How Does The Cosmic Microwave Background Show That The Universe is Expanding?

[Rodrigo Olivera]

TL;DR Summary

I've been searching for weeks and still with the doubt.
I just know scientist look the content of the CMB and with general relativity calculates the expansion rate today that is 73 km/s/Mpc, but nowhere does it say how exactly. Please help.

I've been searching for weeks and still with the doubt.
I just know scientist look the content of the CMB and with general relativity calculates the expansion rate today that is 73 km/s/Mpc, but nowhere does it say how exactly. What does the contents of the universe have to do with the expansion speed of the universe today? Please help.

 

[berkeman]

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

 

[Rodrigo Olivera]

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

I've already check it :(

 

[PeroK]

Summary:: I've been searching for weeks and still with the doubt.
I just know scientist look the content of the CMB and with general relativity calculates the expansion rate today that is 73 km/s/Mpc, but nowhere does it say how exactly. Please help.

I've been searching for weeks and still with the doubt.
I just know scientist look the content of the CMB and with general relativity calculates the expansion rate today that is 73 km/s/Mpc, but nowhere does it say how exactly. What does the contents of the universe have to do with the expansion speed of the universe today? Please help.

You could try:

https://wordery.com/an-introduction-to-modern-cosmology-andrew-liddle-9781118502143

 

[Ibix]

The CMB isn't completely uniform. There are tiny fluctuations in it, evidence of non-uniformity that eventually developed into stars, galaxies and clusters.

My limited understanding is that the power spectrum of these fluctuations is predicted to depend on the mix of matter, radiation, dark matter and dark energy present in the universe. Thus if you measure the power spectrum you can invert the prediction and get an estimate of the amounts of each type in the universe. Then you feed those into the Friedmann equations to get the scale factor and its derivatives at any time, and hence $H_0$.

 

[sunrah]

Summary:: I've been searching for weeks and still with the doubt.
I just know scientist look the content of the CMB and with general relativity calculates the expansion rate today that is 73 km/s/Mpc, but nowhere does it say how exactly. Please help.

I've been searching for weeks and still with the doubt.
I just know scientist look the content of the CMB and with general relativity calculates the expansion rate today that is 73 km/s/Mpc, but nowhere does it say how exactly. What does the contents of the universe have to do with the expansion speed of the universe today? Please help.

The CMB is generally regarded as evidence of the big bang model because it apparently verifies the expansion of space due to the redshifting of the perfect blackbody spectrum measured, but we don't actually know what its temperature (or wavelength) was at recombination via observation. The temperature of recombination can be estimated using equilibrium theory but as far as I'm aware this process is not independent of the current CMB temperature.

The way I see it, the existence of the CMB at microwave wavelengths is enough in most people's eyes to confirm the big bang model, because it would be required by that model. However there is other independent evidence of expanding space such as Hubble and Lemaitre's work on galaxy redshift correlations.

On another note, the CMB also offers indication of inflation as well as evidence of dark energy (accelerated expansion, see "late-time integrated Sachs Wolfe effect", both of which allude to expanding universe.

 

[PeterDonis]

we don't actually know what its temperature (or wavelength) was at recombination via observation

Yes, we do, because we know the redshift of the CMB, and we know its temperature today. Those two things are sufficient to calculate the temperature of the CMB at the time when it was emitted.

 

[sunrah]

Yes, we do, because we know the redshift of the CMB, and we know its temperature today. Those two things are sufficient to calculate the temperature of the CMB at the time when it was emitted.

True.

My issue is just that the CMB redshift estimate is itself dependent on the temperature today (Saha equation). So we are using the observed temperature today to calculate the redshift of recombination, which is then used to calculate the temperature of the CMB at recombination. Which is fine as long as we don't rely on that as evidence of expansion. Maybe it is irrelevant, but it seems a bit self-referential to me. I would say the CMB fits nicely into the current model, but evidence of expansion comes from direct measurements, e.g. galaxy redshift correlations.

 

[PeterDonis]

the CMB redshift estimate is itself dependent on the temperature today

Not entirely. We can detect spectral lines in the CMB, though not with very high precision. So we have at least a rough independent check on calculations involving temperature.

Also, we can measure the temperature of the CMB today very precisely, since we have its spectrum over a very wide range of frequencies. So I don't see why it's an issue that the temperature today is one of the inputs we need to use.

we are using the observed temperature today to calculate the redshift of recombination, which is then used to calculate the temperature of the CMB at recombination

No, you have this backwards. The method of estimating the CMB redshift this way involves first knowing both temperatures--the temperature today, which we measure directly, and the temperature at recombination, which we calculate based on the known properties of hydrogen. The ratio of those two temperatures then gives the redshift of the CMB from then to now.

Which is fine as long as we don't rely on that as evidence of expansion.

The redshift, calculated as above, is direct evidence of expansion, since the redshift directly gives the factor by which the universe expanded from recombination to now. (To be precise, that expansion factor is $1 + z$.) The only possible confounding factor, which is present in observations of galaxies, namely that individual galaxies are not in general exactly comoving with the Hubble flow, is not there with the CMB since it is exactly comoving with the Hubble flow.

it seems a bit self-referential to me

No, it isn't; you simply have an incorrect understanding of the calculation that is actually being made. See above.

 

[PeterDonis]

the CMB redshift estimate is itself dependent on the temperature today (Saha equation).

The Saha equation is not involved at all in our knowledge of the CMB temperature today; we observe that directly. The Saha equation is only involved in calculating the temperature at recombination based on the known properties of hydrogen.

 

[sunrah]

The Saha equation is not involved at all in our knowledge of the CMB temperature today; we observe that directly. The Saha equation is only involved in calculating the temperature at recombination based on the known properties of hydrogen.

Yes, I agree. The Saha equation features in equilibrium calculation and the temperature of recombination is related to the current temperature via redshift (i.e. model-dependent).

It's possible I miss understand the process, true, but this is not really what I meant or what is causing confusion/consternation, and just to add, my initial post was intended to sympathise with OP's lack of satisfaction with the nature of the evidence.

I think the issue here is my (and maybe other people's) understanding of what constitutes observational evidence. If we measure that the background radiation is in the microwave range, there is nothing except our cosmological model that tells us this is due to a redshift. Therefore such a conclusion is not model independent, so can this measurement really be strong evidence of the same model's validity? Of course it confirms some predictions of the model, if and only if the radiation has actually redshifted. (Yes, a static universe might have trouble explaining it, true, but still it is no smoking gun imo.)

Look at spectroscopic redshift measurements. These are actual measurements of motion and are model independent (whatever the actual nature of the motion). We don't need to resort to distance-redshift relations to know that the distance between us and the source is changing somehow, we can actually see it! When we observe that there is also a relationship between the rate of change and distance, and this applies everywhere in the sky, we can conclude really only one of two things: 1) either we are the at the centre of everything, 2) everything is moving away from everything else. In either model we choose we have expansion: provided we believe Einstein's second postulate it can't be peculiar motion.

This is why I say expansion is not immediately evident by measuring a Planck curve with a temperature of 2.7K.

 

[PeterDonis]

If we measure that the background radiation is in the microwave range, there is nothing except our cosmological model that tells us this is due to a redshift

First, as I said, we can measure spectral lines in the CMB. Those are direct (if very rough at present) measures of redshift.

Second, the presence of background radiation in a Big Bang-type cosmology was predicted before it was observed. So finding it counts as evidence in favor of the model that predicted it.

If we had other models that also predicted background radiation consistent with what we observe, our observation of such radiation would also count as evidence in favor of those models. But we don't. No other models predict it.

Look at spectroscopic redshift measurements. These are actual measurements of motion

No, they aren't. They are measurements of redshift. Saying they are "due to motion" is just as much a model-dependent conclusion as saying that the CMB redshift is due to cosmological expansion. You can't look at any redshift measurement and somehow magically tell that it must be "due to motion". You have to compare what you observe with the predictions of whatever models you have. If the model with "motion" in it matches the data better than any other model, then that's the one you adopt. But you can't avoid the "evaluate the model's predictions against the data" step.

We don't need to resort to distance-redshift relations to know that the distance between us and the source is changing somehow, we can actually see it!

Not from the redshift we can't, no. In cases of observations of things like galaxies, we have to have other observations besides the redshift that are indicators of distance. There are at least two of them: luminosity and angular size. But both of those distance measures are also model-dependent, since you have to know the absolute luminosity of the object (which is model-dependent) or the actual linear size of the object (which is model-dependent).

If you want to say that, for the case of the CMB, we do not have those other indicators, that is true. But the CMB redshift is not being used in a redshift-distance relationship anyway. The CMB redshift is not an indicator of "how far away" the CMB is; that would make no sense since the CMB is everywhere. The CMB redshift is an indicator of how much the universe has expanded since it was emitted. You are correct that that interpretation of the CMB depends on the particular model we are using being right; but, as I have already noted, we have no other model that makes the same prediction, so we're just using what we've got.

 

[Buzz Bloom]

and the temperature at recombination, which we calculate based on the known properties of hydrogen.

Hi Peter:

I am hoping you can help me find a reference that will answer the question below related to the temperature of the hydrogen at recombination. I have looked through (admittedly quickly)

http://en.wikipedia.org/wiki/Plasma_(physics)#Temperatures​

and did not find it helpful.

Since not all hydrogen ions become atoms at the same time, a different fraction of the hydrogen is ionized at different temperatures. My question is, how does the fraction of hydrogen being ions relate to the overall average temperature of the gas-ion mixture? Since the answer is likely to involve density and pressure as contributing factors, I would hope the reference will include those facors as well in the context of the state of things during the period of time during which recombination takes place.

Regards,
Buzz

 

[PeterDonis]

I am hoping you can help me find a reference that will answer the question below

Have you looked at the "Saha equation" link that was previously posted?

 

[Buzz Bloom]

Have you looked at the "Saha equation" link that was previously posted?

Hi Peter:

I searched this thread for "Saha Equation", and although it was mentioned several time I did not find a link. I did an online search and found:

https://en.wikipedia.org/wiki/Saha_ionization_equation .​

A quick looks seems to indicate that this article might well be helpful, but it will take me some time to confirm that.

Thanks for your help.

Regards,
Buzz

 

[PeterDonis]

I searched this thread for "Saha Equation", and although it was mentioned several time I did not find a link.

(Saha equation).

The actual article is on recombination and how we calculate what the temperature was at that time.

 

[PeterDonis]

We do not need a cosmological model to compare stellar spectra with a laboratory reference.

Of course not. I didn't say we did. I only said that all that comparison tells you is the redshift. It does not tell you that the redshift is due to motion. You need to have other data to infer that.

I am saying simply that we can see movement.

And you are wrong if by "see movement" you mean "see movement when the only data we have is redshift". That is simply not correct.

the process of comparing astronomical spectra to a reference is analogous to comparing spectra in Earth based settings

No, it isn't, because in Earth-based settings we have lots of other data. We never need to infer motion solely based on observed redshift.

I have already pointed out that in astronomical observations of things like galaxies, we also have other data. I am certainly not claiming that we have no way of estimating the distance to other galaxies. I am only saying that we cannot do so based solely on redshift observations. We have to use other data as well.

Hubble's use of cepheids is also an application of a physical law we can check here on earth

If you mean the period-luminosity relationship, no, we can't, unless you think someone has a Cepheid variable star in their lab somewhere.

However, that's really beside the point. The real point is that this is another example of other data, separate from redshift observations, that we use to estimate distance. We certainly do not estimate the distance to an observed Cepheid variable star based on its redshift. We estimate its distance based on its period, the period-luminosity relationship, and the star's apparent magnitude. So this supports what I am saying and does not support what you are claiming.

In neither case do we resort to speculative cosmology theories.

I never said we had to resort to cosmology models to estimate the distance to things like galaxies or Cepheid variables. But we do have to resort to models. The period-luminosity relationship is a theoretical model; it is based on observations but it is not an observation itself. So are the models of galaxies that are used to estimate absolute luminosity or linear size, in order to infer distance from apparent luminosity and apparent angular size. There is no such thing as a completely model-independent observation of the distance to such objects.

 

[Rodrigo Olivera]

Of course not. I didn't say we did. I only said that all that comparison tells you is the redshift. It does not tell you that the redshift is due to motion. You need to have other data to infer that.
And you are wrong if by "see movement" you mean "see movement when the only data we have is redshift". That is simply not correct.
No, it isn't, because in Earth-based settings we have lots of other data. We never need to infer motion solely based on observed redshift.

I have already pointed out that in astronomical observations of things like galaxies, we also have other data. I am certainly not claiming that we have no way of estimating the distance to other galaxies. I am only saying that we cannot do so based solely on redshift observations. We have to use other data as well.
If you mean the period-luminosity relationship, no, we can't, unless you think someone has a Cepheid variable star in their lab somewhere.

However, that's really beside the point. The real point is that this is another example of other data, separate from redshift observations, that we use to estimate distance. We certainly do not estimate the distance to an observed Cepheid variable star based on its redshift. We estimate its distance based on its period, the period-luminosity relationship, and the star's apparent magnitude. So this supports what I am saying and does not support what you are claiming.
I never said we had to resort to cosmology models to estimate the distance to things like galaxies or Cepheid variables. But we do have to resort to models. The period-luminosity relationship is a theoretical model; it is based on observations but it is not an observation itself. So are the models of galaxies that are used to estimate absolute luminosity or linear size, in order to infer distance from apparent luminosity and apparent angular size. There is no such thing as a completely model-independent observation of the distance to such objects.

Thanks for the answers but there is a way to explain how the CMB shows the expansion of the universe without touching the redshift?

 

[PeterDonis]

there is a way to explain how the CMB shows the expansion of the universe without touching the redshift?

If you are referring to the actually measured redshift of the CMB itself, no, that is not necessary. All we need is the temperature of the CMB today and our knowledge of the ionization energy of hydrogen, which tells us the temperature of the CMB when it was emitted. The ratio of those two temperatures tells us the redshift at which the CMB was emitted. Being able to actually measure the redshift of the CMB directly is a useful confirmation.

 

[Rodrigo Olivera]

If you are referring to the actually measured redshift of the CMB itself, no, that is not necessary. All we need is the temperature of the CMB today and our knowledge of the ionization energy of hydrogen, which tells us the temperature of the CMB when it was emitted. The ratio of those two temperatures tells us the redshift at which the CMB was emitted. Being able to actually measure the redshift of the CMB directly is a useful confirmation.

I'm very sorry for being insistent, but how does that predicts expansion of the universe. In many articles I read this:
"From that portrait [CMB] we are able to accurately measure the ingredients in the universe. How much normal matter, how much dark matter, how much neutrinos, how much radiation and so on. With those ingredients in hand, we can plug them into general relativity to tell us the behavior of the universe. Then we can run the clock forward from the emission of the CMB through all 13.8 billion years of history to the present day and predict what the expansion rate is right now."

It always says "me take this ingredients of the CMB and with some calculations we got the expasion" but never says how exactly. I already found the explanation of universe expansion using redshift, but I've been looking for an explanation that doesn't use redsfhit. Thanks for your time, really appreciate it.

 

[Ibix]

Expansion with a CMB is a prediction of Einstein's field equations if you assume a universe that's homogeneous and isotropic. I'm not aware of any model that has a CMB and no expansion. So the existence of a CMB is evidence for expansion.

Details of the structure of the CMB influence our understanding of the exact history of expansion, that's all.

Does that help?

 

[PeterDonis]

I'm very sorry for being insistent, but how does that predicts expansion of the universe.

It's the other way around. The model of an expanding universe (more precisely, the model of an expanding universe containing matter and radiation that was much hotter and denser in the past) predicts that there will be cosmic background radiation. Observing that radiation is a confirmation of the expanding universe model, since other models (such as the steady state model) do not predict its existence. Observing the temperature of the radiation allows us to infer by what factor the universe has expanded since it was emitted.

In many articles

Please give a specific reference. And if it's not a textbook or peer-reviewed paper, the response is probably going to be that it's not a valid reference.

take this ingredients of the CMB and with some calculations we got the expasion

No, it says we can calculate the rate of expansion now from the observed properties of the CMB and other observations as well.

 

[Rodrigo Olivera]

Expansion with a CMB is a prediction of Einstein's field equations if you assume a universe that's homogeneous and isotropic. I'm not aware of any model that has a CMB and no expansion. So the existence of a CMB is evidence for expansion.

Details of the structure of the CMB influence our understanding of the exact history of expansion, that's all.

Does that help?

How does examining the CMB and its ingredients tell me that the universe is expanding? (Without talking about redshift)

 

[Rodrigo Olivera]

It's the other way around. The model of an expanding universe (more precisely, the model of an expanding universe containing matter and radiation that was much hotter and denser in the past) predicts that there will be cosmic background radiation. Observing that radiation is a confirmation of the expanding universe model, since other models (such as the steady state model) do not predict its existence. Observing the temperature of the radiation allows us to infer by what factor the universe has expanded since it was emitted.

How the temperature of the radiation tells us the universe has expanded?

 

[PeterDonis]

How does examining the CMB and its ingredients tell me that the universe is expanding?

How the temperature of the radiation tells us the universe has expanded?

You have already had these questions answered. There is no point in continuing to repeat the same questions and answers over and over.

Thread closed.