Why do we still see the CMB today?

[GhostLoveScore]

I don't understand, what the question has to do with horizons at all. The CMBR is everywhere, i.e., we live in a thermal bath of photons. They are there and need not come from somewhere. The CMBR was in thermal equilibrium with the cosmic medium until about 380000 y after the big bang, at which time the universe was cooled down to the point, where atoms were formed, i.e., matter became electrically neutral and the photons thus decoupled from matter and are freely moving. This happens at a temperature of about 3000K. Due to the cosmological expansion the photons undergo a redshift, and because there is no scale this means for the thermal-equilibrium radiation that the photons still are described by a Planck spectrum with an accordingly lower temperature, which is about 2.725 K. So we just observe this "red-shifted" Planck spectrum of radiation which is already at our place.

That makes sense. Up until now I thought that what happened in the early universe was this:

Universe was a very hot soup with photons "trapped" in it.
Universe became transparent, releasing those photons.
Photons started moving, and when they all left, that's it, no more CMB.

In fact, what we see is black body radiation of 2.7K that's red shifted? That same radiation exists over entire universe even today. Is that correct?

 

[Ibix]

Universe was a very hot soup with photons "trapped" in it.
Universe became transparent, releasing those photons.
Photons started moving, and when they all left, that's it, no more CMB.

In fact, what we see is black body radiation of 2.7K that's red shifted? That same radiation exists over entire universe even today. Is that correct?

That's right. The only problem is thinking that the universe is some finite size. In an infinite universe there is always CMB from further away to reach us.

 

[PeroK]

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.

It's a flash from everywhere, at all distances from wherever you are. It's not just a flash from one distance.

 

[vanhees71]

That makes sense. Up until now I thought that what happened in the early universe was this:

Universe was a very hot soup with photons "trapped" in it.
Universe became transparent, releasing those photons.
Photons started moving, and when they all left, that's it, no more CMB.

I don't know what you mean by "photons started moving". That doesn't make sense. In the early universe you have a very hot and dense filling the whole universe. On not too small scales it's assumed to be homogeneous and isotropic ("cosmological principle"). At temperatures higher than about 3000K the matter took the form of a plasma, i.e., the relevant degrees of freedom were charged particles, and thus the electromagnetic field was coupled to that medium such that it kept in thermal equilibrium with it. At the moment, when the temperature of the universe fell below 3000K ("Mott transition temperature") the matter became bound to electrically neutral atoms, which made the medium transparent to em. radiation, i.e., the em. radiation decoupled and became a free em. field within the expanding space of the FLRW spacetime, describing the universe on large scales.

In fact, what we see is black body radiation of 2.7K that's red shifted? That same radiation exists over entire universe even today. Is that correct?

That's correct. The point is that at the decopuling of the em. radiation from the matter (about 380000y after the big bang) the electromagnetic radiation was in thermal equilibrium, described by a Planck spectrum of a temparture of the decoupling temperature of about 3000K. Then this em. field became free, and since the em. field is massless, there is no other scale in its description than the temperature of the Planck spectrum. Since space expands the wavelength of each em. wavemode becomes larger too, and due to the scale invariance for the spectrum as whole that means that it always stays a Planck spectrum, but it's temperature also scales with the expansion factor, i.e., today we see a Planckspectrum of about 2.7K, i.e., the light got red shifted by a factor of about 1000 corresponding to the expansion factor changing by a factor 1000 from the time of decoupling of light from the medium (often called "recombination" referring to the combination of the matter into electrically neutral atoms).

 

[enzo5]

There is no centre to the universe and the universe seems to continue indefinitely in all directions.

 

[GhostLoveScore]

I don't know what you mean by "photons started moving". That doesn't make sense. In the early universe you have a very hot and dense filling the whole universe. On not too small scales it's assumed to be homogeneous and isotropic ("cosmological principle"). At temperatures higher than about 3000K the matter took the form of a plasma, i.e., the relevant degrees of freedom were charged particles, and thus the electromagnetic field was coupled to that medium such that it kept in thermal equilibrium with it. At the moment, when the temperature of the universe fell below 3000K ("Mott transition temperature") the matter became bound to electrically neutral atoms, which made the medium transparent to em. radiation, i.e., the em. radiation decoupled and became a free em. field within the expanding space of the FLRW spacetime, describing the universe on large scales.

I mean exactly what you wrote there:

the matter became bound to electrically neutral atoms, which made the medium transparent to em. radiation, i.e., the em. radiation decoupled and became a free em. field

I'll try to write in a more scientific language from now on.

That's correct. The point is that at the decopuling of the em. radiation from the matter (about 380000y after the big bang) the electromagnetic radiation was in thermal equilibrium, described by a Planck spectrum of a temparture of the decoupling temperature of about 3000K. Then this em. field became free, and since the em. field is massless, there is no other scale in its description than the temperature of the Planck spectrum. Since space expands the wavelength of each em. wavemode becomes larger too, and due to the scale invariance for the spectrum as whole that means that it always stays a Planck spectrum, but it's temperature also scales with the expansion factor, i.e., today we see a Planckspectrum of about 2.7K, i.e., the light got red shifted by a factor of about 1000 corresponding to the expansion factor changing by a factor 1000 from the time of decoupling of light from the medium (often called "recombination" referring to the combination of the matter into electrically neutral atoms).

OK, I think I get it now.

 

[GhostLoveScore]

There is no centre to the universe and the universe seems to continue indefinitely in all directions.

I know, but that really bothers me.

 

[vanhees71]

The important point is that in all such considerations photons are a misleading concept, particularly when having in mind a very naive outdated picture of them (at the level of Einstein's 1905 paper). It's much better to think in terms of the electromagnetic field and waves.

The "naive photon picture" used in most GR and cosmology textbooks of course works, but that's because it's nothing else than describing the electromagnetic field in the eikonal approximation, i.e., looking at em. radiation in terms of "ray optics" rather than "wave optics". What you get with this when used in a FLRW spacetime is indeed the correct gravitational frequency shifts (Hubble-Lemaitre red shift) and also the "bending of light" in gravitational fields (i.e., all together the change of the em. wave's wave vector):

https://itp.uni-frankfurt.de/~hees/pf-faq/gr-edyn.pdf

 

[PeroK]

I know, but that really bothers me.

If you worry about the universe having no centre, then that is not a problem geometrically. Think of the surface ofvthe Earth as a 2D analogy.

If you worry about the universe being infinite, then perhaps that can only ever be a model of the universe. I.e. the part of the universe we have information about may only ever be finite. So, it's infinite extent is a moot point from an experimental perspective.

 

[vanhees71]

For an infinite universe an analogon is just our usual 3D Euclidean space, which also has no center but is rotationally symmetric around any point ("isotropic") and no point is distinguished from any other ("homogeneous").

 

[Hornbein]

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 can't quite figure out the way you are looking at this. We are always at the center of our visible Universe. Before the CMB was emitted everything was packed with energy-absorptive ions, nothing any distance away could be seen, so the size of the visible universe was zero or very close to it. After the CMB was emitted the visible Universe grew, presumably at the speed of light. After a year you could see the CMB being emitted a light-year away and so forth. You'd be inside a growing sphere of light. It expect it to be so uniform that there would be no clue to tell you it was growing. There were no heavenly bodies or other objects to come into view. Maybe a vortex would appear. Maybe not.

Even today we are "seeing" the CMB from the Big Bang plus 300,000 years. We get a day older every day while the date of the origin of the CMB remains the same. So every day we can see a "day" (actually now only a fraction of a day) longer into the past. We see the CMB from further away than we did the day before. This is why in an infinite universe we will never see the end of the CMB.

The "flash and it's over" is more or less correct. The flash comes from further and further away though without end, so it never ends. That makes me think of something. If the Universe were static then the amount of energy from the CMB would be a constant. We are at the center of a sphere of ancient emission of CMB. While observed energy from any fixed area of this sphere decreases with the square of time, this is cancelled because the surface area of this sphere grows with the square of time. So the energy from the CMB would be a constant. If the Universe were instead contracting then there would be a steady increase in such heat.

I have read that the "snow" observable on old school TV sets was maybe 25% due to the CMB. So there is still a lot of it around, though not all that energetic. This is because the area radiating the CMB that we see today is very large.

 

[GhostLoveScore]

If you worry about the universe being infinite, then perhaps that can only ever be a model of the universe. I.e. the part of the universe we have information about may only ever be finite. So, it's infinite extent is a moot point from an experimental perspective.

I'll just accept that it's infinite and try not to think about it too much

 

[GhostLoveScore]

... i.e., today we see a Planckspectrum of about 2.7K, i.e., the light got red shifted by a factor of about 1000...

So the spectrum of the CMBR we see today is affected by 2 things: 1) redshift due to expansion of the universe, and 2) by the universe cooling down and its black body spectrum peak moving towards longer wavelength? (Wien's displacement law)

 

[Bandersnatch]

It's the same thing. The background radiation 'cools down' due to the redshift.

 

[GhostLoveScore]

It's the same thing. The background radiation 'cools down' due to the redshift.

Then how can we tell if that radiation is emitted by a black body of 3000K in an expanding universe, or if it's emitted by 2.7K black body that's static in our frame of reference?

 

[Bandersnatch]

Because hydrogen-helium plasma gets transparent at 3000K.

 

[Ibix]

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.

 

[PeterDonis]

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.

 

[GhostLoveScore]

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.

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.

 

[vanhees71]

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

 

[PeterDonis]

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".

 

[vanhees71]

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".

 

[PeterDonis]

The point is that the electromagnetic radiation was in thermal equilibrium with the medium for the entire time till its decoupling.

Yes, agreed.

 

[Pyter]

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?

 

[Ibix]

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.

 

[Pyter]

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.

 

[Ibix]

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.

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.

 

[Pyter]

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?

 

[Ibix]

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.

 

[PeterDonis]

did the outer layers cool first, then the inner ones, up to the the core?

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.

 

[Hornbein]

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.

 

[Ibix]

The link to this paper fails on my smart phone.

Works for me. Try a different device?

 

[Ibix]

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.

 

[Pyter]

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)?

 

[Ibix]

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.