# Expansion of the universe

1. Nov 13, 2013

### CWatters

As I understand it distant objects are so far away from us, not because they are moving away from us through space but because the very space between them and us is expanding.

Am I right in thinking that one bit of evidence for this is that some galaxies are 30 billion light years away? So had they been moving away from us through pre existing space (eg moving in the conventional sense) they would have had to be travelling faster than light?

2. Nov 13, 2013

### abrewmaster

Technically the galaxies could not be moving at all if space is expanding so chances are they are not moving faster than light since that would break the laws of physics.

"Metric expansion is defined by an increase in distance between parts of the universe even without those parts "moving" anywhere".

3. Nov 13, 2013

### Staff: Mentor

That's pretty much correct, Cwatters.

4. Nov 13, 2013

### Buckleymanor

Must remember to use that if I receive a speeding ticket.
"Well me lud it was actualy a metric expansion of the road the vehicle itself was not even moveing."

5. Nov 13, 2013

### marcus

Good question! and you had the right idea. Here is a simple table to illustrate. The earliest stars and galaxies we see emitted the light we're getting at a time when distances were about 1/11 of their present size. The wavelengths of their light have been stretched by a factor of 11. (This is called "redshift 10", for historical reasons the "redshift" is always one less than the wavelength and distance enlargement factor.)

The table says those galaxies emitted the light (that we are getting today) back in year 0.47 billion. And back then they were 2.86 billion LY from us (ie. from the matter than eventually became us.) That's what is called the proper distance--the distance you would have measured with string or rods or radar if you could have paused the expansion to make it possible to measure. And it says how fast that distance 2.86 Gly was expanding at that time, namely a bit over 4c (4 times the speed of light).

$${\scriptsize\begin{array}{|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|} \hline S&T (Gy)&R (Gly)&D_{now} (Gly)&D_{then}(Gly)&V_{now} (c)&V_{then} (c) \\ \hline 11.000&0.47&0.7&31.4&2.86&2.18&4.02\\ \hline 10.000&0.55&0.8&30.7&3.07&2.13&3.74\\ \hline 9.000&0.64&1.0&29.8&3.31&2.07&3.45\\ \hline 8.000&0.76&1.1&28.7&3.59&2.00&3.14\\ \hline 7.000&0.93&1.4&27.5&3.93&1.91&2.81\\ \hline 6.000&1.17&1.8&25.9&4.32&1.80&2.46\\ \hline 5.000&1.54&2.3&23.9&4.78&1.66&2.08\\ \hline 4.000&2.15&3.2&21.2&5.30&1.47&1.66\\ \hline 3.000&3.29&4.8&17.3&5.76&1.20&1.20\\ \hline 2.000&5.86&8.1&11.0&5.52&0.77&0.68\\ \hline 1.000&13.79&14.4&0.0&0.00&0.00&0.00\\ \hline \end{array}}$$

6. Nov 13, 2013

### marcus

Watters, I think you can readily figure out for yourself all the columns of that table except possibly the one labeled R. Credit for table goes to PF member named Jorrie who created a table-making calculator that embodies today's standard cosmic model. He calls the calculator "Lightcone". I have a link to it in my signature. You can adjust the model parameters and also get different ranges of the wavelength&distance stretch factor.

You can see by looking at the S=10 row that a galaxy whose light comes to us wavestretched by a factor of 10 emitted that light back in year 0.55 billion, when it WAS 3.07 Gly from us. And naturally it is NOW 30.7 Gly from us because distances have grown by a factor of 10 while the light was in transit. Distances and wavelengths grow by the same factor while the light is traveling towards us.

The R column is a good way to keep track of the PERCENTAGE distance growth rate. For example the S=1 row refers to the present instant (year 13.79 billion). At the present time, cosmic-scale distances are expanding at percentage rate of 1/144 % per million years.

Back in year 0.47 billion around time when earliest stars and proto-galaxies were forming, distances were growing at the rate of 1/7 % per million years.

You can read percentage growth rates directly off of the R column.

Officially, R is the "Hubble radius", defined as the distance which (at that moment in history) is growing at the speed of light---other cosmic-scale distances growing at speeds proportionate to their size.

So you can see by looking at the S=9 row that back in year 0.64 billion the Hubble radius was about 1 billion LY.
And in a million years it would have grown by a million LY. And that is 1/10 of one percent!
So the percentage growth rate back in that day was 1/10 % per million years. Which is part of what you can read directly off the R column. Just like you can read 1/7 % and 1/144 %.

So it's a useful column and gets included along with the other more intuitive ones like T=Time and Dnow and Dthen. R is your handle on the actual rate of distance expansion.

Be sure to ask if you have questions about the cosmologists' basic standard model! Quite a few people around PF are glad to help out.

7. Nov 13, 2013

### marcus

I redid the table in post#5 to include more rows---more steps between the era when stars were first forming and the present day---and also to show a bit more precision in the R column (two decimal places instead of just one).

You can see that the percentage expansion rates you read from the R column are approximate.
In year 0.47 billion distances were growing approximately 1/7 percent per million years and more precisely at 1/7.1 percent per million years.

For my purposes as relates to most of our discussions here an approximate figure like 1/7 percent is just fine. I don't have to remember or think in terms of higher precision because it gives an adequate idea of the rate of expansion at that time in history.

If you visit the Lightcone calculator and start exploring, open the "column definition and selection" menu and you'll see how to choose which columns to display, with what level of precision. To make this table I checked the "linear steps" box.

$${\scriptsize\begin{array}{|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|} \hline S&T (Gy)&R (Gly)&D_{now} (Gly)&D_{then}(Gly)&V_{now} (c)&V_{then} (c) \\ \hline 11.000&0.47&0.71&31.4&2.86&2.18&4.02\\ \hline 10.500&0.51&0.76&31.1&2.96&2.16&3.89\\ \hline 10.000&0.55&0.82&30.7&3.07&2.13&3.74\\ \hline 9.500&0.59&0.89&30.3&3.19&2.10&3.60\\ \hline 9.000&0.64&0.96&29.8&3.31&2.07&3.45\\ \hline 8.500&0.70&1.05&29.3&3.45&2.03&3.30\\ \hline 8.000&0.76&1.14&28.7&3.59&2.00&3.14\\ \hline 7.500&0.84&1.26&28.1&3.75&1.95&2.98\\ \hline 7.000&0.93&1.40&27.5&3.93&1.91&2.81\\ \hline 6.500&1.04&1.56&26.7&4.12&1.86&2.64\\ \hline 6.000&1.17&1.76&25.9&4.32&1.80&2.46\\ \hline 5.500&1.34&2.00&25.0&4.54&1.73&2.27\\ \hline 5.000&1.54&2.30&23.9&4.78&1.66&2.08\\ \hline 4.500&1.80&2.69&22.7&5.04&1.57&1.87\\ \hline 4.000&2.15&3.19&21.2&5.30&1.47&1.66\\ \hline 3.500&2.62&3.87&19.4&5.56&1.35&1.44\\ \hline 3.000&3.29&4.80&17.3&5.76&1.20&1.20\\ \hline 2.500&4.28&6.14&14.6&5.83&1.01&0.95\\ \hline 2.000&5.86&8.11&11.0&5.52&0.77&0.68\\ \hline 1.500&8.60&10.95&6.3&4.21&0.44&0.38\\ \hline 1.000&13.79&14.40&0.0&0.00&0.00&0.00\\ \hline \end{array}}$$

For easy comparison, I'll bring forward the earlier table from post#5:
$${\scriptsize\begin{array}{|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|} \hline S&T (Gy)&R (Gly)&D_{now} (Gly)&D_{then}(Gly)&V_{now} (c)&V_{then} (c) \\ \hline 11.000&0.47&0.7&31.4&2.86&2.18&4.02\\ \hline 10.000&0.55&0.8&30.7&3.07&2.13&3.74\\ \hline 9.000&0.64&1.0&29.8&3.31&2.07&3.45\\ \hline 8.000&0.76&1.1&28.7&3.59&2.00&3.14\\ \hline 7.000&0.93&1.4&27.5&3.93&1.91&2.81\\ \hline 6.000&1.17&1.8&25.9&4.32&1.80&2.46\\ \hline 5.000&1.54&2.3&23.9&4.78&1.66&2.08\\ \hline 4.000&2.15&3.2&21.2&5.30&1.47&1.66\\ \hline 3.000&3.29&4.8&17.3&5.76&1.20&1.20\\ \hline 2.000&5.86&8.1&11.0&5.52&0.77&0.68\\ \hline 1.000&13.79&14.4&0.0&0.00&0.00&0.00\\ \hline \end{array}}$$

Last edited: Nov 13, 2013
8. Nov 20, 2013

### gabriel.dac

This video may be quite relevant to this topic

Last edited by a moderator: Sep 25, 2014
9. Nov 20, 2013

### CWatters

Thanks for the replies. Pretty sure I understand the basics of what's going on. I just hadn't appreciated that the expansion was so fast.

10. Nov 20, 2013

### Myslius

CWatters, marcus gave the exact data that we observe. It might be a bit difficult to understand because of acceleration.
Here's a simplified version: Suppose from the beginning of the universe a space between a galaxy and us are expanding at the speed of light and it's keeping constant speed. In 13.82 billion years we would see how 5 billion years have passed to the recessing galaxy, not 0. Or to be more precise 13.82/e billion years. Actually we would see other galaxies too, even if those galaxies are recessing faster than c. For constant expansion rate we would get 13.82/e^(v/c) formula. No matter how fast galaxy recesses away from us it only makes to appear younger, but not to become invisible due to expansion.

I'm not quite sure that the fact that those galaxies looks farther away means that it is the space that expands. Special relativity predicts quite the same luminosity as universe expansion.

Last edited: Nov 20, 2013
11. Nov 26, 2013

### whatdoctor

Calculation for rate of expansion

The current estimates ont he size of the Universe put it at about 78 Billion ly across (or a radius of 39 Billion ly).
If we accept that the age of the Universe is 13.8bly and the extra size (assuming it could grow at the speed of light without this extra) is due to extra space being created and this extra space is proportional to how much space there is already.

This give us dy/dt=aY +1
so y = (e^(at) - 1)/a
We have two known points: y=0, t= 0 and y=39, t=13.8
i could not figure out a formula to solve for a so i just plotted it in Excel to find the value of a that corelated with the above.
This yields a value for a of 0.131264519371051 (or 13.12645%) growth per billion years.

This means that the furthest object to which we can ever hope to reach is a mere 5.62 billion ly away. Anything further than that would travel away from us faster than the speed of light.
The only reason we can see things that are 13 billion years old is that they were closer than 5.62 billion ly when they emitted the light we are seeing today.

When I say they are moving away from us faster than the speed of light, they are not breaking the speed limit. It is just that extra space is being created so their distance from us is increasing at a rate faster than light can travel.

12. Dec 1, 2013

### tanzanos

This may sound out of topic but if the universe is expanding then how are some galaxies on a collision course with each other? Should they not all be receding from each other?

13. Dec 1, 2013

### Staff: Mentor

When galaxies are close enough to each other, the strength of gravity is strong enough to overcome expansion.