# Is the CMBR interpretation for dark matter a fudge?

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The likelihood for dark matter appears to be lessening in direct detection and in its utility in explaining astronomical anomalies.
The likelihood for dark matter appears to be lessening in direct detection and in its utility in explaining astronomical anomalies. With regard to the former, a trio of recent dark matter detection experiments (LUX 2016, PandaX II 2017 and Xenon1t 2018) have all failed to show any non-baryonic matter. The remaining parameter space is almost obliterated. Further attempts at CERN have, also, not shown any new physics. As to the latter, work by J. Jalocha, F. Cooperstock, and A. Deur all provide competent alternatives to explain galaxy rotation curves without dark matter or modifying gravity.

Yet, despite this the Planck mission confidently quote Ωc h^2 as 0.12 ± 0.001!

The numerous Planck publications is truly a master class in hiding the significant details in a deluge of information. One clear quotation needed to remove the obscuration for me is a clear unambiguous expression for the two point function Cl.

weirdoguy

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Summary:: The likelihood for dark matter appears to be lessening in direct detection and in its utility in explaining astronomical anomalies.

The remaining parameter space is almost obliterated.
Of what model? There are countless models of dark matter out there that would not leave a detectable signal in the experiments you have mentioned.

That is true to a point. I would add that although the LHC has searched right back to a billionth of a second after the big bang, making the existence of unknown particles unlikely, there theoretically could be such particles. However, the real issue is if these dark matter particles are in no way detectable by reasonable means are we still talking about physics?

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They are detectable gravitationally.

They are detectable gravitationally.
I presume your are referring to astronomical anomalies like galaxy rotation curves and the corresponding Einstein rings, but this presupposes the issue under question as to whether these anomalies can be explained by another method. Anyway, if detecting dark matter gravitationally was the end of the story, why are we spending millions looking for an elusive particle of the stuff?

However, since there now appears two eminent contributors, as judged by their titles within the forum, who have contributed to my thread, are we any nearer a quote for the two point function Cl?

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I presume your are referring to astronomical anomalies like galaxy rotation curves and the corresponding Einstein rings, but this presupposes the issue under question as to whether these anomalies can be explained by another method. Anyway, if detecting dark matter gravitationally was the end of the story, why are we spending millions looking for an elusive particle of the stuff?
My only contribution, I'm afraid, is to suggest that yes, we are still discussing physics; and, in particular, the dark matter model for galaxy rotation etc. That's perfectly valid physics, no matter how hard the particles are to detect in the lab.

That said, I'm completely agnostic about whether dark matter is the answer. It's a fascinating question.

pinball1970
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Greetings,
Summary:: The likelihood for dark matter appears to be lessening in direct detection and in its utility in explaining astronomical anomalies.

As to the latter, work by J. Jalocha, F. Cooperstock, and A. Deur all provide competent alternatives to explain galaxy rotation curves without dark matter or modifying gravity.
A full literature citation would be instructive.

What do those "competent alternatives" have to say about the additional observational evidence consistent with dark matter?

Summary:: The likelihood for dark matter appears to be lessening in direct detection and in its utility in explaining astronomical anomalies.

The numerous Planck publications is truly a master class in hiding the significant details in a deluge of information.
Bit of a gratuitous diatribe is it not?

Best regards,
ES

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I would add that although the LHC has searched right back to a billionth of a second after the big bang
That’s not how the LHC works.

A full literature citation would be instructive.

i) Jalocha, J., Bratek, L. and Kutschera1, M. (2008). ‘Is Dark Matter Present in NGC 4736? An Iterative Spectral Method for Finding Mass Distribution in Spiral Galaxies.’ Astrophysical Journal, vol 679, pp 373–378.

ii) J. D. Carrick and F. I. Cooperstock. ‘General relativistic dynamics applied to the rotation curves of galaxies.’ (2012). Astrophysics and Space Science, Vol. 337, Issue 1, pp 321–329.

What do those "competent alternatives" have to say about the additional observational evidence consistent with dark matter?
The simple answer is nothing, but then do they have to? Surely each piece of evidence has to stand on its own merits. I know the attraction of the dark matter paradigm is it covers multiple areas, but that does not mean it is the correct theory; it just appeals to our sense of elegance.

Bit of a gratuitous diatribe is it not?

Best regards,
ES

Maybe, though I am still waiting for the answer to my question. If you have some expertise here I would value your input.

Regards, A59.

That’s not how the LHC works.

My original aim was to get the forum to help me in my quest to understand how the Planck mission found the dark matter relative density. I would understand this much better if I could find an authoritative quote for the two point function Cl, as I see this as the key to that understanding.

Your question on my understanding of the LHC is secondary for now.

EigenState137
Greetings,
The simple answer is nothing, but then do they have to? Surely each piece of evidence has to stand on its own merits.
I would argue that the total body of evidence need stand on its own in as coherent a manner as possible. I certainly have no objection to exploring theoretical alternatives, but such alternatives contribute no greater understanding unless they ultimately contribute to the full body of available evidence.

Best regards,
ES

Greetings,

I would argue that the total body of evidence need stand on its own in as coherent a manner as possible. I certainly have no objection to exploring theoretical alternatives, but such alternatives contribute no greater understanding unless they ultimately contribute to the full body of available evidence.

Best regards,
ES

Since I have given you the references you requested, are you going to check these?

Regards,
A59

(...) alternatives to explain galaxy rotation curves without dark matter or modifying gravity.

Yet, despite this the Planck mission confidently quote Ωc h^2 as 0.12 ± 0.001!
The Planck mission uses the CMB data. The densities quoted are for the best-fit LCDM model that explains the power spectrum. You need dark matter there, to account for the height of even peaks. I.e. their DM content is not based on rotation curves. Which is why an alternative theory that can account for the rotation curves but not for the power spectrum (and the lensing, and the structure formation, and the Bullet cluster...) is a weaker candidate for the observed effects - even if it does the curves better than DM.

Orodruin
The Planck mission uses the CMB data. The densities quoted are for the best-fit LCDM model that explains the power spectrum. You need dark matter there, to account for the height of even peaks. I.e. their DM content is not based on rotation curves. Which is why an alternative theory that can account for the rotation curves but not for the power spectrum (and the lensing, and the structure formation, and the Bullet cluster...) is a weaker candidate for the observed effects - even if it does the curves better than DM.

Hi Bandersnatch,

I recall your moniker from my previous conversations in the forum. According to Ruth Durrer ('The Cosmic Microwave Background', Cambridge University Press, 2021, p100) '... it is often simply assumed that the dark matter and galaxy power spectra differ only in a multiplicative factor.'

What I am after is something more than the arguments which are usually used to defend the dark matter paradigm. There is a well rehearsed narrative about dark matter over densities pulling in baryons with photons being dragged in, etc. What robust evidence demands that the CMBR peaks have to be that height with the tight constraint on dark matter density.

Regards,

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My original aim was to get the forum to help me in my quest to understand how the Planck mission found the dark matter relative density. I would understand this much better if I could find an authoritative quote for the two point function Cl, as I see this as the key to that understanding.

Your question on my understanding of the LHC is secondary for now.
In the very early universe, prior to the emission of the CMB, the universe was a plasma, and in this plasma was a series of density waves propagating (basically sound waves). When the universe cooled from a plasma to a gas, a slice of these density waves was imprinted on the CMB.

The waves were produced in such a way that they had approximately equal amplitude at every wavelength. And in the very early universe, they had much longer wavelengths than the cosmic horizon (in the inflationary paradigm, they were produced at sub-horizon scales then expanded along with the universe).

As long as the waves are larger than the horizon, speed of light limitations prevent them from oscillating (they do evolve over time, but not by much except expansion). As the horizon size grows in the early universe, these waves become smaller than the horizon, and start oscillating. This horizon-entering dependent upon size sets up an interference pattern, leading to peaks in the power spectrum of the observed waves.

The longest-wavelength peak occurs from the first half of the density wave, where matter was able to infall into denser regions. The second peak is the bounce-back from the first full oscillation: as the matter got more dense, photon pressure pushed it back. The next from 1.5 oscillations, and so on.

Normal matter contributes to both the even and odd peaks in the CMB. Dark matter contributes to only the odd-numbered peaks, because it doesn't experience pressure.

All of the physics described here is extremely linear, and its dynamics can be computed to a very high degree of precision in little time. This linearity is possible because a) we're only measuring relatively large-scale waves on the CMB, b) it was too early for much of any structure formation to occur, and c) the early-universe plasma was almost a perfect ideal gas.

berkeman, Delta2, Bandersnatch and 1 other person
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The linearity of the physics at the time is the critical thing that distinguishes the CMB from all other observations of dark matter, by the way. And, at least in my mind, this makes the CMB measurement the most powerful evidence, even if it is a bit more complex to understand.

The linearity of the physics at the time is the critical thing that distinguishes the CMB from all other observations of dark matter, by the way. And, at least in my mind, this makes the CMB measurement the most powerful evidence, even if it is a bit more complex to understand.

Thanks kimbyd, though I still think we're in the realm of narrative which is plausible. I am trying to drill down to more robust evidence which is more mathematical hence my request for a full expression for the two point function Cl.

The reason for this is that the CMBR anisotropy curve is plotted as l(l+1) Cl / 2 pi against l. It is quite clear to anyone with elementary maths (a bit of a clue to my nationality) that plotting l(l+1) against l by itself gives only a minima. Therefore, the peaks of the above expression must come from the Cl.

Furthermore, noting the many publications show different patterns to the CMBR anisotropy plot when the various cosmic parameters are varied, I presume that Cl must contain these parameters in its equation.

Finally, this must be where the Planck team get there result since the theoretical graph that fits the data gives the values of these parameters.

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The ##C_\ell## are just the multipole expansion coefficients of a function on a spherical surface - in this case the CMB temperature. Much like you would have Fourier coefficients when expanding a function on a finite interval. The value of ##\ell## in essence gives you the scale of variations described by each mode and for each ##\ell## there are ##\ell(\ell + 1)## different mode (hence why this enters as a normalisation factor in the power spectrum).

You typically will not have an expression for ##C_\ell## as you seem to think. For a given cosmological model, you can run a simulation and see what kind of values it would predict for ##C_\ell## (although the qualitative behaviour can be understood in many cases), this should then be compared with observations.

The ##C_\ell## are just the multipole expansion coefficients of a function on a spherical surface - in this case the CMB temperature. Much like you would have Fourier coefficients when expanding a function on a finite interval. The value of ##\ell## in essence gives you the scale of variations described by each mode and for each ##\ell## there are ##\ell(\ell + 1)## different mode (hence why this enters as a normalisation factor in the power spectrum).

You typically will not have an expression for ##C_\ell## as you seem to think. For a given cosmological model, you can run a simulation and see what kind of values it would predict for ##C_\ell## (although the qualitative behaviour can be understood in many cases), this should then be compared with observations.

I think I get about 50% of your answer: when you say 'the multipole expansion coefficients' are you referring to < alm al′m′ >.

I have studied Fourier series, so I know how to expand a function as a Fourier series but one still gets an expression in sinusoidal functions. Besides, there are expressions for Cl out there, eg:

Cl = 2/ π ∫ dk/k k3 < [|1/4 D(k, tdec) jl(kR*) + V(b) sin (k, tdec) jl’(kR*) |2 >;

from Professor Ruth Durrer, ‘The Cosmic Microwave Background’ (second edition) Cambridge University Press: Cambridge, UK, 2021.

My problem was that I have seen variants of this expression, and I am trying to find the definitive version.

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I have studied Fourier series, so I know how to expand a function as a Fourier series but one still gets an expression in sinusoidal functions.
That's because the sine functions form a basis for the vector space of functions on an interval. In the case of functions on a sphere, the basis are the spherical harmonics, which themselves are functions on a sphere. The CMB temperature in the direction given by spherical angles ##\theta## and ##\varphi## is given by
$$T(\theta,\varphi) = \sum_{\ell = 0}^\infty \sum_{m = -\ell}^\ell C_{\ell,m} Y_{\ell m}(\theta,\varphi),$$
where ##Y_{\ell m}## are the spherical harmonics. The coefficients ##C_\ell## are effectively the average of the ##C_{\ell, m}## for a fixed ##\ell##.

That's because the sine functions form a basis for the vector space of functions on an interval. In the case of functions on a sphere, the basis are the spherical harmonics, which themselves are functions on a sphere. The CMB temperature in the direction given by spherical angles ##\theta## and ##\varphi## is given by
$$T(\theta,\varphi) = \sum_{\ell = 0}^\infty \sum_{m = -\ell}^\ell C_{\ell,m} Y_{\ell m}(\theta,\varphi),$$
where ##Y_{\ell m}## are the spherical harmonics.

An interesting equation. So if I give you a specific coordinate (θ, φ), you can give me the temperature of the CMBR.

The coefficients ##C_\ell## are effectively the average of the ##C_{\ell, m}## for a fixed ##\ell##.

So in order to get the smooth relationship for the CMBR anisotropy, that is plotted there must be a nice continuous (in a mathematical sense) relationship? cf Ruth Durrer.

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An interesting equation. So if I give you a specific coordinate (θ, φ), you can give me the temperature of the CMBR.
You need to know the expansion coefficients to do that. The expansion coefficients are experimentally determined - by measuring the CMB temperature in different directions. However, the point of the expansion coefficients is that you can, using cosmological models, determine what they predict for the power spectrum. This is the entire idea behind looking at the power spectrum in the first place. Given a cosmological model, you can figure out, statistically, what the power spectrum should look like.

You need to know the expansion coefficients to do that. The expansion coefficients are experimentally determined - by measuring the CMB temperature in different directions. However, the point of the expansion coefficients is that you can, using cosmological models, determine what they predict for the power spectrum. This is the entire idea behind looking at the power spectrum in the first place. Given a cosmological model, you can figure out, statistically, what the power spectrum should look like.

Apologies, my first point was not totally serious. I didn't think you could pinpoint one area of sky and know its temperature, but I thought your equation was suggesting that.

However, I can't see how the expansion coefficients can be 'experimentally determined' for the theoretical derivation since this seems to be a circular argument.

Whatever you may think of that, can you please comment on my last point of #21.

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However, I can't see how the expansion coefficients can be 'experimentally determined' for the theoretical derivation since this seems to be a circular argument.
No no no. You determine it experimentally by measuring the CMB temperature. Then you compare with the theoretical predictions.
So in order to get the smooth relationship for the CMBR anisotropy, that is plotted there must be a nice continuous (in a mathematical sense) relationship? cf Ruth Durrer.
No. The ##C_\ell##s are discrete and ##\ell## take only integer values. There is really nothing continuous about them. However, you can still make a theoretical prediction about them given a cosmological model and compare this with experimental results. This is the basis of all empirical science.

EigenState137
No no no. You determine it experimentally by measuring the CMB temperature. Then you compare with the theoretical predictions.

I that case, how are the theoretical predictions made?

No. The ##C_\ell##s are discrete and ##\ell## take only integer values. There is really nothing continuous about them. However, you can still make a theoretical prediction about them given a cosmological model and compare this with experimental results. This is the basis of all empirical science.

I agree with your point about l only taking integer values but since the plot goes to 1000 - 2000, it can be considered continuous in practice.

In essence I want to know how the theoretical model, predicts the pretest probabilities. It can't be measured in any way because that defeats the object and ends in a circular argument.

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I that case, how are the theoretical predictions made?
You take the model and figure out what it predicts for the fluctuations in the CMB. I’m not sure I understand your question as this answer should be rather obvious. If you want to know exactly how this is done for our present cosmological models, that is the subject of an upper university cosmology class and not a PF thread.

You take the model and figure out what it predicts for the fluctuations in the CMB. I’m not sure I understand your question as this answer should be rather obvious. If you want to know exactly how this is done for our present cosmological models, that is the subject of an upper university cosmology class and not a PF thread.
I would have thought it was obvious that I have studied and read some advanced cosmology from the references I have given in the thread. The standard model of cosmology has been around for most contemporary physicist's professional careers and it is too well established for many to question its basic premises, it has become insurmountable. What appears obvious to you is because you have bought into this narrative, despite its numerous shortcomings (eg no particle detected, Tully-Fisher, Renzo's law, missing satellites, etc). The evidence that is quoted are astronomical anomalies that could be explained by dark matter but not necessarily.

If you can give some more mathematical pointers to the theoretical model rather than repeat the narrative, or even suggest a good reference paper, that would go some way towards settling the issue.

weirdoguy
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I would have thought it was obvious that I have studied and read some advanced cosmology from the references I have given in the thread.

Well, since you didn't know about spherical harmonics, which are one of the most basic tools in physics (I learned about them in my second year of studing physics at university) it's not that obvious you really read and understood that advanced references...

Well, since you didn't know about spherical harmonics, which are one of the most basic tools in physics (I learned about them in my second year of studing physics at university) it's not that obvious you really read that advanced references...
I don't know how you came to that conclusion because I have met spherical harmonics before. They are used to solve the quantization of energy levels in a hydrogen atom (ref: 'The Principles of Quantum Mechanics', PAM Dirac, 4th Ed., Clarendon Press: Oxford, UK).

EigenState137
I would have thought it was obvious that I have studied and read some advanced cosmology from the references I have given in the thread. The standard model of cosmology has been around for most contemporary physicist's professional careers and it is too well established for many to question its basic premises, it has become insurmountable. What appears obvious to you is because you have bought into this narrative, despite its numerous shortcomings (eg no particle detected, Tully-Fisher, Renzo's law, missing satellites, etc). The evidence that is quoted are astronomical anomalies that could be explained by dark matter but not necessarily.

If you can give some more mathematical pointers to the theoretical model rather than repeat the narrative, or even suggest a good reference paper, that would go some way towards settling the issue.
Why the belligerence towards both those who have attempted to be of assistance here and the scientific community in general?

WMAP publications

Planck publications

Why the belligerence towards both those who have attempted to be of assistance here and the scientific community in general?

WMAP publications

Planck publications
Apologies, if you think my response belligerent. It was not intended. I may have inadvertently stumbled on an answer to my question.

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I would have thought it was obvious that I have studied and read some advanced cosmology from the references I have given in the thread.
Throwing references around is not the same as having reached a proper understanding of those references. So, no, it has definitely not been obvious from how you have generally expressed yourself in this thread that you have understood what you have studied and read. If you had, you would have known that the way to get the prediction for the power spectrum is essentially to consider the Fourier modes of the density perturbations and how these transfer to the surface of last scattering. You would also know that there are a large number of effects influencing the density perturbations in the early Universe and that not all of them can be easily put on a "concise form" as you seem to want.

If you can give some more mathematical pointers to the theoretical model rather than repeat the narrative, or even suggest a good reference paper, that would go some way towards settling the issue.
I can give you some references, but I won't be able to help you understand them. You can start here for an overview:
Wayne Hu's PhD thesis goes into the gory details:
http://background.uchicago.edu/~whu/Papers/thesis.pdf
Both Peeble's and Peacock's texts go over the physics, but they're extremely dense.

Orodruin
Throwing references around is not the same as having reached a proper understanding of those references. So, no, it has definitely not been obvious from how you have generally expressed yourself in this thread that you have understood what you have studied and read. If you had, you would have known that the way to get the prediction for the power spectrum is essentially to consider the Fourier modes of the density perturbations and how these transfer to the surface of last scattering. You would also know that there are a large number of effects influencing the density perturbations in the early Universe and that not all of them can be easily put on a "concise form" as you seem to want.
At last I feel we are getting somewhere. Quickly dealing with your first sentence, I can reassure you that if I quote a reference it is one I have read and understood. I would like to add that until now only I have included any references. Moving to some physics, you mention density perturbations but which of these are you referring to?
However, it appears that another contributor to this thread has provided some references which I would like to check before making any further comment.