I am watching this video of a conversation with Stephen Hawking, Carl Sagan and Arthur C. Clarke and about 9 minutes into the film Carl Sagan says: "The galaxys are running away from each other. The further away they are from each other, the faster they are running away."

Was this just a theory at the time (1988) or am I not understanding something here? That the universe expansion is accelerating was, as far as I am aware, discovered by Adam G Reiss, Brian Schmidt and Saul Perlmutter in 1998.

What you mentioned is just the normal Hubble's law, as was known in the 1920s. It does not require an accelerating expansion to be true. The farther things are from us, the faster they seem to recede from us, as in the well known balloon analogy. I suggest you have a look at Marcus' sticky thread on the balloon analogy.

Jorrie, thanks for the reference to "balloon sticky" thread! There is a ton of stuff in it by now--it keeps growing

I'd like to save the new member some steps and simply emphasize what you just said.

The basic law in cosmology is Hubble Law which says there's a pattern of percentage growth of distance, where the actually percentage rate changes very gradually according to an equation due to Alex Friedmann (which, because the change in the percentage rate is so slow we can almost get away with neglecting in a first discussion.)

Here's a plot of the growth of a generic distance over time: http://ned.ipac.caltech.edu/level5/March03/Lineweaver/Figures/figure14.jpg
You can see the acceleration effect begin to kick in around 7 billion years into the expansion. The actual curve is the heavy dark one. The other curves are what you get by changing the parameters from their measured values.

Then a newcomer could watch a few minutes of the balloon animation: http://www.astro.ucla.edu/~wright/Balloon2.html
See where the galaxies stay in same (long. and lat.) place and the photon wigglers travel at constant speed between them trying to cover distances which keep expanding

I'm beginning to think that the fastest way to get a new member on track is now to suggest he or she go to your online table-making calculator that makes a table of the history of the universe. And ask them to click on the blue dots that get explantions to pop up.

This could be a faster way to get a concrete idea of what's going on, faster than either the excellent FAQ section or the "balloon sticky". Then there is always digging deeper into more detail that could occasion those things.

Well... a bit of a blunder not to do some basic research before posting I must say.
I guess I got carried away a bit there, since Cosmology is a new subject for me where I have much to learn. I'm going to look for that "online table-making calculator" now :)

Baltic, if the percentage rate in the Hubble Law were CONSTANT you would see acceleration all along---exponential growth like money in a bank savings account at constant interest, but look at "figure14" link.

I am trying to imagine a "cosmology in 15 minutes" course for you.

The important thing is how that percentage growth rate of distance changes over time (technically according to an equation, but that is not beginner stuff)

It is because the percentage rate has been DECLINING that figure14 looks more like a straight line growth curve with only a slight hint of exponential growth beginning around year 7 billion.

If you learn to read the columns in Jorries calculator table you can SEE the decline in percentage distance growth rate. Because the percentage is ENCODED in the Hubbletime column labeled "T_Hub"
T_Hub tells you the RECIPROCAL of the percentage growth rate.

Where it says T_Hub = 14.0
that means distances are growing 1/140 of a percent per million years.

Where it says, far in the future like around year 88 billion, that T_Hub = 16.5
that means distances are growing 1/165 of a percent per million years.

The fact that T_Hub almost stops growing means that the percentage almost stops declining and becomes almost constant. Then we will see almost pure exponential growth, at a rate of 1/165% per million years.

That is kind of the paradigm of what they mean by "acceleration", it is the emergence of an exponential distance growth phase because of a certain constant in the Friedmann equation that makes the decline in percentage slow down and level off. Not terribly dramatic---the public got a lot of hype about it. But still, interesting I think.

Ask question! To the extent that the calculator is not yet self-explanatory please do ask.

You can make it show more steps by increasing the number 10 in the Step box.

The present is tagged S=1. You can make it land exactly on the present by checking a certain box right above the top row of the table and then re-calculating.

The YEAR of expansion history is given in the third column.
The rows are according to the stretch factor S, which is the factor by which distances and wavelengths have expanded since that time in the past.

It turns out to be a little more convenient to order the rows by stretch factor S, instead of time. You can see that S=1 (no enlargement of distance) corresponds to the year 13.7 billion, which is the present time.
S=1090 is the amount that the CMB radiation has been stretched and corresponds to year 380,000 when the hot plasma fog cleared and the radiation got free and began to run. So it is a natural place to start the history.

Jorrie, thanks for the reference to "balloon sticky" thread! There is a ton of stuff in it by now--it keeps growing

I'd like to save the new member some steps and simply emphasize what you just said.

Probably the best way to save the newcomers time on the balloon analogy is to start a new thread with just the fully revised balloon analogy suggestions incorperated. 29 pages will typically not get read by the average poster. Have any suggestions for modification on the current balloon thread.

Let's think about Baltic's question some more and think how a quick course called "Expansion Cosmology in 15 Minutes" could be conducted.

"Expansion Cosmology in 15 Minutes" (Course outline and syllabus )

The basic equation in cosmology is Alex Friedmann's equation which tells how the Hubble Rate of expansion evolves over time. Or equivalently how its reciprocal, the Hubble Time, evolves. But let's start with something more intuitive: Here's a plot of the growth of a generic distance over time: http://ned.ipac.caltech.edu/level5/March03/Lineweaver/Figures/figure14.jpg
You can see the acceleration effect begin to kick in around 7 billion years into the expansion. The best-fit curve is the heavy dark one. The other curves are what you get by varying the parameters from their best-fit values.

We don't have any evidence of a boundary, or any "space outside of space", or any large-scale non-uniformity. So to keep it simple we model the universe as approximately uniform and boundaryless. A good 2D analogy for the 3D universe is the balloon model. All space and all existence concentrated on the 2D surface. Watch a few minutes. http://www.astro.ucla.edu/~wright/Balloon2.html
See where the galaxies stay in same place (long. and lat.), getting farther apart all the time, while the photon wigglers travel at constant speed across the surface between them trying to cover distances which keep increasing.

The universe could also be infinite and approximately uniform---infinite space with infinite amount of matter distributed more or less evenly throughout. But the finite ("balloon analogy") model is often easier for people to grasp.

The most important step in understanding is to get QUANTITATIVE experience with the model. A merely verbal concept of the universe doesn't make it. Cosmology means finding the math model (derived from the Einstein law of geometry/gravity) that gives the simplest best fit to all the observational data. So to get a first real feel for the subject go to the online table-making calculator: http://www.einsteins-theory-of-relativity-4engineers.com/TabCosmo6.html

This makes a table of the history of the universe. You decide on the dimensions of the table---e.g. the number of steps---e.g. the range of expansion or time you want it to cover. And Click on the blue dots that get pop-up explanations.

Learn what the numbers in the different columns mean. The second column "a" you can think of as the size of a generic distance---normalized so that it equals 1 at the present day.
The third column "T" is the year count. You can see that the present day is about year 13.7 billion. These two numbers are what you saw plotted in figure14 at the start of this post. The growth of a generic distance---or "scale factor".

In the first column you see the scale factor's reciprocal 1/a, labeled S for "stretch". It is the ratio that distances and wavelengths have expanded since that time in the past. This stretch factor is actually a convenient way to keep track of time because we can actually TELL how much incoming light (e.g. from some galaxy) has been stretched. So we know the S-era it came from. The light is branded with the time it was emitted, and the S number is the brand. Incidentally, until around S=1090 the universe was filled with glowing hot gas, in which light could not travel very far without being scattered. S=1090 is the moment this dazzling "fog" cooled enough to clear and light could run free. So that was the origin of the CMB radiation we now see. The wavelengths have been stretched by a factor of 1090. You may have noticed this number at the top of the S column in the table.

So now a beginner has been introduced to the first three columns of the table:
S, a, and T.
For a first introduction I think there is just one more column---the Hubble Time T_Hub---that one should get acquainted with.

If you take the Hubble Time of any given era (say the present day S=1, 14 billion years), and change years to lightyears, you get that era's Hubble Distance (which you can see at the present day is 14 billion ly).
That is, at that point in time, the distance which is growing at the speed of light. Other distances grow proportionally. A distance twice the Hubble length grows at twice c.
You can work out a bit of arithmetic. When the Hubble time is 14.0 billion years (as it is today) that simply means that distances are growing at percentage rate of 1/140 of a percent per million years. On the other hand at some point in the past when the Hubble time was 7.0 billion years that meant distances were growing 1/70 of a percent per million years.

[To get somewhat better resolution you could change the number of steps from 10 to 26 and check the "exact S=1" box. Then you will see that around year 5 billion the Hubble time was 7 billion years, as in the previous example.]

The main thing is that as you look down the fourth column of the table you can simply read off the listed numbers as percentage growth rates of distance.
You can see, for example, that in the longterm future, many billions of years from now, the distance growth rate will be 1/165 of one percent per million years. And you can see what the growth rate has been in the past. Like that in year 5 billion the corresponding figure was 1/70 of a percent.

So it's time to check out the table-calculator and try some things with it. That could be a 15 minute introduction to cosmology.

Hey Marcus!
Thanks for all the detailed explanations, I will definitely read it through carefully.
Maybe it would be a good idea, just like Mordred said, to put a sticky with this information in the first post, and a very eyecatching topic!

Great, thanks for that.
I am missing one thing, Marcus, perhaps you can give me a hint. Nowhere I found a plot showing the epoch dependence of the Hubble Parameter.

My guess, H(t) is constant during inflation (expansion accelerates exponentially), declines during decelerated expansion, at z = 1 (size of the universe is half compared to today), the begin of accelerated expansion, still declines but less and eventually (depending on the development of the dark energy) will asymptotically reach a constant value again due to exponentially accelerated expansion in the far future.
Please correct, if you don't agree.

I think this is correct. The curve for H(t) is just the inverse of the Hubble radius (or sphere), which is the one usually plotted over time, e.g. the graphs in Marcus' sig., Figure 1.

I have done log-linear graph, though just back to z ~ 1000. I guess to see what happens much further back, one would need log-log. Although, I do not think one would learn too much from it, perhaps just what H(z) would have been at say z ~ 10^{10}, or earlier. From the equation for H that I have used in the calculator (which does not calculate for such high z), with radiation domination, I estimate it of order H_{z=10^10} ~ 10^{28} H_{0}.