I Where Does the Cosmic Microwave Background Come From and How is it Measured?

[Silviu]

Hello! I am reading some basic stuff in cosmology and I am a bit confused by the microwave background. As far as I understand, it is the radiation produced at the beginning of the universe, when the matter density was not that high so the photon can escape and travel freely. So the microwave background we measure on earth, the one having 2.7K, is the one coming from a circle (assuming the universe would be flat for simplicity) of radius 13.9 light years around us and due to the redshift, the initial energy of these photons is reduced such that they have 2.7K. Is this right? Now we have this picture and as far as I understand it represents the whole visible universe. Now I am not sure I understand how it was done. You just look at this circle of 13.9 billion years radius, see the temperature at each point and then you run the time backwards, to see where each point would fit 13.9 billions years ago?

 

[Orodruin]

of radius 13.9 light years around

This is not correct (even if you put in the "billion"). Due to the expansion of the Universe, the distance to where the CMB that we see today originated is about three times as far away. It was also much closer than 13.9 billion light years when it was emitted.

Now we have this picture and as far as I understand it represents the whole visible universe. Now I am not sure I understand how it was done. You just look at this circle of 13.9 billion years radius, see the temperature at each point and then you run the time backwards, to see where each point would fit 13.9 billions years ago?

There is no "radius", there is just direction. You essentially look at the temperature in directions where there is nothing in between the CMB and us and mark it on the celestial sphere, just as you would mark positions on a map.

 

[plillies]

Due to the expansion of the Universe, the distance to where the CMB that we see today originated is about three times as far away. It was also much closer than 13.9 billion light years when it was emitted.

My current understanding, based on another thread, is that the image of the CMB that we are seeing has been redshifted downwards from 3000 K to 2.7 K due to relativistic Doppler effect, which becomes important when the receding object approached the speed of light. That being said the CMB because traveling close to the speed of light should actually be about twice as far from us as it appears, not three times.

 

[Bandersnatch]

My current understanding, based on another thread, is that the image of the CMB that we are seeing has been redshifted downwards from 3000 K to 2.7 K due to relativistic Doppler effect, which becomes important when the receding object approached the speed of light. That being said the CMB because traveling close to the speed of light should actually be about twice as far from us as it appears, not three times.

The cosmological redshift is not due to the Doppler effect. It's not the recession velocity, but the accrued amount of expansion that changes the wavelength. Hence the radiation emitted at the time when the universe was 1090 times smaller is shifted 1090 times (in terms of black body temperature spectrum, that's the factor between 3000 and 2.7).
It is not twice, nor three times as far as it appears (and it's not what Orodruin was saying) - it's 1090 times as far as it appears. It appears to us like it was at emission, which happened at then-distance of 42 million light years. That distance has stretched over the 13.8 billion years it took CMB to make its way against expanding space to reach us, by a factor of 1090, and is now 45 billion light years away.
The region which emitted CMB is currently receding at 3c, and was receding at over 60c at the time of emission. The relativistic Doppler shift, being a special-relativistic effect and not a general-relativistic one, can not be applied to those velocities.

 

[PeterDonis]

My current understanding, based on another thread, is that the image of the CMB that we are seeing has been redshifted downwards from 3000 K to 2.7 K due to relativistic Doppler effect

This is not correct, or at least it's not a good way of looking at it. If you mean the "malleability of space" thread, you evidently didn't see my responses there. Try this post for a start:

https://www.physicsforums.com/threads/the-malleability-of-space.924066/page-5#post-5838077

 

[Orodruin]

The relativistic Doppler shift, being a special-relativistic effect and not a general-relativistic one, can not be applied to those velocities.

It may be pointed out that cosmological redshift may be seen as an infinite series of consecutive infinitesimal Doppler shifts in local normal coordinates for comoving observers such that SR does apply. It should come as no surprise that in local normal coordinates nearby comoving observers see each other receding at a velocity $v = Hd$, where $H$ is the Hubble constant and $d$ the distance between them.

 

[Adrian59]

A recent realization of mine was that the CMBR is actually from the universe when it was 378,000 yrs old. This is when the photons became free of matter. The best description of the CMBR elliptical map that I have read is that it is an attempt the draw the three dimensional sky onto a flat piece of paper like a geographical world map would do. The differences in temperature are minute (10^-5 deg K) but reveal areas of higher and lower densities that eventually lead to structure in the universe. Red shift (z) is approx. 1000 at 378,000 yrs ago.

 

[Chronos]

The notion of us being 42 million light years distant from the surface of last scattering [source of CMB photons] is an illusion. When the CMB photons we observe were emitted, our galaxy - or at least that which was to become our galaxy - was still embedded in the surface of last scattering. So our distance from the source of CMB photons at the time of their emission is not a meaningful concept..

 

[Jorrie]

The notion of us being 42 million light years distant from the surface of last scattering [source of CMB photons] is an illusion. When the CMB photons we observe were emitted, our galaxy - or at least that which was to become our galaxy - was still embedded in the surface of last scattering. So our distance from the source of CMB photons at the time of their emission is not a meaningful concept..

But would it be correct to say that at T=378000 years, the comoving radius around 'that which was to become our galaxy', from where all CMB photons arrive today, was 42 Mlyr?

 

[Orodruin]

Well, the 42 million ly clearly refers to the source of the CMB that we see today (ie, a spherical subset if the LSS), not the CMB in general. I believe this has been pretty clear throughout this thread - even from the OP - so I am not sure I can agree with your objection to how this thread has treated it. Noboody has discussed the "distance to the CMB when it was emitted", buy the "distance to the source of the CMB we see today". There is a distinct and very important difference between those.

 

[plillies]

The cosmological redshift is not due to the Doppler effect. It's not the recession velocity, but the accrued amount of expansion that changes the wavelength. Hence the radiation emitted at the time when the universe was 1090 times smaller is shifted 1090 times (in terms of black body temperature spectrum, that's the factor between 3000 and 2.7).
It is not twice, nor three times as far as it appears (and it's not what Orodruin was saying) - it's 1090 times as far as it appears. It appears to us like it was at emission, which happened at then-distance of 42 million light years. That distance has stretched over the 13.8 billion years it took CMB to make its way against expanding space to reach us, by a factor of 1090, and is now 45 billion light years away.
The region which emitted CMB is currently receding at 3c, and was receding at over 60c at the time of emission. The relativistic Doppler shift, being a special-relativistic effect and not a general-relativistic one, can not be applied to those velocities.

OK. That makes sense. Thanks so much for this explanation. It really clarifies it for me. No Doppler effect. Just accrued expansion. Sorry I took so long to reply. I had to think about it a lot.

Not sure though about the last bit. CMC is curently receding at 3c, previously 60c. Is that a typo? It seems inconsistent with the acceleration of the expansion of the universe.

 

[Orodruin]

That the expansion is accelerating now does not mean it has always done so. That dark energy started being the dominant component is a rather recent occurrence in cosmological terms.

 

[timmdeeg]

Not sure though about the last bit. CMC is curently receding at 3c, previously 60c. Is that a typo?

If you are worried about 60c Figure 1 in

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

might be helpful. In the very early universe comoving objects have been receding superluminal. The worldline of photons emitted then is designated as "particle horizon" which is 46 Glyr away today. In my opinion this article is really worthwhile to read.

 

[plillies]

If you are worried about 60c Figure 1 in

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

might be helpful.

Interesting paper. But it raises a question that I hope someone can answer. It is generally excepted that the observed decreasing velocity of distant stellar objects indicates that the expansion of the universe is accelerating. That's kind of logical if you assume all velocity should be calculated at the time of emission (in accordance with SR, see top p. 15 in the paper), but it's not so logical if observed velocity is a result of the wavelength of the photons being stretched as they move through expanding space. In that case an accelerating universe would entail an observed increasing velocity of distant stellar objects so that their wavelength could be stretched more than expected. So how is it that, if increasing velocity with distance is the result of expanding space, decreasing observed velocity of distant stellar objects indicates that the expansion of space is accelerating?

 

[Bandersnatch]

It is generally excepted that the observed decreasing velocity of distant stellar objects indicates that the expansion of the universe is accelerating.

how is it that, if increasing velocity with distance is the result of expanding space, decreasing observed velocity of distant stellar objects indicates that the expansion of space is accelerating?

Why would you say that? Recession velocity is monotonically increasing with distance.

 

[ISamson]

https://en.wikipedia.org/wiki/Cosmic_microwave_background
:)

 

[plillies]

Why would you say that? Recession velocity is monotonically increasing with distance.

Thanks for answering, but your response does not address my quandary.

First, let me emphasize that I am really just trying to understand the accepted theory about the expansion of the universe, not speculating or proposing anything new. And I hope someone can explain the fallacy in my reasoning.

That being said, let me quote a textbook explanation of why fainter than expected supernovae mean accelerating expansion. This quotation is from a textbook by Rupert W Anderson. "The Cosmic Compendium: The Ultimate Fate of the Universe." p. 74, which can be accessed in google books using the search line: "decelerating universe dimmer OR fainter supernovae"

/Quotation Begins/

A simple derivation of the expansion rate of the universe can be given as follows:

The redshift z directly gives the cosmic scale factor at the time the supernova exploded.

a(t) = 1/(1+z)

/Added Note: Where a(t) is the scale factor expressed as a fraction of the universe's present size = 1./

So a supernova with a measured redshift z = 0.5 implies that the universe was 1/(1+0.5) = 2/3 of its present size when the the supernova exploded. In an accelerating universe, the universe was expanding more slowly in the past that it is today, which means it took a longer time to expand from 2/3 to 1.0 times its present size compared to a non-accelerating universe. This results in a larger light-travel time, larger distance, and fainter supernovae, which corresponds to the actual observation.

/Quotation Ends/

To illustrate my quandary, consider the following:

Hubble's law states that Hs = cz, from which z = Hs/c and dz/ds = H/c

So in an accelerating universe, at later times, H is greater than at earlier times and dz/ds is similarly greater (c being constant); i.e., given the same initial H,

dz/ds in an accelerating universe is greater than dz/ds in a non-acclerating universe ...1)

But the Quotation seems to be saying that it takes a larger change in s in an accelerating universe to achieve the same change in z; i.e., given the same initial H,

ds/dz in an accelerating universe is greater than ds/dz in a non-accelerating universe ...2)

It is evident that equation 1) and 2) are contradictory; hence, my quandary.

 

[PeterDonis]

Hubble's law states that Hs = cz

This is only valid for small z. In order to see the effects of accelerating expansion (or decelerating expansion, for that matter--what we would see if the universe were matter-dominated, not dark energy-dominated, which in fact it was until a few billion years ago), you have to look at large enough z that the linear Hubble law you state no longer holds. The acceleration or deceleration of expansion shows up as a deviation from that linear Hubble law; it's the kind of deviation that tells you which it is (acceleration or deceleration).

in an accelerating universe, at later times, H is greater than at earlier times

This is not correct. H is decreasing for an accelerating universe, if it also has matter in it as well as dark energy. In the limiting case where everything is negligible except dark energy (i.e., de Sitter spacetime), H is constant, which corresponds to exact exponential expansion (as opposed to somewhat slower than exponential for our current universe, which has non-negligible matter in it). For H to be increasing, you need super-exponential expansion, i.e., a "Big Rip" scenario, which, as far as I know, is ruled out (at least to a pretty high degree of confidence) by our current data.

 

[plillies]

This is not correct. H is decreasing for an accelerating universe, if it also has matter in it as well as dark energy. In the limiting case where everything is negligible except dark energy (i.e., de Sitter spacetime), H is constant, which corresponds to exact exponential expansion (as opposed to somewhat slower than exponential for our current universe, which has non-negligible matter in it). For H to be increasing, you need super-exponential expansion, i.e., a "Big Rip" scenario, which, as far as I know, is ruled out (at least to a pretty high degree of confidence) by our current data.

Thank you for this note. I think I am beginning to understand. My intuition was that scale factor (usually designated a) was defined in terms of space (and spatial distance), but I now realize that instead it is defined in terms of red shift z independent of the relationship between scale factor and space. So, of course, the relationship between space and z can vary depending on the nature of the expansion factors operating on space, be they a result of dark energy or general relativity. Hence, no problem understanding that space can expand faster than z is increasing, as indicated by recent supernovae observations. Let me know if I have finally got this right.

 

[PeterDonis]

My intuition was that scale factor (usually designated a) was defined in terms of space (and spatial distance), but I now realize that instead it is defined in terms of red shift z independent of the relationship between scale factor and space.

Actually neither of those are quite true. The scale factor itself is a coordinate-dependent quantity which is defined for convenience; "distance" as cosmologists use the term means distance as defined in those particular coordinates (usually called "comoving coordinates"). The redshift z of light from some distant object is related to the ratio of the scale factor now (when we see the light) to the scale factor when the light was emitted (that ratio is 1 + z). But that ratio is also the ratio of the distance (in comoving coordinates) "now" (when see the light) to the distance when the light was emitted, from us to the distant object. It is often convenient to visualize the universe in terms of these comoving coordinate distances, even though we can't directly measure them, we can only measure their ratios (the redshifts). But you have to keep in mind that that's only a convenience, and can lead to confusion if you interpret it too literally.

no problem understanding that space can expand faster than z is increasing, as indicated by recent supernovae observations.

That's not what the observations tell us. What we actually observe is a relationship between the redshift z and the brightness and angular size of distant objects. We then compare the actually observed relationship with the relationship that is predicted by various possible models of the universe. That comparison is what tells us that, until a few billion years ago, the universe's expansion was decelerating (i.e., was matter dominated), but then it started accelerating (i.e., became dark energy dominated)--because that model is the one that predicts the redshift-brightness-angular size relationship that matches what we actually observe.

 

[plillies]

That's not what the observations tell us. What we actually observe is a relationship between the redshift z and the brightness and angular size of distant objects. We then compare the actually observed relationship with the relationship that is predicted by various possible models of the universe. That comparison is what tells us that, until a few billion years ago, the universe's expansion was decelerating (i.e., was matter dominated), but then it started accelerating (i.e., became dark energy dominated)--because that model is the one that predicts the redshift-brightness-angular size relationship that matches what we actually observe.

Thanks for the great explanation!

A suggestion. You might want to edit the Wikipedia page:

https://en.wikipedia.org/wiki/Accelerating_expansion_of_the_universe

I find the section titled "Evidence for acceleration" is particularly unclear.

 

[PeterDonis]

You might want to edit the Wikipedia page

Unfortunately, I and others have found that trying to edit Wikipedia pages, and keep them edited properly, is a bottomless pit. The best we can do is to make it clear here at PF that in general we don't consider Wikipedia to be a reliable source.