Why do we still see the CMB today?

[GhostLoveScore]

I'm coming upon multiple definitions of what the universe size was at around 378 000 years after the big bang. Some say it was around 42 million ly across, some say it was much larger.

Why am I asking this?
I was thinking about the cosmic microwave background. If the universe was only 42 million light years across at that time, then we wouldn't be able to see CMB anymore, right? Let's say it looked like a flash in the entire universe. And let's say somehow we can be there and watch it as it's happening.
First we see the flash right around our location, then from a little bit further and later a bit further. Some 42 million years later we see the last flash from the very edge of that old universe. And then nothing from that time on.

1: Now, if the universe at that time was much bigger, say, 14 billion years in size, or larger, then it would make sense that we can still see CMB today. The CMB light travelled for 13.8 billion years and reached our telescopes.

2: I even found one answer on quora (https://qr.ae/pybpC5), which says that universe expansion "dragged" that light with it, meaning if the unvierse expanded at 60c, the light was moving away from us at 59c and that it only started moving towards us when the universe expansion slowed to less than c. I don't know special relativity very well, but that doesn't really seem right, universe expansion should only redshift the light.

Which one is it?

 

[PeroK]

The key word in Special Relativity is special. That means no gravity, no curved spacetime and no expanding universe. You need General Relativity to study the cosmos. SR then applies only locally, but not globally across all spacetime.

In answer to your question, space expanded rapidly in the early universe, and you have to take this expansion into account when calculating from how far away the CMBR was emitted at the time of emission.

Finally, the universe is much larger than the current observable universe (and is possibly infinite). We will never stop seeing the CMBR, although eventually it will be extremely redshifted to a very low energy.

 

[GhostLoveScore]

In answer to your question, space expanded rapidly in the early universe, and you have to take this expansion into account when calculating from how far away the CMBR was emitted at the time of emission.

So, from how far away was it emitted?

 

[Ibix]

Which one is it?

None of the above.

The universe is most likely infinite in size and always has been. If it is finite in size it is very, very large, much larger than the hundred-billion light year patch we can see.

Your first model is essentially correct - the CMB microwaves we see today were emitted a bit further away than the ones we saw yesterday, so in an infinite universe we will always be able to see it. In a finite universe it would disappear at some point, but depending on the mix of dark energy that may not happen until such a universe collapses into a Big Crunch.

You've gone wrong in two places. First is in thinking that the universe was only 42 million light years across. That sounds about right for an estimate of how big the observable universe, the part we can see now, was at the time the CMB was emitted, but the universe as a whole was either very much larger or actually infinite. Lots of sources confuse the universe and the observable universe, unfortunately.

The second place you went wrong is that you seem to be trying to apply special relativity to a situation that needs general relativity. Spacetime on cosmological scales is not flat, and SR will mislead you here. There is actually more than one way to conceptualise what's going on, and at a quick glance Larry D King in your quora link seems to have picked one I wouldn't have picked, but I don't think he's wrong. IMO, the simplest way to explain what's going on is to say that space is undergoing metric expansion which means that the distances between objects are expanding (objects that aren't bound by electromagnetic forces or gravity or something, anyway). That means that a light pulse that set out from the CMB may only have had 42 million light years to go when it set out, but that distance grew while it was travelling. So it ended up taking more than 42 million years - closer to 13.8 billion.

 

[PeroK]

So, from how far away was it emitted?

You'd have to look it up, or do some detailed calculations.

 

[Ibix]

You'd have to look it up, or do some detailed calculations.

The temperature at CMB emission was about 3000K and we now see about 3K, so the redshift factor is about 1000, which means the scale was about 1000 times smaller then than now. The current radius of the observable universe is about 45 billion light years, so 42 million is plausible given the high precision of the numbers I'm throwing around here.

 

[PeroK]

There's a great insight on the expanding universe here:

https://www.physicsforums.com/insights/inflationary-misconceptions-basics-cosmological-horizons/

If you want to study cosmology seriously and can handle undergraduate mathematics, then Andrew Liddle's book is highly recommended;

https://www.amazon.co.uk/dp/1118502140/

 

[GhostLoveScore]

There's a great insight on the expanding universe here:

https://www.physicsforums.com/insights/inflationary-misconceptions-basics-cosmological-horizons/

If you want to study cosmology seriously and can handle undergraduate mathematics, then Andrew Liddle's book is highly recommended;

https://www.amazon.co.uk/dp/1118502140/

Thanks, I'll read it the insights article.

I can handle undergrad math, it's the things that I need to imagine in my head that bother me. Like the above mentioned expansion of the universe. I think I understand it but at some point I'll find some small thing that I don't understand and it will make me confused and I'll think about it for days on end.

 

[GhostLoveScore]

You've gone wrong in two places. First is in thinking that the universe was only 42 million light years across. That sounds about right for an estimate of how big the observable universe, the part we can see now, was at the time the CMB was emitted, but the universe as a whole was either very much larger or actually infinite. Lots of sources confuse the universe and the observable universe, unfortunately.

Ah OK, yes, that definitely confused me.

The second place you went wrong is that you seem to be trying to apply special relativity to a situation that needs general relativity. Spacetime on cosmological scales is not flat, and SR will mislead you here. There is actually more than one way to conceptualise what's going on, and at a quick glance Larry D King in your quora link seems to have picked one I wouldn't have picked, but I don't think he's wrong. IMO, the simplest way to explain what's going on is to say that space is undergoing metric expansion which means that the distances between objects are expanding (objects that aren't bound by electromagnetic forces or gravity or something, anyway). That means that a light pulse that set out from the CMB may only have had 42 million light years to go when it set out, but that distance grew while it was travelling. So it ended up taking more than 42 million years - closer to 13.8 billion.

So, it's not like photon was "dragged out" when the universe expanded, it's more like - new space "formed" in all points in space making the distance longer?

 

[PeroK]

Ah OK, yes, that definitely confused me.

So, it's not like photon was "dragged out" when the universe expanded, it's more like - new space "formed" in all points in space making the distance longer?

There's no mechanism, as such, for the expansion of space. It's not like new space is being formed in any sense. It's that the overall spacetime geometry is curved. In comoving coordinates that means that the distance between comoving points increases over time.

In terms of understanding, mathematics is your best bet, IMO.

 

[PeterDonis]

from how far away was it emitted?

As the numbers others have given show, this question needs a bit of clarification.

If we imagine a comoving observer O who, way back at the time of CMB emission, was right at the point where the CMB we are just now observing was emitted, then at the time of emission, that observer was about 42 million light-years away from the position back then of a comoving observer E who is just now, as we observe that radiation, passing by the Earth. (Note that Earth itself is not a comoving object, nor is anything in the solar system.)

That same comoving observer O is now about 42 billion light-years away from Earth now (where "now" means "according to the time of comoving observers").

 

[Ibix]

So, it's not like photon was "dragged out" when the universe expanded, it's more like - new space "formed" in all points in space making the distance longer?

Not really, because you have to remember that spacetime is 4d, and "space now" is a 3d slice of it. "Space 13bn years ago" is a different slice of it. So it's not that "more space has formed" but that you're looking at a different slice where stuff is more spread out.

 

[Jaime Rudas]

In a finite universe it [the CMB] would disappear at some point,

I don't understand why. IMO, the characteristics of the CMB don't depend on whether the universe is finite or infinite.

 

[PeterDonis]

In a finite universe it would disappear at some point

No, it wouldn't. A finite universe would have the spatial topology of a 3-sphere, and if it expanded forever we would eventually start seeing CMB radiation that had circumnavigated the universe. It would never stop altogether.

 

[Ibix]

I don't understand why.

It would never stop altogether.

Ah yes. I was thinking a finite volume releases a finite amount of energy, but it's like light from something falling into a black hole - it gets ever more redshifted but never quite stops.

 

[PeterDonis]

I was thinking a finite volume releases a finite amount of energy

It does, but a given observer observes any given parcel of that energy multiple times, because the CMB radiation circumnavigates the universe if you wait long enough.

it's like light from something falling into a black hole - it gets ever more redshifted but never quite stops.

No, this has nothing to do with what I was describing in a spatially finite universe. It is true that as the universe expands, the CMB gets more redshifted, but the spacetime geometry is nothing like that of a black hole.

 

[Jaime Rudas]

A finite universe would have the spatial topology of a 3-sphere, and if it expanded forever we would eventually start seeing CMB radiation that had circumnavigated the universe.

It should be noted that if the expansion is permanently accelerated, it is not possible for CMB radiation to circumnavigate the universe, even if it is finite. This is because, when there is accelerated expansion, there is a cosmological event horizon.

P.S. On second thought, if there would be a case when CMB radiation circumnavigates the universe: when the event horizon is further than the maximum circumference length of the universe.

 

[PeterDonis]

if the expansion is permanently accelerated, it is not possible for CMB radiation to circumnavigate the universe, even if it is finite

Yes, that's correct.

if there would be a case when CMB radiation circumnavigates the universe: when the event horizon is further than the maximum circumference length of the universe.

There is no such case, because for a spatially finite universe with accelerating expansion, there is no "maximum circumference length"; the circumference increases exponentially with time.

 

[Jaime Rudas]

There is no such case, because for a spatially finite universe with accelerating expansion, there is no "maximum circumference length"; the circumference increases exponentially with time.

Yes, that's correct, but if at any given time, the particle horizon is closer further away than the longitude of the greatest circumference of the universe at that time, it would be possible for CMB radiation to have circumnavigated the entire universe. For example, that would have happened if now the maximum circumference of the universe was 30 Gly.

 

[Bandersnatch]

There is no such case

Maybe not if what you want is eternal circumnavigation. But if you want to circumnavigate just a finite number of times, all you need is for the universe to be particularly small or particularly slow at the time when you embark on your journey.

 

[PeterDonis]

if at any given time, the particle horizon is closer further away than the longitude of the greatest circumference of the universe at that time

I'm not sure this is possible for pure exponential expansion (i.e., de Sitter spacetime in the closed slicing). But it might be if we are including closed universes with matter and/or radiation present as well as dark energy.

 

[Vanadium 50]

Maybe we should take a step back.
1. OP, what do you think we should see, if not the CMBR?
2. OP, if we say the CMBR in the past, and see the answer to #1 today, what was the transition like? Can you tell us, at least qualitatively, when it happened?

 

[Jaime Rudas]

I'm not sure this is possible for pure exponential expansion (i.e., de Sitter spacetime in the closed slicing). But it might be if we are including closed universes with matter and/or radiation present as well as dark energy.

But if, at the beginning of the expansion, the size of the universe, the velocity and the acceleration of the expansion were small enough, it seems to me that the CMB radiation could circumnavigate the entire universe.

 

[PeterDonis]

it seems to me

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).

 

[vanhees71]

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.

 

[Vanadium 50]

I don't understand, what the question has to do with horizons at all

Part of the reason I tried to ask some clarifying questions. Sadly, the OP seems to have lost interest.

 

[Ibix]

It does, but a given observer observes any given parcel of that energy multiple times, because the CMB radiation circumnavigates the universe if you wait long enough.

Yes, and each time more redshifted.

Imagine a CMB radiation detector of some finite area. In a closed universe that doesn't collapse the total energy it receives must be finite, even if you integrate to infinity in the future, because there was only a finite amount of energy released. A similar detector in a flat universe may or may not receive infinite energy given infinite time - at least, you can't argue that it must be finite in the simple way I just did for a closed universe.

It was that "finite energy even if you wait forever and receive energy forever" that I was comparing to the light received from an object falling into a black hole. I do understand that the mechanism is wildly different.

 

[PeterDonis]

the total energy it receives must be finite, even if you integrate to infinity in the future, because there was only a finite amount of energy released

This logic is incorrect, because, as I have said, a given parcel of energy can (but not with exponential expansion--see below) be observed multiple times. Yes, it will be more redshifted each time, but that alone does not justify the claim you are making here. You would need to actually do the math to check.

However, in the case of exponential expansion (de Sitter spacetime, i.e., pure dark energy), as I said in post #24, it is actually impossible for light to circumnavigate the universe (the best it can do is to make it from one pole to the opposite pole). So in that case, yes, the total amount of energy received by any CMB detector will be finite. The CMB still won't cease to be observed, in principle, by a given comoving observer, but it will redshift exponentially and the energy received integrated into the infinite future will be finite.

 

[PeterDonis]

It was that "finite energy even if you wait forever and receive energy forever" that I was comparing to the light received from an object falling into a black hole. I do understand that the mechanism is wildly different.

For the case of de Sitter spacetime, the "mechanism" is actually similar--in both cases you have a horizon and light emitted towards you closer and closer to the horizon is more and more redshifted. The only difference is the type of horizon (black hole event horizon vs. de Sitter cosmological horizon).

 

[Jaime Rudas]

Yes, and each time more redshifted.

These different redshifts would allow us to determine the size of the universe.

 

[PeterDonis]

These different redshifts would allow us to determine the size of the universe.

Only as a ratio to the size when the CMB was originally emitted. By itself that would not tell you the absolute size; you would need additional data to know that.

 

[Hornbein]

the CMB microwaves we see today were emitted a bit further away than the ones we saw yesterday,

Hah, I never realized that. It's not precisely true but close enough for jazz.

Then all this stuff about the CMB "cooling" is misleading. As far as a CMB photon is concerned we are receding rapidly from the place where it was emitted. The Doppler effect reduces the energy. This speed increases with time. It doesn't have much to do with heat.

 

[PeterDonis]

all this stuff about the CMB "cooling" is misleading.

No, it's not. It means that the CMB temperature that comoving observers observe decreases with time.

As far as a CMB photon is concerned we are receding rapidly from the place where it was emitted. The Doppler effect reduces the energy.

No, this is not correct. The spacetime of our universe is not flat, and redshifts do not convert to "recession velocities" the way the relativistic Doppler shift formula would predict. If they did, it would be impossible to have "recession velocities" faster than $c$.

 

[GhostLoveScore]

Maybe we should take a step back.
1. OP, what do you think we should see, if not the CMBR?
2. OP, if we say the CMBR in the past, and see the answer to #1 today, what was the transition like? Can you tell us, at least qualitatively, when it happened?

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.

 

[GhostLoveScore]

Part of the reason I tried to ask some clarifying questions. Sadly, the OP seems to have lost interest.

Sorry for the late reply, I just didn't have the time due to very busy week (work and personal).