What is the recession speed today of the matter which created the CMBR?

[Tanelorn]

TL;DR Summary

What is the recession speed, today, of the matter which created the CMBR?
Also, roughly how long would be before we can start to detect a shift in the CMBR microwave frequency due to greater redshift?

Hello, I am talking to a Quantum Mechanics Physicist friend who is having a hard time accepting some of the Cosmology theories and numbers and I want to be sure that my numbers were correct.

1. Firstly, what is the recession speed, today, of the matter which created the CMBR?
I told him that it 1091.6 times the speed of light. 1091.6 being the red shift.

2. What is the maximum distance to matter today whose radiation can still reach us, if it was emitted today? Is it the event horizon 16Byrs given in this link?
https://explainingscience.org/2021/...8LSmVnb_8X2DePizAXERLBom-kshA1xcxtwmt6u9TIYD0

3. Is there a final limiting value for the radius of the Observable Universe, or according to the standard model does it always continue to get smaller and smaller? Ethan here say 100B years from now even the closest galaxy will be unobservable:
https://www.forbes.com/sites/starts...ve-background-ever-disappear/?sh=30c192cb40e0

4. Also, roughly how long would it be before we can start to detect a shift in the CMBR microwave frequency due to increasing redshift? I was just looking for an estimate, it will depend on instrumentation accuracies, but we do have a lot of time for averaging!

Thanks!

 

[PeterDonis]

I want to be sure that my numbers were correct.

A good general reference to check these kinds of things is Davis & Lineweaver 2003:

https://arxiv.org/abs/astro-ph/0310808

In particular, the diagrams on p. 3 should be helpful.

what is the recession speed, today, of the matter which created the CMBR?

There isn't one single answer, because the CMB was created throughout the entire universe at the same time (actually within a very narrow range of time), so the matter that created it was spread throughout the entire universe and its recession velocity from us now takes all possible values.

If you are asking about just the particular pieces of matter that created the CMB radiation that we are observing right now, which is what seems to be the case given that you assign this matter a redshift equal to the CMB redshift, this would be approximately the recession velocity of matter at our particle horizon. Looking at equation 18 in the paper referenced above, this would be the Hubble constant today times the proper distance today of the particle horizon, or 70 km/s/Mpc times 46 Glyr. Unfortunately those units aren't very convenient; if we convert them to meters and inverse seconds, we get [Edit: corrected numbers] $H = 2.31 \times 10^{-18} \text{s}^{-1}$ and $D = 4.28 \times 10^{26} \text{m}$, so $v_\text{rec} = H D = 9.87 \times 10^{8} \text{m} \text{s}^{-1} = 3.29 c$.

Note that this is not the same as $cz$, where $z$ is the redshift. That formula is an approximation that only works for small redshifts.

What is the maximum distance to matter today whose radiation can still reach us, if it was emitted today? Is it the event horizon 16Byrs given in this link?

Yes.

Is there a final limiting value for the radius of the Observable Universe, or according to the standard model does it always continue to get smaller and smaller?

It continues to get smaller and smaller. The best depiction in the paper referenced above is the bottom diagram on p. 3: note that the "event horizon" cone reaches an apex at the top.

 

[Bandersnatch]

we get

You seem to have borked those numbers a bit. 46 Gly is ~4.3*10^23 m, not ^26. And H is similarly three order of magnitude lower. The result is then not ~3200000c but ~3.2c - as it should be.
Btw, a simpler way to calculate this w/o resorting to converting those units, is to take the distance in question (46 Gly) and divide it by the Hubble radius, where the Hubble law shows recession velocities are c. 46/14.4=~3.2.

It continues to get smaller and smaller. The best depiction in the paper referenced above is the bottom diagram on p. 3: note that the "event horizon" cone reaches an apex at the top.

I'm not sure I agree. I mean, I'm sure we agree with what the graphs show, but the usual meaning of the observable universe is the base of the past light cone, i.e. numerically equivalent to the particle horizon. People say observable universe and think 46 Gly, same as what you have used above. Not the event horizon. Besides, that one shrinks only in comoving coordinates - as you well know. In terms of proper distance (which I think is more along the lines of the OP's reasoning) it tends to a constant radius.
So I don't think it's fair to say the OU will always shrink. There will be less and less galaxies observable with time, due to their fading away beyond detection, but that's a more subtle statement. In terms of the proper distance (or even comoving, so the number of galaxies on our past light cone) to the particle horizon, for example, the OU will always grow.

Also, to the OP's question - the closest galaxies will always be observable, as they are all gravitationally bound together.

@Tanelorn check out this calculator: http://jorrie.epizy.com/lightcone7/2022-05-14/LightCone7.html?i=2
It basically draws the same kind of graphs as in the paper Peter linked above. You can get all these numbers from there, graphed or in tables. It should also let you get an answer to the last question, if you compare the changes in z in the future (the negative z's) with some arbitrarily chosen detection capabilities.

 

[PeterDonis]

46 Gly is ~4.3*10^23 m, not ^26

No, ^26 is correct here. 1 light year is about 10^16 meters (3 times 10^8 meters per second times about 3.1 times 10^7 seconds). 46 times that is about 4 times 10^26 meters.

Rechecking, what I got wrong was the value of $H$. See below.

And H is similarly three order of magnitude lower.

Actually, it's 6; I had incorrectly done it in terms of parsecs, not megaparsecs. So the recession speed is similarly 6 orders of magnitude lower. I have edited my post to fix the numbers.

 

[PeterDonis]

the usual meaning of the observable universe is the base of the past light cone

The OP's meaning of "observable universe" might not be the standard one. But from the context of that question it seems clear to me that what is meant is the region that remains observable as we go further and further into the future, i.e., that we can continue to receive light signals from. The boundary of that region in the far future becomes the event horizon.

that one shrinks only in comoving coordinates - as you well know. In terms of proper distance (which I think is more along the lines of the OP's reasoning) it tends to a constant radius.
So I don't think it's fair to say the OU will always shrink.

Yes, I should have phrased this better; the comoving distance gets smaller and smaller but the proper distance does not.

There will be less and less galaxies observable with time, due to their fading away beyond detection

I would say, due to their proper distances from us increasing to the point where they cross the event horizon. The "fading away beyond detection" is a consequence of this.

the closest galaxies will always be observable, as they are all gravitationally bound together.

Yes, although over time, internal dynamics of gravitationally bound systems like galaxy clusters (and eventually galaxies themselves) will cause some members to achieve escape velocity while others become more tightly bound. So we can't say that all "closest galaxies" will always be observable. Only those that remain in the gravitationally bound system containing our galaxy will.

 

[Bandersnatch]

No, ^26 is correct here

Ah, yes. Giga is not Mega. Arithmetic - how does it work, right?

 

[PeterDonis]

Giga is not Mega.

I've always wanted to add "Ooga" and "Booga" as metric prefixes, but nobody else would support me...

 

[Tanelorn]

Thanks for very thoughtful, helpful replies. I had struggled for a week or so.

Yes, I was interested in proper distance.
I am interested in the observable universe in which if light was emitted today that it would still be possible to reach us here eventually. To confirm, this is the event Horizon, and it remains about the same, at a radius of around 16B Lyrs far into the future?

Regarding today's recession speed of the CMBR matter, I thought it might have been higher than 3.2c, but not as high as 10^6c! In comparison, how fast would this galaxy, with a redshift of 16.7 currently be receding from us?
https://phys.org/news/2022-08-farthest-galaxy-broken-million-years.html
Is there a reliable online calculator for this? This one doesn't seem to provide current or past recession speed:
https://www.astro.ucla.edu/~wright/CosmoCalc.html
This one I presume is not for galaxies?
http://jorrie.epizy.com/lightcone7/2022-05-14/LightCone7.html?i=3
I found this link here for different calculations depending on z:
https://www.cloudynights.com/articl...part-1-redshift-and-recession-velocity-r3213?
Equation 11 yields Vp = 2.53c, which I am glad to see is less than the CMBR Vp = 3.2c.

I saw you did not attempt to answer question 4. I assume that it is because it would just be a wild guess.
Someone online said it might be possible after 100 years. If true it would probably also require a 100 years of averaging! Perhaps we should get started?

If I may, I would also like to ask if there is any known correlation and/or causation between the rate at which all forms of matter is converted into energy and the expansion rate of the Universe? For example, inflation was extremely high when matter and antimatter were being annihilated in the first moments of the BB. Now it has slowed down greatly, as did the rate at which mass is being converted to energy everywhere throughout the universe. However, correlation does not always prove causation comes to mind, but interesting to me, nevertheless.

One other thing if I may, shouldn't the JWST be seeing a multitude of small galaxies in the first few hundreds of Millions of years after the BB instead of the odd ones or twos? I assume we see many more galaxies per unit volume a little later on?

Thanks again.

 

[Bandersnatch]

I've always wanted to add "Ooga" and "Booga" as metric prefixes, but nobody else would support me...

My friend, you've been talking to the wrong people. When do we march on the palace?

 

[JimJCW]

1. Firstly, what is the recession speed, today, of the matter which created the CMBR?
I told him that it 1091.6 times the speed of light. 1091.6 being the red shift.

Using LightCone8 calculator and PLANCK(2018+BAO) data, for z = 1091.6, we can get the following information:

At t = 379,500 year, the CMB photons we receive today were located at a distance of 0.04144 Gly from our location. Nearby matter had a recession speed of 66.416c. Now the matter is located at a distance of 45.277 Gly from our location with a recession speed of 3.133c.​

 

[JimJCW]

2. What is the maximum distance to matter today whose radiation can still reach us, if it was emitted today?

Using the calculator and data mentioned in Post #10, we can get the following result:

Lights emitted outside the event horizon now (Dhor > 16.58 Gly) will never reach our location, even the emitters are inside the observable universe (Dpar < 46.189 Gly).

 

[JimJCW]

3. Is there a final limiting value for the radius of the Observable Universe, or according to the standard model does it always continue to get smaller and smaller? Ethan here say 100B years from now even the closest galaxy will be unobservable:
https://www.forbes.com/sites/starts...ve-background-ever-disappear/?sh=30c192cb40e0

The radius of the observable universe becomes bigger and bigger with increasing age of the universe. Using the calculator and data mentioned in Post #10, one gets the following:

The Webpage you cited gives the following message:

 

[JimJCW]

4. Also, roughly how long would it be before we can start to detect a shift in the CMBR microwave frequency due to increasing redshift? I was just looking for an estimate, it will depend on instrumentation accuracies, but we do have a lot of time for averaging!

From the calculation result shown below, it is estimated that it takes 1.45 Myr for the wavelengths of the CMB to increase by a factor of 1.0001.

z​	Scale (a)​	Tnow Gyr​	Time from now Gyr​
0.000000000E+00​	1.000000000E+00​	1.378704250E+01​
-1.000000000E-04​	1.000100010E+00​	1.378848776E+01​	1.445260000E-03​
-1.000000000E-03​	1.001001001E+00​	1.380150466E+01​	1.446216000E-02​
-9.900000000E-03​	1.009998990E+00​	1.393115785E+01​	1.441153500E-01​
-1.000000000E-02​	1.010101010E+00​	1.393262428E+01​	1.455817800E-01​

 

[Tanelorn]

Thanks Jim, this is another link to Ethan's article:
https://www.patreon.com/posts/ask-ethan-will-40189763

Interesting that it would be 1.45 Myr for the wavelengths of the CMB to increase by a factor of 1.0001
The accuracy of an atomic clock error is 1 in 10^14, so we should be able to see a change in the frequency of the CMBR redshift in years, certainly decades. This would be a very interesting measurement which we could make starting now, assuming that the frequency of the CMBR can also be measured accurately.

Regarding the galaxy CEERS-93316 with redshift 16.7 the current distance is 34.7B LYRS and its current velocity Vp is 2.53c. What were the distance and velocity when the light which we see on Earth now, was first emitted?Interesting that the observable universe gets larger in the distant future. What are Dhor and Dpar and what is the y-axis in your chart? How big is today's observable universe in BLyrs if light was emitted today and how big would it be in 90Gyrs? I assume, as Ethan says, that there would only be our local group of galaxies filling that massive void.

 

[JimJCW]

Thanks Jim, this is another link to Ethan's article:
https://www.patreon.com/posts/ask-ethan-will-40189763

I think Ethan overlooks the existence of event horizon in his article when he writes,

In other words, the Universe will never run out of photons for us to see. There will always be a faraway place, from our perspective, where the Universe is first forming stable, neutral atoms. At that location, the Universe becomes transparent to the ~3000 K photons that were previously scattering off of the ions (mostly in the form of free electrons) that were omnipresent, enabling them to simply stream freely in all directions. What we observe as the Cosmic Microwave Background are the photons emitted from that location that happened to be traveling in our direction at that moment.​

The following result from LightCone8,

z​	Scale (a)​	Tnow Gyr​	Dthen Gly​	DHor Gly​
1.09160e+3	9.15248e-4	3.70503e-4	4.14394e-2	5.66145e-2

suggests that the CMB photos we receive today were located at a distance of 41.44 Mly from our location. At that time, the event horizon had a radius of 56.61 Mly. This means that any CMB photons outside the event horizon at the recombination time will never reach our location (due to the expansion of space). See the thread, Is the supply of the observable CMB radiation limited?

 

[PeterDonis]

any CMB photons outside the event horizon at the recombination time will never reach our location (due to the expansion of space).

That's not the same as saying we will run out of CMB photons, though. The CMB will continue to redshift forever, and the energy per photon will continue to decrease. We will continue to receive CMB radiation forever, it will just be more and more redshifted, and from a spacetime perspective, will be coming from emission points closer and closer to the event horizon, without ever reaching or exceeding it.

 

[JimJCW]

We will continue to receive CMB radiation forever, it will just be more and more redshifted, and from a spacetime perspective, will be coming from emission points closer and closer to the event horizon, without ever reaching or exceeding it.

If we have a tank of water and use half of the remaining amount a day, maybe we can use it forever.

 

[PeterDonis]

If we have a tank of water and use half of the remaining amount a day, maybe we can use it forever.

This isn't a good analogy. A better analogy to the increasing redshift of the CMB would be taking an increasing amount of time between extracting each amount of water from the tank.

 

[PeterDonis]

See the thread, Is the supply of the observable CMB radiation limited?

And see the reason that thread got closed. Please do not hijack this thread by rehashing your arguments in that other thread that were the reason it got closed. This is not your thread.

 

[Tanelorn]

Thanks all. My main, remaining unanswered questions are:

1. Interesting that it would be 1.45 Myr for the wavelengths of the CMB to increase by a factor of 1.0001. The accuracy of an atomic clock error is 1 in 10^14, so we should be able to see a change in the frequency of the CMBR redshift in years, certainly decades? For me this would be a very interesting measurement which we could make starting now, assuming that the frequency of the CMBR can also be measured accurately. I have to admit that I sometimes have a 10^-9 doubt that the CMBR is what they say it is and such a measurement would remove all remaining doubt.

2. Regarding the galaxy CEERS-93316 with redshift 16.7 the current distance is 34.7B LYRS and its current velocity Vp is 2.53c. What were the distance and recession velocity of galaxy CEERS-93316 when the light which we see on Earth now, was first emitted?

 

[PeroK]

If we have a tank of water and use half of the remaining amount a day, maybe we can use it forever.

It gets tricky when you are down to your last $H_2 O$ molecule.

 

[Bandersnatch]

What were the distance and velocity of galaxy CEERS-93316 when the light which we see on Earth now, was first emitted?

The relationship between the distance at reception $D_r$ and the distance at emission $D_e$ (aka angular diameter distance) is rather easy to calculate if you know the former and the observed redshift (or vice versa). It's $D_e=D_r/(z+1)$.
Intuitively, since z+1 is the amount of stretching of space a beam of light has experienced while traveling between emission and reception, and all distances in the universe that are subject to expansion stretch by the same proportion at each moment in cosmic time, the same stretch must have been applied also to the initial distance.
E.g. taking the CMB radiation, with its z=1089, and the proper distance to the surface of last scattering $D_r=~45 Gly$ we get 45 Gly/1090 = ~42Mly.

So, with the numbers provided above, the galaxy at emission must have been 16.7+1 times closer than the current 34.7 Gly, i.e. approx. 2 Gly.

The accuracy of an atomic clock error is 1 in 10^14,

I think you should look at the precision involved in the actual measurements, rather than base this off the atomic clocks alone. It takes more than just a clock to measure a redshift. You won't see anything even close to fourteen significant number reported anywhere.

 

[Tanelorn]

Thanks Bander,
So, the light from CEERS-93316 (redshift 16.7) was emitted 235.8 million years after the BB, when it was 2GLYRS from us and its recession velocity at that time was 6c.
Its current distance is 34.7GLYRS and its current recession velocity Vp is 2.53c.
I agree measuring the CMBR frequency is going to be hard, because it is spread over such a wide bandwidth. This is link illustrates this well.
https://asd.gsfc.nasa.gov/archive/arcade/cmb_spectrum.html
https://en.wikipedia.org/wiki/Cosmic_microwave_background

It probably requires a mathematician/statistician (not me) to answer whether a more precise measurement of frequency can be made using very long term averaging. Perhaps comparing the average value of one decade with the next and so on..

 

[PeterDonis]

It gets tricky when you are down to your last $H_2 O$ molecule.

This argument does not apply to the case of the CMBR, however. See my post #18.

 

[Bandersnatch]

So, 235.8 million years after the BB the light from CEERS-93316 was emitted when it was 2GLyrs from us. What was its recession velocity at that time?

You'd need to know the value of the Hubble parameter at the time. But since this is a more involved calculation, it's easier to use a calculator (like the one linked to in post #3). You'll find H then was approx 2800 km/s/Mpc. And since the distance was 2 Gly, which is approx 2/3rds of a Gpc, you end up with ~1,900,000 km/s, or ~6c.
The same calculator can get you this value to a better precision if you fiddle with the column selection tab.

 

[Tanelorn]

Thanks, wow 6c! that accuracy is fine, I was just trying to visualize this.

 

[PeroK]

This argument does not apply to the case of the CMBR, however. See my post #18.

Even your analogy doesn't work. For a finite number of water molecules and a finite time between processing each molecule the total time is finite.

You need a continuous process like redshift. Something with water temperature cooling would work. Getting closer to absolute zero but never reaching it.

 

[PeterDonis]

Even your analogy doesn't work. For a finite number of water molecules and a finite time between processing each molecule the total time is finite.

Not if the time between processing each molecule increases without bound. Each individual time might be finite, but if they increase fast enough the total time required can still diverge.

I agree that a continuous process is a better analogy, though, because it is not correct to think of the CMB as consisting of a finite number of photons.

 

[PeroK]

Not if the time between processing each molecule increases without bound. Each individual time might be finite, but if they increase fast enough the total time required can still diverge.

Well, no it can't. Not without an infinite number of molecules. All finite sums of finite numbers are finite.

 

[PeterDonis]

no it can't. Not without an infinite number of molecules.

Ah, I see. Yes, I was mixing up with the continuous case, where the "number of photons" is not finite.

 

[Tanelorn]

These are the numbers I passed on:

At t = 379,500 years after the BB, the CMB photons we receive today were located at a distance of 0.04144 Gly from our location with redshift 1092. The matter which emitted those photons had a recession speed of 66.416c at that time. Now, today, that matter is located at a distance of 45.277 Gly from our location with a recession speed of 3.133c.

Also, the light from CEERS-93316 (redshift 16.7) was emitted 235.8 million years after the BB, when it was 2Gly from us and its recession velocity at that time was 6c. Its current distance is 34.7Gly and its current recession velocity Vp is 2.53c.

This all happened in what was our observable universe. Today's observable universe for photons emitted today is called the event horizon and it currently has a radius of 16GLyrs. The observable universe gets larger over Billions of years, but there will be fewer and fewer galaxies within it as the time goes by.

 

[JimJCW]

Also, the light from CEERS-93316 (redshift 16.7) was emitted 235.8 million years after the BB, when it was 2Gly from us and its recession velocity at that time was 6c. Its current distance is 34.7Gly and its current recession velocity Vp is 2.53c.

This all happened in what was our observable universe. Today's observable universe for photons emitted today is called the event horizon and it currently has a radius of 16GLyrs. The observable universe gets larger over Billions of years, but there will be fewer and fewer galaxies within it as the time goes by.

Similar to the result for z = 1091.6 (see Post #10), for z = 16.7, we can get the following information:

At t = 230.329 Myr, the CEERS-93316 photons we receive today were located at a distance of 1.9621 Gly from our location. At that time, CEERS-93316 had a recession speed of 2.40314c. Now it is located at a distance of 34.7291 Gly from our location with a recession speed of 2.40314c. The Hubble parameter at z = 16.7 was 2817.7 (km/s)/Mpc.​

About the event horizon, I copied from a website the following:

The cosmic event horizon is also a sphere centered on us, which is the boundary inside which light, if it is emitted today, may still reach us sometime in the future. If it is emitted outside this horizon, the expansion of the Universe ensures that the light will never reach us.​

​

The current cosmic event horizon has a radius of 16.5803 Gly.

 

[George Jones]

The observable universe gets larger over Billions of years, but there will be fewer and fewer galaxies within it as the time goes by.

No. Anything that is now in our observable universe remains in our observable universe. Some (but not all) things that now are not in observable universe will move into our observable universe in the future; once in, always in.

 

[PeterDonis]

Anything that is now in our observable universe remains in our observable universe.

This is probably a good time to again reference Davis & Lineweaver 2003, which I referenced in post #2:

https://arxiv.org/abs/astro-ph/0310808

Fig. 1, particularly the bottom diagram in it, is helpful in understanding exactly what the various statements being made in this thread mean. The "light cone" in that diagram is the current boundary (in spacetime) of our observable universe, i.e., of the set of events we have observed up to now. The "event horizon" is the boundary in spacetime that includes all of the events we will ever observe. As we move into the future, the "light cone" obviously approaches the "event horizon".

The quoted statement above from @George Jones means that, as we move into the future and the "light cone" moves up the diagram and approaches the "event horizon", more and more comoving worldlines (vertical lines up the diagram) become included in the "light cone", but no comoving worldline ever leaves the "light cone"--once some part of a comoving worldline is in the "light cone", a part of it will always be in the "light cone". However, we see the objects following those comoving worldlines, as they enter the "light cone" region and become part of our observable universe, as they were near the beginning of the universe, and the later and later we see them enter our observable universe, the less and less of their total lifetime we are able to observe (because their comoving worldline intersects the "light cone"--which ultimately reaches the "event horizon"--closer and closer to the bottom of the diagram, i.e., at earlier and earlier times).

Now, consider this statement:

Today's observable universe for photons emitted today is called the event horizon and it currently has a radius of 16GLyrs.

If we look at the horizontal "now" line in the bottom diagram of Fig. 1, and see where it intersects the "event horizon" line, we find that this is at a comoving distance of about 16 GLyrs; and since at the "now" instant, comoving distance and proper distance are equal, this also corresponds to a proper distance of 16 GLyrs. So a photon emitted "now" from a point that far away will be on the event horizon and will never quite reach us; a photon emitted just inside that point will reach us very, very far in the future.

As was noted in earlier posts, the comoving distance to the event horizon decreases with time, but the proper distance to the event horizon increases, though more and more slowly, approaching a fixed value (which depends on the dark energy density aka cosmological constant) asymptotically. So more and more comoving objects go behind the event horizon as time goes on.

So, in appropriate senses, comoving objects are both entering our observable universe (in the very far past, near the Big Bang) and leaving it (passing behind the event horizon so we will never see their more recent history) as we move into the future.

 

[Tanelorn]

I thought I read various articles which state that only our local group of galaxies remain in our observable universe many 100s Billions of years in the future?