

7. Jan 15, 2010

### Chalnoth

The problem is that the cosmological event horizon depends upon the entire future expansion history of our universe, and is therefore highly model-dependent. Sure, you could write down a more accurate estimate based on some particular model, but since we don't know whether or not that model is correct, you'd just be over-estimating your certainty as the the actual value.

So personally, I'd prefer just to say something more vague like 15-16 billion light years. It's more honest to what we actually know about the cosmological event horizon.

8. Jan 15, 2010

### marcus

I'm happy with that. And it should be made clear that this estimate for the cosmological event horizon arises in the context of the standard LCDM cosmo model. When we've been discussing the standard picture I often take that for granted and neglect to mention it.

9. Jan 15, 2010

### Skolon

Thank you both.
I hope you will not be cross with me if I will ask you other thinks related to expansion. I really must try to clarify a lot of miss-understanding I have related to it.

1. I know that a(tP) is the scale factor for today (tP~13.7Gyr) and usually is equal with 1. For this a(tP) we have lP, the comoving distance at present epoch. What is lP? A distance from us to ... where? What it is its value (in lyrs)?
The equation a'(tP)=H0 (=70.8 (Km/s)/Mpsec) is correct? If is so, a'(t)=constant does mean that H will ever be equal with H0?
[Note: I know that in our Universe H=a'(t)/a(t) will be greater than H0 and its grow rate is decreasing (it's an asymptotic grow to a value). But my questions are for a better understanding of used terms.]

2. If a''(t)=0 than a'(t)=constant and this imply that Universe is expanding, you said. But, if a'(t)=0 (0 it is also a constant, isn't it) this mean we are in a static Universe?
Let suppose that a'(t)=constant and it is not zero. Because the expansion started some time ago there exist galaxy which are receding from us with a very closely to speed of light velocity (if velocity is the right word, I never understood the distinction between velocity and speed in English language). So, if we will send a message to it until our signal will arrive to the present location of that galaxy that will have a receding velocity much greater than c (and it will far away from present location).
So, why marcus said that "In the zero acceleration case there is no galaxy that we cannot send a light-signal to"?

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