# Questions Regarding The Expansion of The Universe

Hi

I got into some thinking recently and I could really need some help unsolving these mysteries currently going on inside my head.
First of all, the universe is expanding, is this a fact?
2nd, if now the universe is expanding, and we know this by looking at objects further away from us because we see them moving away from us, and the further away, the faster they move away from us (right? I know there are more proofs than this one I just barely mentioned).
But, let's say now we are looking at the earliest galaxies of the universe we have seen, we see they moving away from us extremely fast (faster than nearby galaxies), but, they were as said very far away from us when the light left the galaxy (and today they are even further away), is this how fast they were moving away from us when the photons left that galaxy?

I might though have mixed up this thinking with something else, my other piece of mind says that we know the current expansion rate of the universe due to math/physics, like some kind of inversed "math/engineering"-thingy?

I hope you understood what I'm trying to ask, shortly:

Current expansion,- light from far away,- expansion now?- expansion then?
The way we see galaxies moving away from us now, is that how they were moving away from us then?

I should stop! Thanks in advance

## Answers and Replies

Chalnoth
Science Advisor
Hi

I got into some thinking recently and I could really need some help unsolving these mysteries currently going on inside my head.
First of all, the universe is expanding, is this a fact?
Yes. Redshift increases with distance, which means expansion.

2nd, if now the universe is expanding, and we know this by looking at objects further away from us because we see them moving away from us, and the further away, the faster they move away from us (right? I know there are more proofs than this one I just barely mentioned).
Yes...

But, let's say now we are looking at the earliest galaxies of the universe we have seen, we see they moving away from us extremely fast (faster than nearby galaxies), but, they were as said very far away from us when the light left the galaxy (and today they are even further away), is this how fast they were moving away from us when the photons left that galaxy?
No. The redshift is best-understood not as being related to recession velocity, but instead as recording the amount of expansion that has occurred since the light left. We usually use the variable $z$ to denote redshift, and $z+1$ is the multiple by which distances have changed since the light was emitted. So if we observe an object at a redshift of $z=1$, then our universe is now twice the size in each direction (that is, things are twice a far apart) as when the light was emitted.

If you instead try to talk about velocity causing the redshift, this leads to all sorts of caveats and nasty things you have to take into account. The description above is the simplest and easiest: redshift records the amount of expansion, such that in the time required for the wavelength of a photon to double, so has the average distance between galaxies.

Current expansion,- light from far away,- expansion now?- expansion then?
The way we see galaxies moving away from us now, is that how they were moving away from us then?

I should stop! Thanks in advance
Basically, we measure the relationship between distance and redshift across the universe, using a variety of methods. This gives us a measure of how our universe has expanded through time.

This gives us a measure of how our universe has expanded through time.

And does that mean the amount of expansion that has occured during the time t, that it took for the photons to reach us?
Z=8 must then mean that the photons have traveled for a certain time >t if t was for photons at redshift <8? = the space between us and "z=8(time>t)" photons have expanded more than photons (t)?
I hope that wasn't way too fuzzy to understand but I think I have my lightbulb ON now:)!

Chalnoth
Science Advisor
And does that mean the amount of expansion that has occured during the time t, that it took for the photons to reach us?
Z=8 must then mean that the photons have traveled for a certain time >t if t was for photons at redshift <8? = the space between us and "z=8(time>t)" photons have expanded more than photons (t)?
I hope that wasn't way too fuzzy to understand but I think I have my lightbulb ON now:)!
I really don't understand what you're trying to say here. But my primary point was just that the expansion affects the distance between the crests of a light wave in the exact same way that it affects the distance between galaxies.

Ahh I see, thanks though for the quick and brief replies!

marcus
Science Advisor
Gold Member
Dearly Missed
And does that mean the amount of expansion that has occured during the time t, that it took for the photons to reach us?
Z=8 must then mean that the photons have traveled for a certain time >t if t was for photons at redshift <8? = the space between us and "z=8(time>t)" photons have expanded more than photons (t)?
I hope that wasn't way too fuzzy to understand but I think I have my lightbulb ON now:)!

You seem to want to get some definite numbers, for instance for z = 8.

Try this calculator if you want. Google "cosmos calculator" or find the link at the bottom of this post.
At the start of every session you type 3 standard numbers into the boxes at the left:

.27
.73
71

for matter fraction
cosmological constant
Hubble rate

and then you type some redshift like 8, into the last box and press calculate.

It should be fairly self-explanatory.

marcus
Science Advisor
Gold Member
Dearly Missed
So Robin this is completely optional. It often helps people to get some direct handson experience with standard cosmology model which is what is implemented in this calculator (after you put in the 3 parameters .27, .73, 71 )

Find the "morgan" link in my signature, or google "cosmos calculator" and prime it with the 3 parameters and then type in a redshift like 8.

If you do that, what it will give you (for redshift 8) is

age of univ now 13.66 billion yr
distance to object now 29.82 billion LY (how long it would take light to get to it now if you would freeze expansion)
distance now growing at 2.16c
Hubble rate now 71 km/s per Mpc

age of univ THEN (back when object emitted light) 0.65 billion years
distance to object then 3.31 billion LY
distance then growing at rate of 3.38c
Hubble rate back then 997.94 km/s per Mpc

===================

By convention the redshift is defined as ONE LESS than the expansion factor. So if the light from the object has Z = 8 that means the distance to the object has expanded by factor of NINE. Z+1 = 9
And the wavelengths of the light has been stretched out by a factor of 9 while the light was in transit.

So you can check the calculator answers. It should be true that 29.82/3.31 is equal to 9.
That is the ratio of the distance now to the distance back then when the light started on its way to us.

If you play around with the calculator some and have some questions, I encourage you to ask. People will probably reply and you can learn stuff that way.

The redshift of the Cosmic Microw. Background is right about z = 1100. You can check out the distances (then and now) and their expansion rates (then and now) for the CMB too. Or other sources like the most distant quasar or whatever you can find out the redshift of.

As I recall the redshift of the socalled Hubble distance is around 1.42

Last edited:
By convention the redshift is defined as ONE LESS than the expansion factor.

This confuse me a little.
I thought we measure the redshift of a distant light and find how far is the source of it.
If practically we do like just I said (i.e. we measure the redshift not the expansion factor), why we use the above definition?

Chalnoth
Science Advisor
This confuse me a little.
I thought we measure the redshift of a distant light and find how far is the source of it.
If practically we do like just I said (i.e. we measure the redshift not the expansion factor), why we use the above definition?
Redshift, by convention, is defined as being zero when there is no redshift. This means that at a redshift of $z$, the wavelength is multiplied by $z+1$.

The expansion of the universe multiplies the wavelength of light by the same factor it multiplies the average distances between galaxies. So when we observe a redshift of $z$, we know that the distance between galaxies has increased by a factor of $z+1$.

Does that help?

Redshift, by convention, is defined as being zero when there is no redshift.
??
The first word must be "expansion factor", right?

If I remember right z can be defined as:
$$z = \frac{\lambda _o}{\lambda _e} - 1$$
where λo, λe are the observed and emitted wavelengths respectively

So, if $z$ is zero then λo = λe. We can conclude the source of light it is not moving to us. If $z = 1$ then λo = 2*λe, the observed wavelength is twice as emitted wavelength.
But how can we conclude the distance between us and the emitter is double (at the moment when we measure) in this case?

I don't understand how the increasing wavelength are related to increasing the distance using the exact same scale.

Chalnoth
Science Advisor
I don't understand how the increasing wavelength are related to increasing the distance using the exact same scale.
As I mentioned before, the expansion affects the distance between wave peaks in the exact same way that it affects the distance between galaxies. You can calculate this explicitly within General Relativity by demanding conservation of the stress-energy tensor.

So Robin this is completely optional. It often helps people to get some direct handson experience with standard cosmology model which is what is implemented in this calculator (after you put in the 3 parameters .27, .73, 71 )

Find the "morgan" link in my signature, or google "cosmos calculator" and prime it with the 3 parameters and then type in a redshift like 8.

If you do that, what it will give you (for redshift 8) is

age of univ now 13.66 billion yr
distance to object now 29.82 billion LY (how long it would take light to get to it now if you would freeze expansion)
distance now growing at 2.16c
Hubble rate now 71 km/s per Mpc

age of univ THEN (back when object emitted light) 0.65 billion years
distance to object then 3.31 billion LY
distance then growing at rate of 3.38c
Hubble rate back then 997.94 km/s per Mpc

===================

By convention the redshift is defined as ONE LESS than the expansion factor. So if the light from the object has Z = 8 that means the distance to the object has expanded by factor of NINE. Z+1 = 9
And the wavelengths of the light has been stretched out by a factor of 9 while the light was in transit.

So you can check the calculator answers. It should be true that 29.82/3.31 is equal to 9.
That is the ratio of the distance now to the distance back then when the light started on its way to us.

If you play around with the calculator some and have some questions, I encourage you to ask. People will probably reply and you can learn stuff that way.

The redshift of the Cosmic Microw. Background is right about z = 1100. You can check out the distances (then and now) and their expansion rates (then and now) for the CMB too. Or other sources like the most distant quasar or whatever you can find out the redshift of.

As I recall the redshift of the socalled Hubble distance is around 1.42

Wow this calculator is awesome! And I honestly had no clue that the expansion rate was happening so incredibly fast at "just" z=8. Huuuuuuuuuuge thanks!

Is there any limit of max "z"? I recently tried 9999, but the larger the number is, the less the difference is. Example z=1100 and z=2200, not much difference. But z=1 and z=8 = huuuuuge difference :)!

Chalnoth
Science Advisor
Is there any limit of max "z"? I recently tried 9999, but the larger the number is, the less the difference is. Example z=1100 and z=2200, not much difference. But z=1 and z=8 = huuuuuge difference :)!
A redshift of $z=1089$ is the limit of the visible universe, because before that point our universe was opaque.

Furthermore, the math used in that calculator assumes the standard big bang theory, which has a singularity in the finite past. This singularity is an artifact in the math, and cannot describe reality. As you increase the redshift, you get closer and closer to this singularity. This basically means that the standard big bang cannot describe the very early universe (that is, very high redshifts).

As I mentioned before, the expansion affects the distance between wave peaks in the exact same way that it affects the distance between galaxies. You can calculate this explicitly within General Relativity by demanding conservation of the stress-energy tensor.

What I intend to say is that redshift, for me, explain what happened with the light along its way not with its source after the light was emitted. This is way I don't understand how we can tie a phenomenon that manifests on light with the evolution of its emitter. Especially when the emitter is very far away now.

Perhaps it is an extrapolation of all measurements (or a large number of measurements) of redshifts of light not only draw a conclusion for each measurement separately. Maybe this is why we can tell what are actually happening now with the farthest galaxies we can see.

Chalnoth
Science Advisor
What I intend to say is that redshift, for me, explain what happened with the light along its way not with its source after the light was emitted. This is way I don't understand how we can tie a phenomenon that manifests on light with the evolution of its emitter. Especially when the emitter is very far away now.
It's because the two are affected by the same phenomenon: the curvature of space-time. The light after it is emitted is certainly not affected by its emitter any longer. But the exact same space-time curvature which increases the distances between galaxies also increases the distances between the wave peaks of the light wave.

Perhaps it is an extrapolation of all measurements (or a large number of measurements) of redshifts of light not only draw a conclusion for each measurement separately. Maybe this is why we can tell what are actually happening now with the farthest galaxies we can see.
Well, in cosmology we generally don't talk about what is happening now in far-away galaxies, except in exceedingly general terms.

Thank you for your patience, Chalnoth.

marcus
Science Advisor
Gold Member
Dearly Missed
Wow this calculator is awesome! And I honestly had no clue that the expansion rate was happening so incredibly fast at "just" z=8. Huuuuuuuuuuge thanks!

Hey Robin, that makes me feel really good! Thanks for getting back to me about it. I'm glad you found it usable and helpful.

If you get curious about other online versions of the same calculator you could google "wright calculator". Ned Wright is a good teacher too, but his version of the calculator is more technical, with a bit more jargon. It has more decimal places of accuracy which is nice. It doesn't give the rate of expansion (back then and now) though. I happen to like Siobhan Morgan's version, which is the one you tried. It is the same basic underlying math model that Ned Wright uses, but implemented in a way that I think is more immediate/intuitive.