I Why do we still see the CMB today?

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  • #51
Because hydrogen-helium plasma gets transparent at 3000K.
 
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  • #52
Bandersnatch said:
Because hydrogen-helium plasma gets transparent at 3000K.
And everything else has redshift that increases with distance and the CMB comes from beyond it all. So you'd need a mechanism to redshift everything else but leave the CMB alone while redshifting everything else.

There are also predicted to be other cosmic backgrounds of neutrinos and gravitational waves that may become detectable (recent pulsar timing experiments may have seen the latter, but they're not sure). That would provide a separate confirming measure of redshift of the stuff that emitted the CMB, or even further away.
 
  • #53
GhostLoveScore said:
1: We should see light from some later age of the universe, I'm going to make up some numbers here:
Let's say that when universe became transparent it was 5 billion light years across. Imagine we are sitting in the middle of that universe. For the next 2.5 billion years we would see CMB until the light from 2.5 billion ly away reached us. Since CMB no longer exists (because the universe became transparent) we would just see some old galaxies.
But if the universe at the time when it became transparent was at least 30 billion years across (again, imagine we are in the middle of the universe) then CMB would be visible for the 15 billion years, so - visible today.

2: I imagine it like a flash. In the entire universe at that time photons started their journey when the universe became transparent. Flash and it's over.
I understand you were responding to V50's question as he asked it, but you realize that all of this is wrong, yes?

More precisely, 2. is sort of correct, in that the CMB was generated in a very short time period in the early universe and that was it. It wasn't quite instantaneous, like a "flash", but compared to cosmological time scales it was extremely short.

1., however, is all wrong. In the coordinates you are using, space is expanding, and that means that, while the CMB emitted from some distant point is moving towards you at ##c## measured locally, it does not get one light year per year closer to you. The universe has expanded by a factor of about 1000 since the CMB was emitted, so the point in space that emitted the CMB radiation we are just seeing now was 1000 times closer to us when the CMB was emitted. The approximate figures, IIRC, are 42 million light years away when the CMB was emitted, and 42 billion light years away now. The CMB was emitted about 13.7 billion years ago (about 300,000 years after the Big Bang, but that time is rounding error compared to the total age), so even though the point of emission of the CMB radiation we are seeing now was only 42 million light years away when the radiation was emitted, it still took that radiation 13.7 billion years to reach us.
 
  • #54
PeterDonis said:
I understand you were responding to V50's question as he asked it, but you realize that all of this is wrong, yes?
Yes, I know 1st one is wrong, but I wrote what I initially thought how it was.
PeterDonis said:
1., however, is all wrong. In the coordinates you are using, space is expanding, and that means that, while the CMB emitted from some distant point is moving towards you at ##c## measured locally, it does not get one light year per year closer to you. The universe has expanded by a factor of about 1000 since the CMB was emitted, so the point in space that emitted the CMB radiation we are just seeing now was 1000 times closer to us when the CMB was emitted. The approximate figures, IIRC, are 42 million light years away when the CMB was emitted, and 42 billion light years away now. The CMB was emitted about 13.7 billion years ago (about 300,000 years after the Big Bang, but that time is rounding error compared to the total age), so even though the point of emission of the CMB radiation we are seeing now was only 42 million light years away when the radiation was emitted, it still took that radiation 13.7 billion years to reach us.

That was why I was confused. I forgot to take into consideration that the universe is expanding. Sounds stupid, I know, but initially I thought that the universe expanded like this:
farthest points of the universe moved even farther but everything else stayed in place. Imagine that you drew a black circle on the paper, representing current universe. Then you add one thick ring around it to "expand" the circle, then one more, then another... I know that's wrong, and now I know there's a less wrong way to imagine it.
 
  • #55
PeterDonis said:
I understand you were responding to V50's question as he asked it, but you realize that all of this is wrong, yes?

More precisely, 2. is sort of correct, in that the CMB was generated in a very short time period in the early universe and that was it. It wasn't quite instantaneous, like a "flash", but compared to cosmological time scales it was extremely short.
The CMB was "generated" over the entire 380000 y after the big bang, during which the "cosmic substrate" was opaque for electromagnetic radiation. Since this medium was in thermal equilibrium so the electromagnetic radiation was during this time. That's why it's an almost perfect Planck spectrum. At the "Mott transition", i.e., at T~3000 K the plasma (consisting mostly of H and He nuclei and electrons) became a gas of neutral atoms and the universe became transparent to electromagnetic radiation. From this point on the electromagnetic radiation can be considered as free and thus is subject to the Hubble-Lemaitre redshift. Since electromagnetic waves are described by the massless em. field, the only relevant scale-dependent parameter of it's (energy) distribution is the temperature, and thus the Planck spectrum at decoupling stays a Planck spectrum after decoupling with the temperature decreasing with the increasing scale parameter, ##T(t)=T_{\text{dec}} a_{\text{dec}}/a(t)##.

The covariantly written Planck spectrum reads
$$\mathrm{d} N/\mathrm{d}^3 k =2 f_{\text{B}}(u \cdot k),$$
where ##u## is the four-velocity of the observer relative to the (local) rest frame of the CMBR. For a "fundamental observer", i.e., an observer at rest in the usual FLRW coordinates, ##u=(1,0,0,0)##.

The "effective temperature" for the moving observer is given by
$$\beta'=\frac{1}{T'}=\frac{\beta(t)}{\sqrt{1-v^2}}(1-|v| \cos \theta),$$
where ##\theta## is the angle between ##\vec{v}## and ##\vec{k}##, i.e., you get a Doppler shift of the temperature ##T(t)=1/\beta(t)##. That's the usual "dipole piece" of the CMBR measurements, which usually is subtracted in the pictures showing the (almost) isotropic CMBR distribution. One gets a velocity of our solar system of about 370 km/s towards the Leo constallation (as first measured by the COBE satellite). See, e.g.,

https://wwwmpa.mpa-garching.mpg.de/~komatsu/cmb/lecture_cosmo_iucaa_2011.pdf
 
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  • #56
vanhees71 said:
The CMB was "generated" over the entire 380000 y after the big bang
You're quibbling over words. Most people would say the CMB was "generated" during what you call the Mott transition. That's what I meant by "generated".
 
  • #57
The point is that the electromagnetic radiation was in thermal equilibrium with the medium for the entire time till its decoupling. It's one of the pillars of the "Cosmological Standard Model", explaining the abundancies of the various "ingredients" of the expanding universe from its "thermal history".
 
  • #58
vanhees71 said:
The point is that the electromagnetic radiation was in thermal equilibrium with the medium for the entire time till its decoupling.
Yes, agreed.
 
  • #59
I'm jumping on this thread because I never fully grasped the CMBR too.
For instance, I was wondering: did the whole matter in the Universe cool down to the Mott's temperature at the same instant, or did the outer layers cool first, then the inner ones, up to the the core?
 
  • #60
Pyter said:
For instance, I was wondering: did the whole matter in the Universe cool down to the Mott's temperature at the same instant, or did the outer layers cool first, then the inner ones, up to the the core?
There are no outer layers or inner layers. The universe is either infinite in extent or a closed spherical geometry (a 3-sphere not a 2-sphere, so you might prefer to call it hyperspherical), but in either case it has no edges or core.

In an idealised model, the universe is the same everywhere. So yes, everywhere is at the same temperature at the same cosmological time. The microwaves we currently receive from the CMB were emitted at that time and have been in flight ever since.

The reality is that the universe is not perfectly uniform, so the transition to a transparent universe will have happened at slightly different times in different places. However, that's random noise and not a systematic "outer layers cool first", because there are no outer layers - just slight random variations in density that developed into the stars and galaxies that we see today.
 
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  • #61
Ibix said:
The universe is either infinite in extent or a closed spherical geometry
By "universe" do you mean the energy/matter present in the universe, or the empty space?
I thought that there was also a model contemplating a finite amount of matter expanding in a flat, infinite 3D Euclidean space.
 
  • #62
Pyter said:
By "universe" do you mean the energy/matter present in the universe, or the empty space?
The universe is filled with matter everywhere, so I don't understand the distinction you're trying to make.
Pyter said:
I thought that there was also a model contemplating a finite amount of matter expanding in a flat, infinite 3D Euclidean space.
No. The flat and negative curvature space models are both infinite in extent and filled with matter everywhere.
 
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  • #63
Ibix said:
The flat space model is infinite in extent and filled with matter everywhere.
In that model, that for me is easier to visualize than the others, what is it that "expands" after the BB?
 
  • #64
Pyter said:
In that model, that for me is easier to visualize than the others, what is it that "expands" after the BB?
Everything. Pick any pair of particles. Measure the distance between them. Wait a while then measure it again and the distance will have increased.

In an ideal model, this works for literally any pair of particles. In the real universe most things have a bit of random motion and local interaction on top of that, and that can make them move together or orbit or whatever, so you only see the pure systematic expansion when you measure distances between galaxies that are separated enough that they are not gravitationally bound to each other.
 
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  • #65
Pyter said:
did the outer layers cool first, then the inner ones, up to the the core?
Pyter said:
By "universe" do you mean the energy/matter present in the universe, or the empty space?
Remember that the matter in the universe at the time of the CMB formation was very, very different from what it is today. It was not stars and galaxies separated by empty space. It was plasma which turned into ordinary gas as atoms formed from electrons and ions at recombination: that was what formed the CMB. The plasma/gas was uniform to about one part in 100,000 (i.e., the density only varied on that very small scale) at that time. How do we know? Because that's the degree to which the CMB itself is uniform. So there were no "outer layers", "inner layers", or "core", and there was no empty space. It was all uniform plasma/gas everywhere.
 
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  • #66
PeterDonis said:
This is one of those cases where "seems" isn't good enough. We need to actually look at the math. If you look at the Penrose diagram of de Sitter spacetime, as shown, for example, in Fig. 2 of this paper, you will see that the best a photon can do during the infinite history of the universe from ##I^-## to ##I^+## is to just make it from the "North Pole" to the "South Pole" (i.e., halfway around the 3-sphere of the universe).
The link to this paper fails on my smart phone.
 
  • #67
Hornbein said:
The link to this paper fails on my smart phone.
Works for me. Try a different device?
 
  • #68
If you only want to see the picture Peter references it's a square with dotted lines across the diagonals. The top and bottom edges are labelled ##\mathcal{I}^+## and ##\mathcal{I}^-## respectively, and the sides are labelled north and south pole.

I note that it's one of the most stunningly dull diagrams I have ever seen, considering the subject matter.
 
  • #69
Ibix said:
Everything. Pick any pair of particles. Measure the distance between them. Wait a while then measure it again and the distance will have increased.

In an ideal model, this works for literally any pair of particles. In the real universe most things have a bit of random motion and local interaction on top of that, and that can make them move together or orbit or whatever, so you only see the pure systematic expansion when you measure distances between galaxies that are separated enough that they are not gravitationally bound to each other.
So right after the BB, let's say one Planck time interval after, there already was infinite matter spanning infinite 3D Euclidean space (assuming the flat space model holds)?
 
  • #70
Pyter said:
So right after the BB, let's say one Planck time interval after, there already was infinite matter spanning infinite 3D Euclidean space (assuming the flat space model holds)?
If the universe is infinite in extent now then it always was, yes. Something finite cannot grow into something infinite in finite time.
 
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  • #71
Ibix said:
If the universe is infinite in extent now then it always was, yes. Something finite cannot grow into something infinite in finite time.
In that case the accepted CMB explanation starts to make sense to me.

But this "infinite matter" model is at odd with other cosmology notions I've gleaned, namely the enigma of the prevalence of matter over antimatter.
As you surely know, it is argued that at the beginning they should've been present in equal quantity and thus annihilate each another, except that for some unknown reason the matter was slightly more than the antimatter, and our current universe is made of the matter that survived the annihilation.

I've always thought that these considerations implied that the matter in our universe was finite from the beginning. Unless the initial matter was a "double infinite", the antimatter a "single infinite", and thus the difference stays infinite, or something to that effect.
 
  • #72
Pyter said:
I've always thought that these considerations implied that the matter in our universe was finite from the beginning. Unless the initial matter was a "double infinite", the antimatter a "single infinite", and thus the difference stays infinite, or something to that effect.
The best way to describe it is "different densities".
 
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  • #73
Pyter said:
this "infinite matter" model is at odd with other cosmology notions I've gleaned, namely the enigma of the prevalence of matter over antimatter.
No, it isn't. "Infinite matter" as you use the term here actually means "a spatially infinite universe with uniform average density of stress-energy everywhere". It does not require the stress-energy to have any particular form. It could all be radiation. It could all be matter. It could all be antimatter. It could be any mixture of any of those things. It could include dark energy. There is no contradiction in any of this.

Pyter said:
it is argued that at the beginning they should've been present in equal quantity and thus annihilate each another, except that for some unknown reason the matter was slightly more than the antimatter, and our current universe is made of the matter that survived the annihilation.

I've always thought that these considerations implied that the matter in our universe was finite from the beginning.
Then you thought wrong. They imply no such thing.

Pyter said:
Unless the initial matter was a "double infinite", the antimatter a "single infinite", and thus the difference stays infinite, or something to that effect.
This is word salad.
 
  • #74
Pyter said:
I've always thought that these considerations implied that the matter in our universe was finite from the beginning. Unless the initial matter was a "double infinite", the antimatter a "single infinite", and thus the difference stays infinite, or something to that effect.
We are taught in mathematics it makes no sense to subtract one infinity from another. But the infinite ton gorilla does as it pleases.
 
  • #75
Ibix said:
If the universe is infinite in extent now then it always was, yes. Something finite cannot grow into something infinite in finite time.
Actually it can if it grows infinitely quickly. But this is even harder to imagine actually happening.

The trick is double in size in y time, then again in y/2 time, again in y/4 time, y/8, and so forth.
 
  • #76
Hornbein said:
We are taught in mathematics it makes no sense to subtract one infinity from another
No such subtraction has to take place anywhere in the actual mathematical account of matter-antimatter annihilation in the early universe.
 
  • #77
PeterDonis said:
No such subtraction has to take place anywhere in the actual mathematical account of matter-antimatter annihilation in the early universe.
Correct.
 
  • #78
Hornbein said:
We are taught in mathematics it makes no sense to subtract one infinity from another. But the infinite ton gorilla does as it pleases.
In maths this is legal: ## 2\delta(x) - \delta(x) = \delta(x) ## . Perhaps also in physics, in branches other than cosmology apparently.

So there's currently no cosmological model based on finite matter/energy, at least no one able to explain the CMB convincingly?
 
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  • #79
Pyter said:
So there's currently no cosmological model based on finite matter/energy, at least no one able to explain the CMB convincingly?
A closed universe is boundaryless but finite.
 
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  • #80
Ibix said:
A closed universe is boundaryless but finite.
With that model, has it been said in the previous posts that the observed CMB should stop at one time, since there's no infinite matter from which it might come from?
 
  • #81
Pyter said:
With that model, has it been said in the previous posts that the observed CMB should stop at one time, since there's no infinite matter from which it might come from?
In which posts is this said?
 
  • #82
Pyter said:
So there's currently no cosmological model based on finite matter/energy, at least no one able to explain the CMB convincingly?
The cosmological model most accepted by the scientific community today is the ΛCDM model, which explains the CMB in a finite universe quite convincingly.
 
  • #83
Pyter said:
With that model, has it been said in the previous posts that the observed CMB should stop at one time, since there's no infinite matter from which it might come from?
No. In a naive matter-dominated closed universe model the universe ends before light can circumnavigate it. In a dark-energy dominated model, which lives longer, you start to receive photons that have circumnavigated the universe once, then twice, and so on. There is a finite energy in the CMB in this case, though, so it's possible to imagine it all being absorbed, but it would take a very, very, very long time.
 
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  • #84
Jaime Rudas said:
In which posts is this said?
#4. Wrongly, as pointed out by you and Peter. I had forgotten we were in that thread... 😁
 
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  • #85
Ibix said:
In a dark-energy dominated model, which lives longer, you start to receive photons that have circumnavigated the universe once, then twice, and so on.
In fact, in a realistic dark-energy dominated model, photons can't circumnavigate the universe.
 
  • #86
Pyter said:
there's currently no cosmological model based on finite matter/energy, at least no one able to explain the CMB convincingly?
Yes, there is, a spatially closed, spatially finite universe. This is one of the basic FRW models.

Pyter said:
With that model, has it been said in the previous posts that the observed CMB should stop at one time, since there's no infinite matter from which it might come from?
This is wrong. The CMB does not require "infinite matter" (i.e., infinite spatial extent) in order to continue traveling around the universe. @Ibix explained why in post #83.

Ibix said:
There is a finite energy in the CMB in this case, though, so it's possible to imagine it all being absorbed
No, it isn't, because it would just be re-emitted again, since whatever absorbed it would then be at a slightly higher temperature than the CMB.
 
  • #87
Jaime Rudas said:
in a realistic dark-energy dominated model, photons can't circumnavigate the universe.
What is your basis for this statement?
 
  • #88
PeterDonis said:
What is your basis for this statement?
As I hinted in post #17, in a realistic dark-energy dominated model there is a cosmological event horizon that is smaller than the particle horizon (i.e., the boundary of the observable universe) which, in turn, is smaller than the entire universe.
 
  • #89
Jaime Rudas said:
As I hinted in post #17, in a realistic dark-energy dominated model there is a cosmological event horizon that is smaller than the particle horizon (i.e., the boundary of the observable universe) which, in turn, is smaller than the entire universe.
This is not a sufficient basis for the claim you are making now. It is true that there exist dark energy dominated models with the property you describe. But that does not support the claim you are making, that all "realistic" dark energy dominated models have the property you describe.
 
  • #90
PeterDonis said:
This is not a sufficient basis for the claim you are making now. It is true that there exist dark energy dominated models with the property you describe. But that does not support the claim you are making, that all "realistic" dark energy dominated models have the property you describe.
What I assume by "realistic" are those models that can reasonably well describe the observations we make of the real universe.

On the other hand, I notice that you changed your mind from what you stated in post #18
 
  • #91
Jaime Rudas said:
What I assume by "realistic" are those models that can reasonably well describe the observations we make of the real universe.
And if so, then you need to explain why you think this requires all "realistic" models to have the property you describe. Note that I am not saying that is not possible; I'm just saying that you haven't done it.

Jaime Rudas said:
I notice that you changed your mind from what you stated in post #18
How so?
 
  • #92
PeterDonis said:
And if so, then you need to explain why you think this requires all "realistic" models to have the property you describe. Note that I am not saying that is not possible; I'm just saying that you haven't done it.
What we observe of the universe is that the Hubble constant ##H_0## is close to 70 km/s/Mpc, that ##\Omega_{0,\Lambda}## is close to 0.7, that ##\Omega_{0,m}## is close to 0.3 and that ##\Omega_{0,k}## is close to 0. I don't know of any model that meets those conditions and that doesn't meet the ones I stated in post #88
 
  • #93
Jaime Rudas said:
What we observe of the universe is that the Hubble constant ##H_0## is close to 70 km/s/Mpc, that ##\Omega_{0,\Lambda}## is close to 0.7, that ##\Omega_{0,m}## is close to 0.3 and that ##\Omega_{0,k}## is close to 0. I don't know of any model that meets those conditions and that doesn't meet the ones I stated in post #88
What would these figures imply about the particle horizon vs. the event horizon? Can you give any relevant math?
 
  • #94
PeterDonis said:
What would these figures imply about the particle horizon vs. the event horizon? Can you give any relevant math?
See equations A.19 and A.20 on page 117 and figure 1.1 on page 8 of this paper.
 
  • #95
Jaime Rudas said:
See equations A.19 and A.20 on page 117 and figure 1.1 on page 8 of this paper.
The figure is similar to the one in Davis & Lineweaver 2003, which has been referenced in plenty of PF threads. It does clearly show the particle horizon "now" being further away than the event horizon "now"; the two horizons cross at a redshift of about 0.4, so at earlier times than that the particle horizon was closer than the event horizon.

The equations you reference just give formulas for the particle horizon and event horizon.

What the figure and equations you reference do not give is the connection between the above and the Hubble constant and Omega values that you gave.
 
  • #96
PeterDonis said:
The figure is similar to the one in Davis & Lineweaver 2003, which has been referenced in plenty of PF threads.
Of course it is similar because the author is the same: Tamara M. Davis.
PeterDonis said:
It does clearly show the particle horizon "now" being further away than the event horizon "now"; the two horizons cross at a redshift of about 0.4, so at earlier times than that the particle horizon was closer than the event horizon.
No, they don't intersect at a redshift of about 0.4, but at a scale factor of about 0.4 which corresponds to a redshift of 1.5, i.e. when the universe was dominated by matter. The universe only became dominated by dark energy (which is the kind of universe I refer to in post #88) at a redshift of about 0.5 (scale factor of about 0.67).
PeterDonis said:
The equations you reference just give formulas for the particle horizon and event horizon.

What the figure and equations you reference do not give is the connection between the above and the Hubble constant and Omega values that you gave.
Those connections are shown in equations A.16, A.17 and A.18 on the same page 117. They are also shown in this post.
 
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  • #97
Jaime Rudas said:
the author is the same: Tamara M. Davis
Yes, I know.

Jaime Rudas said:
they don't intersect at a redshift of about 0.4, but at a scale factor of about 0.4
Yes, sorry, I misstated it.

Jaime Rudas said:
i.e. when the universe was dominated by matter
In this particular model, yes.
 
  • #98
PeterDonis said:
In this particular model, yes.
Yes, that's precisely the particular model I proposed in post #92
 
  • #99
Jaime Rudas said:
Yes, that's precisely the particular model I proposed in post #92
To say that you "proposed" that model is something of a misstatement. At the very least, it's confusing. You are just pointing at our current best-fit model for our actual universe and saying that's the model you're talking about. You're not "proposing" this model as something new.

In other words, you are saying that, in our current best fit model for our actual universe, it is the case that, for the time period which is dark energy dominated, the particle horizon is further away than the event horizon. Yes, I agree that's the case, but that's a much more limited statement than the one I thought you were making.
 
  • #100
PeterDonis said:
To say that you "proposed" that model is something of a misstatement. At the very least, it's confusing. You are just pointing at our current best-fit model for our actual universe and saying that's the model you're talking about. You're not "proposing" this model as something new.
I accept that I'm not the person who proposed the standard cosmological model. I'm sorry for the confusion.
PeterDonis said:
In other words, you are saying that, in our current best fit model for our actual universe, it is the case that, for the time period which is dark energy dominated, the particle horizon is further away than the event horizon. Yes, I agree that's the case, but that's a much more limited statement than the one I thought you were making.
Although I don't know what statement you thought I was making, I'm sorry for the confusion.

On the other hand, I still maintain that in a realistic dark-energy dominated model, photons can't circumnavigate the universe.

Do you know of any dark-energy dominated model where photons circumnavigate the universe two or three times, as @Ibix proposed presented in post #83?
 
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