# Redshift, Distance & Expansion rate question

1. Jul 26, 2010

### DLuckyE

I'm a bit confused about redshift and the apparent increase in acceleration. If I understood it correctly redshift is caused by the expansion of the universe (space itself).

What I don't understand though, if galaxies further away have a higher increase in redshift vs distance than galaxies closer to us, then how do we get from that to the conclusion that the expansion is accelerating?

I must be missing something, but wouldn't that mean it was actually slowing down since light that has been traveling longer has a higher increase in redshift than light that has been traveling for a shorter period? I'm assuming that if the expansion is at a steady rate the increase would be linear since light would be continuously stretched out over the whole journey?

Can someone please point out where i'm making the error? ;)

2. Jul 27, 2010

### Chalnoth

The way it was originally measured through supernovae is this.

Type I-A supernovae are what are called "standard candles". They are all right around the same brightness (not exactly the same brightness, but close enough for our purposes: we just need to measure lots and lots of supernovae to smooth out the variations). So, we can tell how far away a supernova is by looking at its apparent brightness, and we can tell how fast it is moving from the redshift.

These two things combine to give us an account of how quickly the universe has expanded through time. What we find is that if we go far enough away, the supernovae start to appear dimmer for a given redshift than we would expect if there were no acceleration. This means that for the same redshift, they are now further away than we would otherwise expect.

This measurement, by the way, has been confirmed by a variety of other cosmological measurements, and is on pretty solid ground today.

3. Jul 29, 2010

### DLuckyE

Thanks for the reply, so my error is that I assumed red shift was measured to increase faster when further away while it's the other way around?

In other words, the difference in redshift between a supernova 11 billion light years away and 12 billion light years away is smaller than that of 1 billion light years away and 2 billion light years away?

4. Jul 29, 2010

### Chalnoth

I'd have to run through the calculations. I'm not so sure this is the case, though, because the acceleration didn't take over until a few billion years ago (before which the expansion was decelerating). I mean, I think you could make the statement that the redshift difference between objects 1 billion and 2 billion years ago would be greater than between objects 2 and 3 billion years ago, but I'm not so sure about 11-12 billion years ago.

Anyway, usually we don't calculate things in these terms. It's relatively easy to compute a distance from a redshift, but it isn't quite so easy to go in the other direction.

5. Jul 29, 2010

### zebb

I'm not a physics scientist or student. I don't have the practical background to look at the math to prove or disprove what we are being told is true about what is essentially the doppler effect for explaining the fact that the universe is expanding. I trust what Hubble and Einstein have concluded by I would like it in terms I can understand. My question is that objects moving away from us are in the red spectrum. So the "convincing" evidence then is that objects appear to be deeper into the red spectrum the further away they are in the universe? Is there some formula that proves this? Considering the vastness of space, how can we be so sure that they are moving away at an accelerated rate if practically everything is in the red spectrum? Is thre a very minute difference or is the difference pretty obvious? In my opinion this is one of the most important discoveries in the universe, along with the presence of background gamma radiation. It points to a finite beginning point and therefore proof of a creation point. So further review of the "red shift" observation is warranted.

6. Jul 29, 2010

### Calimero

Yes, there is very simple law called Hubble law. See: "[URL [Broken]

As for your 'everything is in the red spectrum' statement, it is not quite true. We call stretching of EM wavelengths - redshifting. That does not mean that everything is in the red part of spectrum, it just means that wavelengths are increasing, or frequencies decreasing, depending of recession velocities, or distance. For example CMB radiation is stretched to microwave part of spectrum (nothing to do with red), and there are plenty of objects which are observable in the infrared part of spectrum.

Last edited by a moderator: May 4, 2017
7. Jul 30, 2010

### DLuckyE

Sorry to keep going at this, but i'm still confused :P

If you look at various sites showing graphs and calculators they all seem to show that the further galaxies are away the faster the red shift increases over distance?

8. Jul 30, 2010

### Chalnoth

Well, there are two difficulties with properly estimating this. First, you have to compare against a "baseline" universe where there is neither acceleration nor deceleration. This would be an empty universe where $\Omega_m = \Omega_\Lambda = 0$, $\Omega_k = 1$. Second, you have to find a proper measure of velocity (redshift does not equate to velocity). You could use the relativistic doppler shift to compute velocity from redshift:
http://en.wikipedia.org/wiki/Relativistic_Doppler_effect

This isn't strictly the velocity we use in cosmology, but it should be halfway decent.

9. Jul 30, 2010

### nismaratwork

You may be thinking of the emergence of recession speeds "augmented" by the expansion of space, which leads to apparently superluminal recession speeds, or you're thinking of what Chalnoth already addressed.

10. Jul 31, 2010

### DLuckyE

Unless I understood it wrong, cosmological redshift are caused due to the expansion of space and thus the photons getting stretched out. So even if there was no acceleration redshift would increase over distance right? Since the photon will be stretched for a longer period of time.

11. Jul 31, 2010

### Janus

Staff Emeritus
Correct. The difference between a universe expanding at a steady rate and one with an accelerating (or decelerating) expansion, is in how exactly redshift changes with distance.

With a steady rate expansion, the recessional speed and distance would be in exact lock step. Double the distance and you exactly double the recession speed. There's a one to one ratio.

For an accelerating universe, this isn't the case, the ratio of distance and recession speed changes as we look deeper and deeper into the universe. This because as we look further out we are seeing the universe as it was earlier in time when the recession speed was less. Thus we can form a picture of how fast the universe been expanding over time.