# CMB Sphere Size: Distance & Diameter

• jety89
In summary: CMB radii.In summary, the distance between our point in space and the points from which the Cosmic Microwave Background radiation emanated that we detect today at the moment that that radiation was created was about 42.17 million light years. The diameter of this 'sphere' is unknown, but could have been infinite. The age of the universe is estimated to be about 380,000 years at that time, so you could attempt to calculate it on that basis, but the results are misleading.
jety89
Hi

What was the distance between our point in space and the points from which the Cosmic Microwave Background radiation emanated that we detect today at the moment that that radiation was created.
Or similarly, what was the diameter of the sphere, the surface of which we detect today as CMB.

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As I recall, it was about 47 million light years and has since expanded by a factor of about 1100.

Really, this is the kind of thing that you should be able to find with Google quite easily.

Using Jorrie's cosmo-calculator, http://www.einsteins-theory-of-relativity-4engineers.com/cosmocalc_2010.htm, The CMB was at a distance of 42.17 million light years when the photons we now observe were emitted. The diameter of this 'sphere' is unknown. It could even be infinite. The age of the universe is estimated to be about 380,000 years at that time, so you could attempt to calculate it on that basis, but, the results are misleading. It requires unsupported assumptions to attempt such a calculation.

Thanks for the quick responses.

As I found out, this post actually answers my question,
https://www.physicsforums.com/showpost.php?p=1899571&postcount=11

but I still feel that it might be valuable to put it out as a separate thread.

As for the diameter of the sphere of CMB, it must have been 82.34 million light years back then, and 90 billion light years today.

The distance to the CMB is not the radius of the CMB 'sphere'.

Then what is it?

Chronos, could you please elaborate on the Why?
You statement seems wildly counter-intuitive to me.
Since the distances to the CMB, are the same in every direction, they add up to a sphere, at least that is my understanding.

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I am also puzzled. If not the surface of last scattering, then what "sphere" are you referring to?

cepheid said:
the surface of last scattering

That is exactly what I am referring to.
So what Is the source of my misunderstanding?
Nonlinear geometry of spacetime, perhaps?
You seem to know something that I don't.

jety89 said:
That is exactly what I am referring to.
So what Is the source of my misunderstanding?
Nonlinear geometry of spacetime, perhaps?
You seem to know something that I don't.

Nope. I was asking *Chronos* what he meant by "cmb sphere" if not the last scattering surface. Edit: the comoving distance to the last scattering surface is definitely around 46 Billion ly in the concordance model of cosmology.

jety89 said:
Thanks for the quick responses.

As I found out, this post actually answers my question,
https://www.physicsforums.com/showpost.php?p=1899571&postcount=11

but I still feel that it might be valuable to put it out as a separate thread.

As for the diameter of the sphere of CMB, it must have been 82.34 million light years back then, and 90 billion light years today.

I also was puzzled by Chronos' answer, but what you have said here makes complete sense to me. So I would say just stick with that and not to worry: the proper distance (at emission) is estimated at around 42 million ly so the diameter was around 84 million ly. Depending on whose calculator/which precise parameters you use. Your 82 is just as good an estimate.

The distance to that same sphere of material NOW is put at around 46 billion ly, making the diameter NOW 92 billion ly. The distance now can be called either the proper distance at the present moment or the comoving distance. In either case it is what you would measure by any ordinary means if you could stop the expansion process today to give time to measure.

46 billion was what Cepheid said so let's take that as benchmark---then just as a check, the expansion ratio z+1 that pretty much everybody agrees on for the CMB is z+1 = 1090.
So if you divide 46 billion by 1090, you get 42.2 million. Round off to 42 so as not to seem too precise.

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I've looked at the cosmological calculator in some greater detail, and played with it a little bit. I took the omega values and Hubble constant it gave for "the moment the universe was lit up" and fed it back into the calculator, using the same redshift value, z=1088. Apparently, the proper distance to a hypothetical last scattering surface back "then" then would have been a mere 800 light years. This is fun!
I've tried to do it twice in a row, but the result was just 0.

The calculator most people have heard of is Ned Wright's

google "wright calculator" and put in 1088, see what you get.

I get 0.0419 Gly (look down to "angular size distance")

That is the same as 41.9 million ly.

Ned is one of the principal people in studying CMB, teaches cosmology at UCLA.

Or take what he says for "comoving distance" and divide it by 1089...same answer.

http://www.astro.ucla.edu/~wright/CosmoCalc.html
====================

The link to Jorrie's latest calculator (version A27) is in my signature
http://www.einsteins-theory-of-relativity-4engineers.com/CosmoLean_A27.html
The quick way to use it: go there, in "upper limit" put 1089
in "step size" put -1, press calculate.

putting step = -1 gets you a table with 2 rows. Tabular output can be really interesting but it's not what you are looking for.
You will see the same two distance numbers: essentially 46 Gly for Dnow (distance now) and 42 Mly for Dthen (distance then).
====================

What calculator were you using? You seem to have gotten some strange results twice in a row.

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Incredible to think that the radius of the entire observable unverse, in other words the radius of the CMBR sphere, and what was to become 100s of billions of galaxies, was originally just 400 times the diameter of the milky way.

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Tanelorn said:
Incredible to think that the radius of the entire observable unverse, in other words the radius of the CMBR sphere, and what was to become 1000s of billions of galaxies, was originally just 400 times the diameter of the milky way.

The answer to my original question is 42 MILLION light years, NOT 800 light years. I got the second figure by fooling around with this calculator:
http://www.einsteins-theory-of-relativity-4engineers.com/cosmocalc_2010.htm

... sorry for the confusing statement.

jety89, 400 times 100,000 light years is 40Million light years

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I used the word 'sphere' instead of sphere because the topology of the surface of last scattering is unknown. Using Jorrie's calculator with z=1088, tells you the distance to the surface of last scattering at the time the photons we now observe was 42.17 Mly. It tells you nothing about the radius of the surface of last scattering. Deducing the radius of the surface of last scattering to then be 42.17 Mly makes as much sense as deducing the radius of the sun is 93 million miles.

Chronos said:
I used the word 'sphere' instead of sphere because the topology of the surface of last scattering is unknown. Using Jorrie's calculator with z=1088, tells you the distance to the surface of last scattering at the time the photons we now observe was 42.17 Mly. It tells you nothing about the radius of the surface of last scattering. Deducing the radius of the surface of last scattering to then be 42.17 Mly makes as much sense as deducing the radius of the sun is 93 million miles.

Have to think about this, Chronos. I have a hard time picturing how you are imagining this.
Maybe someone else will clarify (or we can get back to it in the morning.)

In the meantime, for Jety89 the OP who asked the question, and others thinking about the surface of last scattering in the usual way, it is a hollow sphere with us as center. The radius now is estimated to be 46 Gly. We've been thru this several times already in this thread (and in other threads.)

That is the socalled "comoving distance" to the matter which gave us the CMB we are now receiving---emitted the CMB photons back in year 380,000. It is also the proper distance at the present time.

Back in year 380,000 the proper distance to that same matter was about 46 Gly/1090 = 42 Mly. In other words the distance has expanded by a factor of 1090 and the wavelengths of the ancient light have been stretched out by a factor of 1090. Or say 1089 if you prefer. So the radius of the sphere (with us, or the matter that became us, as center) would have been 42 Mly.

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Looks like an open question in science -- the topology of the last scattering surface. My understanding is, if spacetime is flat, then it makes sense to talk about a sphere intead of a 'sphere', but that is an unconfirmed assumption -- or is it?

Apologies. I agree all observers share the illusion of being uniformly surrounded by a cmb that was 42 mly distant when the universe was 380,000 years old. Claiming this tells us nothing about the 'true' size or topology of ther cmb was confusing.

That about concludes this topic, i guess.

## What is CMB Sphere Size?

The CMB Sphere Size refers to the size of the Cosmic Microwave Background (CMB) radiation, which is the oldest light in the universe. It is often described as a sphere because it is the spherical surface from which the CMB radiation is emitted.

## How is the CMB Sphere Size measured?

The CMB Sphere Size is measured using the angular size of the CMB radiation on the sky. This is typically measured in degrees, with one degree being equivalent to the diameter of the full moon. The CMB Sphere Size is estimated to be about 45 billion light-years in diameter.

## What is the significance of the CMB Sphere Size?

The CMB Sphere Size is significant because it represents the farthest distance in the observable universe that we can see. This is because the CMB radiation was emitted about 380,000 years after the Big Bang, when the universe was just beginning to become transparent, allowing the light to travel freely through space.

## How does the CMB Sphere Size relate to the age of the universe?

The CMB Sphere Size is closely related to the age of the universe. Since the CMB radiation was emitted about 380,000 years after the Big Bang, the CMB Sphere Size represents the maximum distance that light could have traveled in the universe since its birth. This means that the CMB Sphere Size is a key factor in determining the age of the universe.

## How does the CMB Sphere Size change with distance?

The CMB Sphere Size remains the same regardless of distance. This is because the CMB radiation is uniformly distributed throughout the universe. However, as we observe the CMB radiation from farther distances, we are essentially looking back in time, and the CMB Sphere Size appears smaller due to the expansion of the universe. This is known as the "cosmological redshift."

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