Confusion about redshift in a universe with accelerating expansion

[Xilor]

Hello, I've been trying to internally conceptualize as much of physics as I could, and doing so I realized that something I thought I understood at first does not actually make any sense in my head anymore. And since it doesn't, I'm afraid that I might have misunderstood a lot of other concepts, so I was hoping you folks over could tell me where I'm making my mistake. So, what I don't understand is how the observed redshifts show that the expansion of the universe is accelerating rather than decelerating.

From what I gather, astronomers have looked at supernovas at very large distances. Supernovas of which we can determine their distance to us by means of luminosity when it's known what kind of supernovas they are. Measured redshifts of these supernovas are compared to their distances, and from that it is seen that supernovas which are further away have a larger redshift than what would be predicted by a linear expansion. The further the supernova, the bigger the increase in redshift compared to linear expansion.
We see redshifts in all directions, these redshifts are correlated with distance and some of the redshifts observed would mean that some objects would be moving away at superluminal speeds. Because of these reasons, these redshifts are considered not to be a Doppler-shift effect, but are rather created through something that is happening in the space between the objects. The objects don't really move away, the distances to them just increase through expansion while the photons travel. These photons are redshifted during their travel because they are pulled apart by the expansion. Am I correct so far? If not then that could already solve the confusion.

In the case that that is correct (or correct enough) though, why would that show accelerated expansion?

These redshifts happen after the photon has left an object, so I'd think that we should look at the photon and not the object they are emitted from, what is happening to the photon during its travel?

With no expansion, a photon would arrive with no redshift.

With linear expansion, the photon throughout its travel will continually be slowly redshifted at equal rates. During the early part of its travel it will redshift just as much as in the later part.

With accelerated expansion, the photon throughout its travel should experience different rates of redshift. Acceleration expansion over time obviously means that there will be more expansion during the later part of its travel than during the early parts, that's what accelerated means. So, initially the expansion would be closer to no expansion, and the photons won't be stretched out as much. Near the end however, while the expansion has increased, the stretching apart and the accompanying redshift should be greater.
So when observing this, shouldn't it be the other way around? The end part, or the most recent movement of photons is the part with the highest redshifting of the photons and it is from the point of the observer the closest area. So the closest area should show the highest expansion compared to linear expansion, and thus the strongest stretching of photons and redshift. A source of photons within this close area should have the highest redshift per distance traveled. And sources further away should have less redshift per distance traveled, because the photons emanated from these further sources were going through space that wasn't expanding as much yet.
This seems like the complete opposite of the data to me, further supernovas show larger redshifts and closer novas show smaller redshfts. The data seems to say that there has been a deceleration instead to me. Further and older sources have been redshifted more than linear redshift (calculated with closer sources) would suggest, so the photons from them had to experience stronger redshift and expansion at the start. More expansion during early times, less expansion during later times = decelerating expansion.

So, I don't understand at all how I come to such a completely different conclusion, where is my logic going wrong?

 

[mfb]

We see redshifts in all directions, these redshifts are correlated with distance and some of the redshifts observed would mean that some objects would be moving away at superluminal speeds.

If you plug the observed redshift in the SR-formula for Doppler shift, you always get a subluminal velocity. Superluminal speeds appear only as a result of the calculation for the relative velocity (for some choices of coordinates) where redshift comes from the expansion of the universe.

The objects don't really move away, the distances to them just increase through expansion while the photons travel. These photons are redshifted during their travel because they are pulled apart by the expansion. Am I correct so far?

If you use comoving coordinates (coordinates which expand together with the universe) for your description.

In the case that that is correct (or correct enough) though, why would that show accelerated expansion?

Based on the assumption of no acceleration and the distance, you can calculate the expected redshift. You know the current redshifting rate (from the observation of galaxies nearby) - if the observed redshift deviates from the expectation, this indicates a different redshift rate in the past.

 

[Xilor]

If you plug the observed redshift in the SR-formula for Doppler shift, you always get a subluminal velocity. Superluminal speeds appear only as a result of the calculation for the relative velocity (for some choices of coordinates) where redshift comes from the expansion of the universe.

Ah, well that's interesting to know. So an object 'expanding away' from us at a certain ' speed' will always have a different redshift than the redshift from an object actually moving away at the same speed? Or is that only true with non-linear expansion?

Based on the assumption of no acceleration and the distance, you can calculate the expected redshift. You know the current redshifting rate (from the observation of galaxies nearby) - if the observed redshift deviates from the expectation, this indicates a different redshift rate in the past.

I understand that. What I don't understand is why this deviation indicates an acceleration rather than a deceleration of the expansion. Larger redshifts than the expectations on further objects (further in the past) seems to indicate more expansion in the past to me.

 

[mfb]

With special relativity only, you simply get wrong numbers - you get time dilation where you don't expect it.

What I don't understand is why this deviation indicates an acceleration rather than a deceleration of the expansion.

Depends on the deviation?

Larger redshifts than the expectations on further objects (further in the past) seems to indicate more expansion in the past to me.

To say "larger", you have to compare two numbers.
Compare it with the past expansion rate and linear acceleration: Larger redshift
Compare it with the current expansion rate and linear acceleration: Smaller redshift

 

[Xilor]

Let me use 2 graphs to illustrate what I mean with larger redshift.This first graph illustrates what I would call a larger than expected redshift

http://i.imgur.com/H6uhU.png
This second graph illustrates what I would call a smaller than expected redshift

http://i.imgur.com/EfSUX.png

From what I understand, the first graph is what is measured.

And from that first graph I cannot understand how that would imply accelerated expansion, following the argument in the original post. I'd think the first graph would imply decelerated expansion, and the second would imply accelerated expansion. This because we are looking in the past and not the future. A graph as seen from the photon in which time flows from left to right would seem to have to be like the third grap, so that total redshifts and distances match up with how they would be on the first graph on all points of the line.

http://i.imgur.com/1r66s.png

 

[marcus]

This first graph illustrates what I would call a larger than expected redshift
This second graph illustrates what I would call a smaller than expected redshift
From what I understand, the first graph is what is measured.
...

What was measured was a SMALLER than expected redshift, at any given distance. Or conversely, what was measured was a BIGGER DISTANCE corresponding to a given redshift.

Supernovae with a given redshift are DIMMER than would be expected without the slight acceleration effect of the cosmological constant. The dimness indicates that they are farther away than had been expected pre-1998 assuming zero constant.

Sorry I didn't have time to look at your graphs, just wanted to point out that you seem to have the opposite notion to what the measurements found.

 

[Xilor]

Thank you, in that case my confusion vanishes instantly. I'm only left wondering why I thought it was the other way around.

 

[phinds]

Thank you, in that case my confusion vanishes instantly. I'm only left wondering why I thought it was the other way around.

Well, you're not alone. I've seen several people ask exactly the same question here over the year or two I've been a member.

 

[Chronos]

You may find it helpful to read the SA article written by Adam Riess and Michael Turner [Riess was one of the Nobel laureates for discovery of accelerated expansion] -
http://www.scientificamerican.com/article.cfm?id=expanding-universe-slows-then-speeds&page=4. An interesting feature of this discovery is expansion has not always been accelerating. In fact, expansion has only been accelerating for about as long as Earth has been around. Prior to about 5 billion years ago, the data suggests expansion was actually deaccelerating.