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I have read other posts on this but I'm still confused. I'm trying to conclude how an accelerating and decelerating expansion rate graph would look like when it's plotted against the redshift Z. However, my reasoning collides with how the graph lines actually should look like.

My reasoning is as follows: enter image description here

It shows a star at a the same original distance D0 from the observer, that is emitting light at t=0 towards the observer (yellow arrows). After a time D0 / c (t=now), as soon as the observer receives the light, the star has moved a ΔD distance. At t=0 the star has the same speed in all 3 scenarios, thus also the same initial redshift z(t=0). However, depending on the rate of expansion, the received redshift either stays the same, is larger or is less than the initial redshift z(t=0).

This means that if the expansion rate is accelerating, an observer measures that the star has a larger received Z and he would underestimate the initial distance D0 if he considers that received Z as being constant over time. A decelerating expansion would make the observer overestimate the initial distance D0 if he considers the decreased received Z as being constant over time. Furthermore, the observer would therefore respectively understimate and overestimate the ΔD traveled by the star.

According to the picture, a star at a same distance D0 that is accelerating or decelerating over time would have respectively a larger and smaller received redshift Z than if the expansion was constant, thus deviating from it with increasing distance. Thus, I'd plot the following graph for redshift over the distance (graph color represent the arrows color in the scenarios):

enter image description here

However, sources like this suggest that the blue line should be the decelerating scenario and the red line the accelerating one, so it's the other way round from what I reasoned. What am I reasoning wrong here?

Phy
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  • Cosmological redshift is not due to the "speed" of an object. It is to do with by how much the wavelength has been stretched by cosmic expansion during the time that the light has been travelling towards us. – ProfRob May 08 '17 at 15:28
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    See if this helps https://physics.stackexchange.com/questions/68493/according-to-hubbles-law-how-can-the-expansion-of-the-universe-be-accelerating?noredirect=1&lq=1 – ProfRob May 08 '17 at 15:40
  • A post in that link says that redshift accumulates over time during the journey of a photon to the observer. Does that mean that in my scenario of a constant expansion rate, the redshiftt z at t=0 is different (less) than the received redshift z? Even though the expansion rate was constant all along? – Phy May 08 '17 at 16:04
  • The term "redshift z at t=0" is meaningless. An observer near the source in question measures no redshift. An observer far away measures a redshift. I fear you are thinking of the redshift in terms of the doppler effect. – ProfRob May 08 '17 at 16:09
  • That's what I'm fearing as well. Let me formulate my question better; suppose there's another observer B between the star and the initial observer in my picture. If the expansion rate was constant all along, would that new observer B measure a smaller redshift than the initial observer? – Phy May 08 '17 at 16:13
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    Nope. Don't follow. A closer observer will always measure a smaller redshift. – ProfRob May 08 '17 at 16:32
  • But isn't that what I'm saying? Another observer between the initial observer and the star, thus being closer to the star, will measure a smaller redshift than the initial observer? Even if the expansion rate was constant? – Phy May 08 '17 at 16:35
  • If I understand this, then there are possibly a few issues here. (1) An observer has no idea of the distance / redshift at $t=0$. The best that they can do is, measure the wavelength at $t=now$ and then estimate $D$ from it to know how far the object is. (2) So with no previous record, even if expansion has since slowed down, the observer can at best estimate where the distant object is now, without being able to tell that it was previously accelerating away faster. (3) To deduce whether expansion rate has decreased or increased, a bulk of sources from the same direction will be needed. – Dhruv Saxena May 10 '17 at 21:49
  • Thanks, this helped me. Also, can't one see if expansion rate has changed based on if the proportionality between redshift and distance breaks at very large distances? – Phy May 29 '17 at 14:20

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