# Expansion of the universe

1. Mar 14, 2012

### C. Bernard

Should not we say "the universe WAS expanding" rather than "IS expanding" since
the red shift augments as we go back in time to the farthest and therefore the oldest
galaxies?

2. Mar 14, 2012

### Drakkith

Staff Emeritus
What do you mean? To our knowledge the universe is still expanding.

3. Mar 15, 2012

### C. Bernard

What i mean is:is the speed of the expansion slowing or accelerating?
It seems to me that it is slowing since it is greater as we go back in time.

4. Mar 15, 2012

### AlchemistK

The expansion is increasing, and that too at an exponential rate. In fact, even faster than the speed of light.

5. Mar 15, 2012

### dpa

i think i got C.bernard's argument.
The red shifts we observe are of light from stars far distant and hence are older than present. So should we not say cosmos was expanding?

6. Mar 15, 2012

### Drakkith

Staff Emeritus
The recession velocity of galaxies increases as we look further back in time. The acceleration of the expansion turns out to be increasing.

The rate of expansion causes objects to accelerate in velocity away from us. Since the speed of light is a velocity, not a measure of acceleration, nothing can accelerate at the speed of light.

In the absence of something stopping the expansion I don't see how you can say that.

7. Mar 15, 2012

### C. Bernard

The speed of the expansion could be greater than the speed of light since it's the universe that is expanding, nevertheless we are measuring it with galaxies that no longer exist!
So i am still of the opinion that we should speak of it as being greater in the past.

8. Mar 15, 2012

### alexg

But observation show us that it wasn't.

9. Mar 15, 2012

### marcus

My take on it is that we "measure the speed of expansion" by fitting a mathematical model to the data. We compare what the model says we ought to see with what we actually do see, and adjust the parameters (tweak a few knobs) to get the simplest best fit.

Are you comfortable with calculus? The model is a couple of simple equations and it generates curves---like there is one called a(t) the "scale factor". It is a number that increases with time.

the time derivative da/dt of a(t) could be written a'(t). Are you used to that prime-for-slope notation?
That is the closest thing I can think of that corresponds to the idea of "speed of expansion".

It is not a speed that you could write down in meters per second. Or write in terms of lightyears per century or whatever.

a(t) is a curve, at each time t it is a definite number that is currently around 1, and it's currently increasing by about 1/140 of one percent in a million years.
Right now today it is 1.00000
and in exactly one million years from now it will be 1.00007.

Right now today the time derivative of the scale factor is a'(t) = 0.00007 per million years. (a kind of "James Bond" number, if you like.)
When people say "expansion is accelerating" they mean that a'(t) is increasing. They do not mean that some uniquely defined SPEED is increasing. A speed is something you can express in meters per second.
You could call a'(t) a *rate* I guess, and say the *rate* is increasing.

At some times in the past we are confident that a'(t) has been extremely much bigger than the "James Bond" size it has today. And we are certainly confident that in the relatively recent past it has been LESS than today's value.
So the expansion rate---correctly expressed as a'(t) the timederivative of the scalefactor--has in the past been both bigger and smaller than it is today.

We can be pretty confident in the model (nothing in science is completely sure but this is unusually well supported) because it agrees well with masses and masses of data, millions of datapoints with more coming in all the time. And because the model is a straight shot derivation from the Einstein 1915 law of gravity, an equation which has been checked to exquisite precision by numerous experiments in the solar system.
So we don't look out and measure some particular speed which is "the speed of expansion of the universe". there is no such speed. We fit a model to a huge amount of data, we get a snug fit, and we calculate a curve a(t) and the slope of that curve is a'(t). It is not a speed but it is what popularizers and journalists call "the speed of expansion".

And that bad translation of a math quantity into words is responsible (along with other bad verbalizations) for much of the confusion.

Last edited: Mar 15, 2012
10. Mar 15, 2012

### C. Bernard

Thanks Markus for your effort and trouble in trying to make me understand that it is the rate of expansion and not the speed. Unfortunately i am very unconfortable with calculus.
Furthermore i was under the impression that the theory was a question of cosmological reshift and the stretching of wavelength discovered by Hubble.
Since it seems to be based on thousands of measures of something else i confess my ignorance and can only hope that not everybody aggrees with your explanation.

11. Mar 16, 2012

### marcus

Getting the simplest best fit model is based on many (hundreds of thousands) measurements of redshift. Once you have a model that predicts in broad outline what has been observed then that model tells you things like "speed of expansion" --- it gives you the curve a(t) which is the expansion history of the universe.

What one directly measures is redshift (and some other things like angular size, luminosity, correlation with microwave sky temperature, periodic behavior but for simplicity let's just focus on redshift). And one makes COUNTS of how many galaxies one sees in a particular ranges of redshift. How the count varies with redshift. So you make direct measurements and you get a kind of "census data". The model has to predict that. In broad outline it has to reproduce nature.

And the model also has to derive from the law of gravity that is the most accurate we known so far (1915 Gen Rel).

So then, at the end of all that---the best fit model gives you a curve. Actually because of uncertainty it gives a range of very similar curves. that curve a(t) is the expansion history. It is a picture of how the scalefactor has increased over time. The slope of that curve, at any given time, is the "speed of expansion" at that time. It started off very steep and then leveled off slightly and is now increasing gradually. It has always been positive slope---a(t) has always been climbing---but the slope has varied.

The point I'm trying to make is that we measure redshifts directly. We do not measure the slope of the scalefactor curve a(t) directly. We fit a model that matches and summarizes all that redshift census data (and other direct observation data) and then that model gives us the expansion history curve.

"Speed of expansion" has no other meaning.

12. Mar 16, 2012

### Khashishi

What we are measuring is the amount of expansion that occurred between when the light was emitted and when the light finally reaches us. We assume that the redshift occurs because the light is expanded mid-flight. So yeah, this is measuring the expansion that occurred in the past, but not just at the point of emission.

13. Mar 16, 2012

### marcus

Exactly right! When you measure a redshift number z, for some object, then
1+z is the ratio of scalefactor now to scalefactor back then when the light was emitted
1+z = a(now)/a(then)

That is one small bit of information about the curve a(t) the expansion history of the universe, and from many many such measurements one reconstructs the whole a(t) curve.

The "speed of expansion" has no other meaning besides the slope of that curve (which we do not measure directly but are able to construct by a kind of curve-fitting, I suppose you could call it, more exactly I'd call it model-fitting, to the data.)

The present slope of the the a(t) expansion history curve is
0.00007 per million years.
that is the fractional increase of any distance between two wide-separated stationary observers that occurs over the course of a million years.

14. Mar 16, 2012

### C. Bernard

It seems i am beginning to see the light (no pun intended). So can we say we measure the expansion that occured during the time it took the light to get to us?
And that it is an integral of all the various expansions that took place (which could have varied one way or the other)? And the overriding trend is an augmentation of the rate of expansion?

15. Mar 16, 2012

### marcus

That sounds good to me. You could try it on other folk and see if works for them too.
Translating from a partly mathematical scheme into a purely verbal english language description is often awkward. It's likely to be either inconveniently wordy or else imperfect in some other way. But IMHO you got it right.

16. Mar 22, 2012

### eltodesukane

It was, and it is. And it's accelerating.

17. Mar 29, 2012

### bill alsept

I think what a lot of people are saying and it seems more every day is that what we are actually seeing is not what’s happening but is being interpreted that way. The greatest scientist in the world use to look up at the heavens and knew for sure that earth was the center of it all because it was so obvious.

18. Mar 29, 2012

### Chronos

Science is about model building. It is imperfect, but, the most productive approach to date. Just because certain observations are inconsistent with a model does not mean the model is flawed, perhaps incomplete, but, not necessarily flawed. It's not like there is no such thing as inaccurate deductions drawn from observation, or simple observational errors. If you put your pants on backwards it is tempting to blame the tailor for the poor fit.

19. Apr 2, 2012

### John15

I have the same problem with redshift. I have seen the graphs and yes speed over distance shows acceleration but change distance for time and you get a deceleration i.e. redshift in light say 10 million years old is much less than that for 10 billion year old light. so the question is should we be using distace or time?

20. Apr 2, 2012

### space_buster

Charts of supernova as a function of red shifts are used to determine the speed of expansion of universe. Adam Riess first looked at the results, he was quite surprised–the expansion of the universe was not decelerating, but accelerating–it was expanding faster and faster! The most likely explanation was that old cosmological constant term of Einstein!