CMBR anisotropy and cosmic abundances

[Adrian59]

What is (are) the original paper(s) relating to the interpretation of the CMBR anisotropy in setting the cosmic abundances? I did pose the same question last year but it got lost in another thread. I had found papers by Hu and Dodelson from 2002, Hu and white from 1996 and Seljak from 1994 as well as a recent review by Tojerio 2006. More recently I have read Hu & Sugiyama (1995) paper. A clear technical answer appears to elude me for the mechanism of the relative heights of the peaks as evidence for the cosmic abundances of baryonic matter, dark matter and dark energy.

 

[kimbyd]

Cosmic abundances? You mean cosmic light element abundances? Or something else?

 

[Adrian59]

Cosmic abundances? You mean cosmic light element abundances? Or something else?

No, I mean the ratios of dark energy 68%, dark matter 27%, baryonic matter 5% or something close to these since different references can differ slightly with these values but I think the ones I have quoted are to the nearest 1% the currently excepted values.

 

[kimbyd]

I don't think estimation of these cosmological parameters was really possible until the WMAP satellite's first data release, so that would make this paper the first publication of somewhat-precise measurements of these values:
https://arxiv.org/abs/astro-ph/0302209

But are you looking for something else? As in, are you more interested in the theoretical underpinnings of how these cosmological parameters impact the CMB data? Are you more interested in the data processing that extracts information from the CMB (e.g. determining the power spectrum or determining cosmological parameters from the power spectrum)?

 

[Adrian59]

I don't think estimation of these cosmological parameters was really possible until the WMAP satellite's first data release, so that would make this paper the first publication of somewhat-precise measurements of these values:
https://arxiv.org/abs/astro-ph/0302209

But are you looking for something else? As in, are you more interested in the theoretical underpinnings of how these cosmological parameters impact the CMB data? Are you more interested in the data processing that extracts information from the CMB (e.g. determining the power spectrum or determining cosmological parameters from the power spectrum)?

Probably the latter but I will try the reference first; thanks for your help.

 

[kimbyd]

Probably the latter but I will try the reference first; thanks for your help.

Let me know! There's a lot of rich history involved in CMB science, most of it since 1990.

 

[Adrian59]

Let me know! There's a lot of rich history involved in CMB science, most of it since 1990.

Thanks. I have now read the reference you embedded. As suggested above I was looking more for as you said

in the data processing that extracts information from the CMB … determining cosmological parameters from the power spectrum)

.

I still find this paper does a similar slight of hand trick as the other papers I have read, in that results are quoted (as in table 1) without really showing how they were calculated. One often sees interactive graphics that show the CMBR isotropy change as you alter the ratios, but no idea of the algorithm behind the graphic.

 

[kimbyd]

I still find this paper does a similar slight of hand trick as the other papers I have read, in that results are quoted (as in table 1) without really showing how they were calculated. One often sees interactive graphics that show the CMBR isotropy change as you alter the ratios, but no idea of the algorithm behind the graphic.

Are you talking about the power spectrum of the CMB? These might be the videos you're referring to?
http://space.mit.edu/home/tegmark/cmb/movies.html

If so, Max Tegmark has a number of other resources on CMB data analysis. A lot of the info is a bit old, but still relevant. For the power spectrum itself, the relationship between cosmological parameters and the CMB is computed by simulating the behavior of the early universe using approximations which make the simulations tractable.

This paper describes the first algorithm which was used for rapid computation of the expected CMB power spectrum given a set of model parameters:
http://xxx.lanl.gov/abs/astro-ph/9603033

Today's computations haven't changed all that much from the above algorithm.

 

[George Jones]

I still find this paper does a similar slight of hand trick as the other papers I have read, in that results are quoted (as in table 1) without really showing how they were calculated. One often sees interactive graphics that show the CMBR isotropy change as you alter the ratios, but no idea of the algorithm behind the graphic.

No sleight of hand. The paper states

We begin by outlining our methodology (§2). Verde et al. (2003) describes the details of the approach used here to compare theoretical predictions of cosmological models to data.

In other words, a brief outline for experts is given is section 2 "BAYESIAN ANALYSIS OF COSMOLOGICAL DATA", and a a more detailed treatment, again for experts, is given in

https://arxiv.org/abs/astro-ph/0302218

An advanced but possibly more readable treatment is given in chapter 6 "Cosmological parameter estimation" from the book "The Cosmic Microwave Background" by Ruth Durrer.

 

[Adrian59]

Thanks everyone, it appears I have some more reading.

 

[Adrian59]

Are you talking about the power spectrum of the CMB? These might be the videos you're referring to?
http://space.mit.edu/home/tegmark/cmb/movies.html

If so, Max Tegmark has a number of other resources on CMB data analysis. A lot of the info is a bit old, but still relevant. For the power spectrum itself, the relationship between cosmological parameters and the CMB is computed by simulating the behavior of the early universe using approximations which make the simulations tractable.

This paper describes the first algorithm which was used for rapid computation of the expected CMB power spectrum given a set of model parameters:
http://xxx.lanl.gov/abs/astro-ph/9603033

Today's computations haven't changed all that much from the above algorithm.

Your first link to Max Tegmark site shows something like what I meant though his graphic doesn't appear to allow a freeze frame to show exactly what the CMBR anisotropy would look like with a particular choice of parameters. I'm afraid the second linked site is currently unavailable.

 

[Adrian59]

No sleight of hand. The paper states
In other words, a brief outline for experts is given is section 2 "BAYESIAN ANALYSIS OF COSMOLOGICAL DATA", and a a more detailed treatment, again for experts, is given in

https://arxiv.org/abs/astro-ph/0302218

An advanced but possibly more readable treatment is given in chapter 6 "Cosmological parameter estimation" from the book "The Cosmic Microwave Background" by Ruth Durrer.

I have read the paper you provided a link to. It seems very much the same group of authors for the link previously given. I have to admit that I am yet to be totally convinced that dark matter is a feature of our universe. As yet I still feel a paper which clearly goes from direct observational data on the CMBR to evidence of dark matter is missing. There appears to be an assumption that dark matter exists before the analysis. For example in part 6. Lyman α Forest Data it says as I quote, 'The Lyman α forest traces the fluctuations in the neutral gas density along the line of sight to distant quasars. Since most of this absorption is produced by low density unshocked gas in the voids or in mildly overdense regions that are thought to be in ionization equilibrium, this gas is assumed to be an accurate tracer of the large-scale distribution of dark matter.' In other words there appears an implicit assumption that there is dark matter.

 

[kimbyd]

I have read the paper you provided a link to. It seems very much the same group of authors for the link previously given. I have to admit that I am yet to be totally convinced that dark matter is a feature of our universe. As yet I still feel a paper which clearly goes from direct observational data on the CMBR to evidence of dark matter is missing. There appears to be an assumption that dark matter exists before the analysis. For example in part 6. Lyman α Forest Data it says as I quote, 'The Lyman α forest traces the fluctuations in the neutral gas density along the line of sight to distant quasars. Since most of this absorption is produced by low density unshocked gas in the voids or in mildly overdense regions that are thought to be in ionization equilibrium, this gas is assumed to be an accurate tracer of the large-scale distribution of dark matter.' In other words there appears an implicit assumption that there is dark matter.

It is difficult to track through the whole thought process for why the CMB is such powerful evidence for dark matter, but it is all there. Max Tegmark's movies linked above provide a nice visual for how dark matter influences the CMB (basically, it changes the even/odd peak structure). And the Seljak and Zaldarriaga paper demonstrates how that link is calculated in practice (if you want to trace the calculations back, they also provide references for how dark matter was originally included).

Finally, if you're concerned about how dark matter is "assumed" from the start, bear in mind that if dark matter didn't exist, the above analysis procedure would measure its density to be zero. It doesn't.

 

[Adrian59]

It is difficult to track through the whole thought process for why the CMB is such powerful evidence for dark matter, but it is all there. Max Tegmark's movies linked above provide a nice visual for how dark matter influences the CMB (basically, it changes the even/odd peak structure). And the Seljak and Zaldarriaga paper demonstrates how that link is calculated in practice (if you want to trace the calculations back, they also provide references for how dark matter was originally included).

Finally, if you're concerned about how dark matter is "assumed" from the start, bear in mind that if dark matter didn't exist, the above analysis procedure would measure its density to be zero. It doesn't.

I believe, I have with your help finally tracked down what I would consider the main papers in interpretation of the CMBR anisotropy. The original Hu & Sugiyama (1995) paper gives a model to the CMBR anisotropies. Seljak & Zaldarriaga (1996) formulate an analytical technique using line of sight integration for analysing the data from the CMBR probes. Then from the WMAP results Verde et al in 2003 show how the data is analysed using, first Baye’s theorem and then Markov chains with a Monte Carlo stimulation. Finally, the Spergel et al paper, also in 2003, shows the final results from WMAP using this analysis.

It is a tortuous path from theory to observation. I did find a good lecture from the summer school on cosmology from ICTP in 2016 (https://www.youtube.com/watch?v=wdOUiPicWM8) which did link all these approaches together. So, I think I am more or less there in understanding this area at the level I am happy with.

 

[Adrian59]

It is difficult to track through the whole thought process for why the CMB is such powerful evidence for dark matter, but it is all there. Max Tegmark's movies linked above provide a nice visual for how dark matter influences the CMB (basically, it changes the even/odd peak structure). And the Seljak and Zaldarriaga paper demonstrates how that link is calculated in practice (if you want to trace the calculations back, they also provide references for how dark matter was originally included).

Finally, if you're concerned about how dark matter is "assumed" from the start, bear in mind that if dark matter didn't exist, the above analysis procedure would measure its density to be zero. It doesn't.

I have spotted an interesting conundrum with the Mark Tegmark movie in that let one label the peaks 1 to 7; at low baryon fraction you have only peaks 1-3 with 4 and 5 beginning to appear. As the baryon fraction increases, peak 1 increases but peak 2 decreases and eventually almost disappears. The lower peaks 4-7 become progressively more apparent as the baryon fraction increases. So the question is: which peak is the second peak in the WMAP data is it peak 2 or 3 with a now absent peak 2, indicating a greatly increased baryon fraction that the current standard model assumes.

 

[kimbyd]

I have spotted an interesting conundrum with the Mark Tegmark movie in that let one label the peaks 1 to 7; at low baryon fraction you have only peaks 1-3 with 4 and 5 beginning to appear. As the baryon fraction increases, peak 1 increases but peak 2 decreases and eventually almost disappears. The lower peaks 4-7 become progressively more apparent as the baryon fraction increases. So the question is: which peak is the second peak in the WMAP data is it peak 2 or 3 with a now absent peak 2, indicating a greatly increased baryon fraction that the current standard model assumes.

There are two important effects that are necessary to understand what this is doing to the power spectrum:
1) The acoustic oscillations themselves which set up the interference pattern. For pure baryonic matter, the odd and even peaks will be of equivalent primordial magnitude. If there is much dark matter, the even-numbered peaks are suppressed.
2) The surface of last scattering, which is marked by the transition of the early universe from a plasma to a gas state, did not happen instantaneously. It took a few hundred thousand years. This has the impact of blurring the CMB signal, suppressing power at small angular scales.

The combination of these two effects means that you need to measure, at a minimum, the first three peaks of the CMB to get a positive determination of the ratio of normal matter to dark matter. The first two peaks alone don't get you very far, because the second peak will always be measured to be smaller than the first. The third peak, however, if there is nothing but baryonic matter, will be smaller still than the second peak. This isn't the case in our universe: the third peak is roughly the same magnitude as the second, despite the blurring introduced by the fact that the plasma to gas phase transition wasn't instantaneous.

 

[Adrian59]

There are two important effects that are necessary to understand what this is doing to the power spectrum:
1) The acoustic oscillations themselves which set up the interference pattern. For pure baryonic matter, the odd and even peaks will be of equivalent primordial magnitude. If there is much dark matter, the even-numbered peaks are suppressed.
2) The surface of last scattering, which is marked by the transition of the early universe from a plasma to a gas state, did not happen instantaneously. It took a few hundred thousand years. This has the impact of blurring the CMB signal, suppressing power at small angular scales.

The combination of these two effects means that you need to measure, at a minimum, the first three peaks of the CMB to get a positive determination of the ratio of normal matter to dark matter. The first two peaks alone don't get you very far, because the second peak will always be measured to be smaller than the first. The third peak, however, if there is nothing but baryonic matter, will be smaller still than the second peak. This isn't the case in our universe: the third peak is roughly the same magnitude as the second, despite the blurring introduced by the fact that the plasma to gas phase transition wasn't instantaneous.

However, in the Mark Tegmark movie it appears that the even peaks decrease with increasing baryons, so assuming a fixed matter component, dark matter will be decreasing not increasing as the even peaks are progressively depressed. Purely by chance I found a paper by Stacy S. McGaugh from 1999, 'Distinguishing Between CDM and MOND: Predictions for the Microwave Background' which does report exactly what I have observed with disappearing even peaks of the CMBR depending on what cosmological model you are using. Interestingly, and here I am stating up front that I am not a supporter of MOND, this paper shows how CMBR anisotropies can be explained in a MONDian universe!

 

[kimbyd]

However, in the Mark Tegmark movie it appears that the even peaks decrease with increasing baryons, so assuming a fixed matter component, dark matter will be decreasing not increasing as the even peaks are progressively depressed. Purely by chance I found a paper by Stacy S. McGaugh from 1999, 'Distinguishing Between CDM and MOND: Predictions for the Microwave Background' which does report exactly what I have observed with disappearing even peaks of the CMBR depending on what cosmological model you are using. Interestingly, and here I am stating up front that I am not a supporter of MOND, this paper shows how CMBR anisotropies can be explained in a MONDian universe!

What movies are you looking at? I'm not entirely sure that I see any of them that are really good at showing this result. The combo movies don't show small enough angular scales to really show what's going on (only the first two peaks are visible for most of the "Baryons" movie). The old movies may be misleading due to them not showing what the other parameter choices were.

 

[kimbyd]

BTW, NASA has a site where you can put in your own parameter choices and get out an estimate of the CMB power spectrum. It's quite complicated (lots and lots of parameters go into these models), but fairly quick to use:
https://lambda.gsfc.nasa.gov/toolbox/tb_camb_form.cfm

I did a simple run where I set the Baryon density to the current measured sum of the dark matter and baryon densities, and set the dark matter density to zero. The link to the results is here, though I don't know if it's accessible by others:
https://lambda.gsfc.nasa.gov/tmp/camb/camb_27375040.cfm

In case the above link doesn't work, I've attached the plot:

As you can clearly see, the peaks decrease monotonically in amplitude, with no even/odd variation visible at all.

 

[Adrian59]

What movies are you looking at? I'm not entirely sure that I see any of them that are really good at showing this result. The combo movies don't show small enough angular scales to really show what's going on (only the first two peaks are visible for most of the "Baryons" movie). The old movies may be misleading due to them not showing what the other parameter choices were.

I was looking at your reference http://space.mit.edu/home/tegmark/cmb/movies.html though this observation was in the section marked CMB movies old. Also, the graphic changes quite rapidly so to see what is happening your have to freeze the frame at different points.

 

[kimbyd]

I was looking at your reference http://space.mit.edu/home/tegmark/cmb/movies.html though this observation was in the section marked CMB movies old. Also, the graphic changes quite rapidly so to see what is happening your have to freeze the frame at different points.

Yeah, I'm quite sure the "Baryons" movie there uses a model which has a lot of dark matter.

The "Baryons" movie in the "Combo Movies" section is far more representative (since it keeps $\omega_b + \omega_d$ constant), but you can't see the effect I described because the scale of the graph is off.