# I How certain is dark matter?

#### ohwilleke

Gold Member
The Tully-Fisher relationship is definitely predicted by LCDM (https://arxiv.org/abs/1204.1497). Whether the low scatter is fully-explained is somewhat less certain, but this definitely warrants at worst a "maybe" rather than a "no".
No one has every produced a DM fit to the Tully-Fisher relationship without an extra 16 parameters highly tuned to the actual reality. Further, the attempts to fit the Tully-Fisher relationship with LCDM are attempts at post-diction not examples of prediction.

Their argument appears to be that the data set doesn't have the resolution required to distinguish the baryonic oscillations which occur in the modified gravity model.

That's fine, but that just argues for a reanalysis of the data which is designed to focus in on the baryonic oscillations themselves, and to include more than one old data set (2006). I don't buy Moffat and Toth's argument that we don't yet have enough data. I do buy that the way in which data is often processed might hide this effect, but the raw galaxy data sets are quite large. I'm quite sure that they could bin the data in such a way that these oscillations would be made more apparent, and there's a ton more data that could be included.
Maybe we are moving towards a consensus. You appear to have dropped your original position that a modified theory hasn't been tried to explain the matter power spectrum, as it has. Your final point about reanalysis with a larger data set appears correct but I still don't think the original graph drawn by Scott Dodelson is correct.

Doing some background searching I have found that Scott Dodelson is much more open to alternative theories than I thought, only hearing him second hand. Speaking in 2006 he says, “To definitively claim that dark matter is the answer, we need to find it,” Dodelson explained to PhysOrg.com. “We can do this in one of three ways: produce it in the lab (which might happen at Fermilab, the soon-to-start LHC, or ultimately the International Linear Collider), see a pair of dark matter particles annihilate and produce high energy photons (there are about a half dozen experiments designed to look for this), or see a dark matter particle bump a nucleus in a large underground detector (again, about 10 experiments are looking for this). Until one or more of these things happen, skeptics are still allowed'.

Also, speaking more recently he says, ' We're living in an era of cognitive dissonance. There is all this cosmological evidence for the existence of dark matter, but over the last 30 years, we've run all these experiments and haven't found it. My bet is that we're looking at things all wrong. Someone who's 8 years old today is going to come around and figure out how to make sense of all the data without evoking mysterious new substances.'

#### ohwilleke

Gold Member
The point about the 21cm data is more impressive with a diagram.

The predicted 21cm absorption with dark matter (red broken line) and without (blue line). Also shown (in grey) is the signal observed by EDGES.

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#### kimbyd

Gold Member
2018 Award
The point about the 21cm data is more impressive with a diagram.

View attachment 229279

The predicted 21cm absorption with dark matter (red broken line) and without (blue line). Also shown (in grey) is the signal observed by EDGES.
We'll see. It's too early to be very confident in those results. Also, the red dotted curve is just incorrect: the dark matter contribution to that graph depends critically upon what type of dark matter is assumed. Milli-charged dark matter at 100MeV could still explain the data as it stands, or there might be something else that hasn't been considered.

But there's a fair chance the data is just incorrect. That's usually the case when a new observational window is opened on the universe. It's usually best to be patient with this sort of thing.

I would call unmodified GR a "no" for galaxy rotation and Tully-Fisher. I would say that TeVeS and MOG are both compatible with the Standard Model of Particle Physics, in the sense of not adding new particles although that is really untrue for all five including unmodified GR. Not sure why you think TeVeS fails in terms of gravitational redshift. On cluster dynamics DM is a "maybe" not a "yes". MOG would be a maybe or yes on a reasonable cosmological simulation.

Also MOG really refers to a specific modified gravity theory of Moffat, while f(R) is a different modified gravity theory. MG is the commonly used abbreviation for "modified gravity" theory, in general.
Some interesting responses: we were both involved in a thread last year when the issue of a paper by Carrick and Cooperstock was discussed. I have found your remarks then from 26/10/17:

‘I am pretty sure neither Cooperstock (in a classical GR framework) or Deur (in a quantum gravity framework) are actually applying mainstream GR to get their results and actually subtly deviate from mainstream interpretation of GR. But, the fact that both investigators can get such impressive results with such very, very subtle tweaks to GR interpretation is in my view very promising. It is not at all obvious that conventional GR does not have a subtle flaw or two that make a big difference at large scales in weak gravitational fields.

Everyone agrees that Newtonian gravity has to be modified. GR is a Newtonian gravity modification. The question is whether GR has to be modified.’

So, I would propose that unmodified GR can explain galaxy rotation curves or at least there should be a ‘maybe’ in the box. Correct me if I am wrong about the Tully-Fisher relationship but since it is a relationship between baryonic matter and galaxy rotation, maximum orbital velocity any theory that doesn’t have putative extra mass should agree with this relationship. The issue with TeVes comes from a paper by Wojak et al ref: ‘Gravitational redshift of galaxies clusters as predicted by general relativity.’ Nature volume 477, pages 567–569 (29 September 2011).

The reason that I elected to signify that TeVeS and MOG didn’t fit the standard model is because don’t these theories postulate extra fields which presumably if they exist will need an extension of the standard model of physics. I've noted your final point on nomenclature.

#### ohwilleke

Gold Member
So, I would propose that unmodified GR can explain galaxy rotation curves or at least there should be a ‘maybe’ in the box. Correct me if I am wrong about the Tully-Fisher relationship but since it is a relationship between baryonic matter and galaxy rotation, maximum orbital velocity any theory that doesn’t have putative extra mass should agree with this relationship.
The Tully-Fischer relationship is a trivial corollary of the radial acceleration relationship which is basically another version of MOND. You need either DM or MG for it to work. It is completely inconsistent with unmodified GR without dark matter.

The reason that I elected to signify that TeVeS and MOG didn’t fit the standard model is because don’t these theories postulate extra fields which presumably if they exist will need an extension of the standard model of physics. I've noted your final point on nomenclature.
The pedantic point would be that GR, a classical theory, is still incompatible with the Standard Model, because there isn't a quantum gravity theory that is necessary for them to be theoretically consistent. This is a non-trivial big deal, but surely not what you intended to indicate.

Even GR or vanilla quantum gravity require extra gravitational fields beyond the SM (two of them in theories with a cosmological constant (GR) and/or dark energy (vanilla quantum gravity)).

I would normally think of TeVeS and MOG as equally compatible with the SM as GR because all of the fields added in each case are purely gravitational. GR with a cosmological constant has a scalar field and a tensor field. TeVeS and MOG have a scalar field, a tensor field and a vector field. Vanilla quantum gravity has a scalar dark energy field and a tensor graviton. MOND isn't relativistic and is admittedly an incomplete toy model, and so it doesn't really make sense to talk about it in that sense.

The non-gravitational part of the resulting complete theory wouldn't be changed in any of them except as necessary for a quantum gravity version (all of the popular live theories except Deur's are at their root classical theories).

This isn't really perfectly true, however. There is basically a solid consensus that GR, vanilla quantum gravity, TeVeS, MOG, MOND, Deur's approach, and any other attempt to integrate any remotely realistic theory of gravity in any form with the Standard Model in a quantum gravity form, changes the beta functions (which change the values of these constants with respect to energy scale as they run) of all of the experimentally measured constants of the Standard Model (all 12 fermion mass constants, 3 boson mass constants, all 4 CKM matrix constants, all 4 PMNS constants and all 3 coupling constants).

This isn't a huge impact on the SM, but it would potentially impact, for example, gauge unification, which might happen in an alternative to the SM without gravity, but not one with it, or it could cause the SM coupling constants to unify (in principle, I haven't run the numbers on that and the exact form of the modified beta function is not a consensus issue even though the need to modify it in some manner when gravity is included is a consensus issue).

Indeed, given that all of the variations from GR take place in the weak field limit (with possible quantum gravity differences that would be the same for quantum versions of all realistic modified gravity theories), the way that any integration of quantum gravity or modified quantum gravity impacts the SM beta functions would probably be experimentally indistinguishable, even though there would be some slight differences.

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The Tully-Fischer relationship is a trivial corollary of the radial acceleration relationship which is basically another version of MOND. You need either DM or MG for it to work. It is completely inconsistent with unmodified GR without dark matter.
I didn't see the Tully-Fisher relationship as similar to a galaxy rotation curve as you seem to be implying. Of course that is the underlying problem that both dark matter and MOND are trying to solve. As I am not a supporter of MOND, it is always with care that I reference Stacy McGaugh but non the less his paper from 2016 entitled ‘The Radial Acceleration Relation in Rotationally Supported Galaxies’ is an observational paper and as such can be read independently of Stacy McGaugh's preferred solution of MOND. I understood the observations to show a tight relation between baryonic mass and rotational velocity. It is surely meant to question the validity of dark matter as in order for dark matter theories to be compatible with these observations one has to invoke complex 'feed back' mechanisms. To my way of thinking any theory that can explain galaxy rotation velocities without dark matter will be compatible with these observations.

The pedantic point would be that GR, a classical theory, is still incompatible with the Standard Model, because there isn't a quantum gravity theory that is necessary for them to be theoretically consistent. This is a non-trivial big deal, but surely not what you intended to indicate.
Exactly.

Even GR or vanilla quantum gravity require extra gravitational fields beyond the SM (two of them in theories with a cosmological constant (GR) and/or dark energy (vanilla quantum gravity)).
I also fully agree with this but moving on would you not agree that within the theoretical framework of SM a field requires a boson (I don't know if a future theory of quantum gravity can dispense with this requirement) but look how desperate the physics community was in its search for the Higg's boson.

However, returning to an earlier post in this thread, you alluded to being a supporter of a version of MG. I don't know if you are prepared to say which and why if it is not too off topic for this thread.

#### kimbyd

Gold Member
2018 Award
It is surely meant to question the validity of dark matter as in order for dark matter theories to be compatible with these observations one has to invoke complex 'feed back' mechanisms.
I don't think I'll ever understand why this is an objection. The feedback mechanisms are either there or they aren't. They shouldn't be dependent upon any unknown physics. Every aspect of these feedbacks should be measurable through a combination of observations and simulations. The only aspect of the feedbacks that relies upon unknown physics is the degree to which dark matter interacts (both with itself and with normal matter). Everything else just depends upon understanding in detail the normal matter within galaxies.

When I hear somebody complaining about the inclusion of these feedbacks being necessary, I interpret that as a statement akin to, "That math is too complicated, so I don't believe you." If adding more complicated effects to the simulations improves the fits, that's a good thing. If those more complicated effects depend upon some parameters that aren't yet measured, but are measurable, then that's even better: it provides an additional test to the theory. If somebody comes up and says they have an answer that doesn't require that hard work, I'm going to be immediately suspicious.

I don't think I'll ever understand why this is an objection. The feedback mechanisms are either there or they aren't. They shouldn't be dependent upon any unknown physics. Every aspect of these feedbacks should be measurable through a combination of observations and simulations. The only aspect of the feedbacks that relies upon unknown physics is the degree to which dark matter interacts (both with itself and with normal matter). Everything else just depends upon understanding in detail the normal matter within galaxies.

When I hear somebody complaining about the inclusion of these feedbacks being necessary, I interpret that as a statement akin to, "That math is too complicated, so I don't believe you." If adding more complicated effects to the simulations improves the fits, that's a good thing. If those more complicated effects depend upon some parameters that aren't yet measured, but are measurable, then that's even better: it provides an additional test to the theory. If somebody comes up and says they have an answer that doesn't require that hard work, I'm going to be immediately suspicious.
I am partly in agreement. Einstein's general theory of relativity (as a graduate of physics I have struggled with connection coefficients and Riemann Tensors) is far more complex than Newton's theory of gravity but because it makes correct predictions it is regarded as the correct theory. However, epicycles never worked. So complexity is allowed if it ticks all the boxes. As Albert Einstein himself said, ‘Everything should be made as simple as possible, but not simpler.’

#### kimbyd

Gold Member
2018 Award
I am partly in agreement. Einstein's general theory of relativity (as a graduate of physics I have struggled with connection coefficients and Riemann Tensors) is far more complex than Newton's theory of gravity but because it makes correct predictions it is regarded as the correct theory. However, epicycles never worked. So complexity is allowed if it ticks all the boxes. As Albert Einstein himself said, ‘Everything should be made as simple as possible, but not simpler.’
Right. The difference is that epicycles were an idea that had no physical process behind them. Furthermore, it turned out that epicycles were just a way to do Fourier transforms on the path, and as such they can fit any closed trajectory provided enough epicycles were used. It's not terribly infrequent that people examine data today using methods that are conceptually similar to epicycles, in that they amount to nothing but curve fitting as the parameters involved have no connection to any physical model.

General Relativity is also an interesting comparison. In an important way, it isn't actually more complex than Newtonian gravity. Conceptually, it's as simple as, "What is the simplest possible non-trivial theory of gravity as space-time geometry?" A super-rough sketch of the logic is this:
1. To ensure the theory doesn't depend upon coordinates, the equations of motion can only depend upon coordinate-free parameters.
2. The only coordinate-free parameter available is the Ricci scalar R.
3. The simplest non-trivial function of R is $A + BR$, with A and B being constants (by convention, A and B are often expressed in terms of $\Lambda$, $G$, and $c$).
4. Use the above as the Lagrangian of the space-time geometry, which is added to the matter Lagrangian.
5. Be careful that all calculations take into account that space-time is curved.

That's it. That's all that General Relativity is. But the consequences of the theory can be inordinately complex at times. The construction above has an incredible simplicity to it, but the calculations one has to perform to determine what happens as a result of the theory can be tremendously challenging. It's really easy to make mistakes in the theory because it breaks a lot of our intuitions about how space-time behaves, and the choice of coordinates can have unexpected consequences if coordinates are not handled carefully (this is why many calculations try to avoid using coordinates at all).

GR really is the holy grail of a scientific theory. It has so few parameters, and so few assumptions, but explains so much. Most things that we try to understand scientifically end up being way more complicated in practice. The reason why galaxies are complicated is because baryonic matter is incredibly complicated. I see no problem with simulations of galaxies requiring 16 parameters (or however many parameters they fit). But those parameters absolutely should be things that are tied to physical processes that actually happen within galaxies, and we should be able to test the veracity of each and every one of those parameters through a combination of small-scale simulations and observations.

#### ohwilleke

Gold Member
I didn't see the Tully-Fisher relationship as similar to a galaxy rotation curve as you seem to be implying. Of course that is the underlying problem that both dark matter and MOND are trying to solve. As I am not a supporter of MOND, it is always with care that I reference Stacy McGaugh but non the less his paper from 2016 entitled ‘The Radial Acceleration Relation in Rotationally Supported Galaxies’ is an observational paper and as such can be read independently of Stacy McGaugh's preferred solution of MOND. I understood the observations to show a tight relation between baryonic mass and rotational velocity. It is surely meant to question the validity of dark matter as in order for dark matter theories to be compatible with these observations one has to invoke complex 'feed back' mechanisms. To my way of thinking any theory that can explain galaxy rotation velocities without dark matter will be compatible with these observations.
This is true. But, general relativity without dark matter is inconsistent with the Tully-Fischer relationship.

would you not agree that within the theoretical framework of SM a field requires a boson (I don't know if a future theory of quantum gravity can dispense with this requirement) but look how desperate the physics community was in its search for the Higg's boson.
All quantum gravity theories except the loop quantum gravity class of theories (e.g. causal dynamic triangles) and entropic theories, require a bosonic graviton at a minimum. LQG like GR focuses on space-time as the mechanism in lieu of gravitons. Entropic theories, IIRC, rely in part on quantum entanglement as a mechanism.

However, returning to an earlier post in this thread, you alluded to being a supporter of a version of MG. I don't know if you are prepared to say which and why if it is not too off topic for this thread.
I think that A. Deur's efforts to explain dark matter phenomena and dark energy are the closest to the truth (whether or not they are perfectly correct). His insights as a primarily QCD physicists inform his analysis in ways that other MG and GR researchers don't benefit from that are likely to be valid, he is quantum from the bottom up, his approach of starting from the non-abelian self-interacting scalar graviton static case and generalizing from that case is a smart one, and his back of napkin analysis suggests that he is in the right ball back to be explaining all of the dark matter and dark energy phenomena (solar system, galaxies, galaxy clusters, coincidence problem, dark energy, other cosmology issues) with no non-SM particles except a massless self-interacting graviton, but without a separate scalar or vector field. He made a successful prediction regarding apparent dark matter halo size in elliptical galaxies unique to his theory. It actually has one less free experimentally determined parameter than GR as it doesn't have a cosmological constant, in principle at least (he hasn't derived some constants that could be calculated from first principles). The fact that is provides a mechanism from which GR and MOND phenomena arise that is consistent with GR to the same extent of any vanilla attempt to do a quantum gravity theory that replicates GR, except one subtle issue regarding how self-interaction terms in non-spherically symmetric systems are treated, is big too

I didn't want to fixate too much on a particular theory that is not widely accepted and get into a debate over that particular theory, however. There are links summing up the key papers and a good powerpoint explanation above. None of the papers are terribly challenging for a physics grad student although the powerpoint presentation provides good motivation and context.

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#### ohwilleke

Gold Member
Thanks for the paper. Good catch.

FWIW, the statistical significance of the result is not great: 2.65 sigma tops, and that is before their final error estimate which they never neatly sum up in relation to their hypothesis. They also note a host of other studies that have attempted to make the same determination and come up with wildly different answers from each other than this study.

#### kimbyd

Gold Member
2018 Award
Thanks for the paper. Good catch.

FWIW, the statistical significance of the result is not great: 2.65 sigma tops, and that is before their final error estimate which they never neatly sum up in relation to their hypothesis. They also note a host of other studies that have attempted to make the same determination and come up with wildly different answers from each other than this study.
Which is fine. More data will help with that.

3. The simplest non-trivial function of R is A+BRA+BRA + BR, with A and B being constants (by convention, A and B are often expressed in terms of ΛΛ\Lambda, GGG, and ccc).
I agree with your equation and even if the variables are tensors, the underlying equation looks linear. Also, I can appreciate the difficulty with baryons in that one is dealing with potentially all four fundamental forces and not just the one.

I think that A. Deur's efforts to explain dark matter phenomena and dark energy are the closest to the truth (whether or not they are perfectly correct). His insights as a primarily QCD physicists inform his analysis in ways that other MG and GR researchers don't benefit from that are likely to be valid, he is quantum from the bottom up,
I'll have a look at your suggestion. Incidentally, I have updated my table in the light of points raised in this thread though my initial motivation for producing the summary table was to challenge the view that dark matter was an almost complete theory. There are several major weaknesses in the dark matter paradigm which makes consideration of the alternatives completely necessary.

#### George Jones

Staff Emeritus
Gold Member
IAs I am not a supporter of MOND, it is always with care that I reference Stacy McGaugh but non the less his paper from 2016 entitled ‘The Radial Acceleration Relation in Rotationally Supported Galaxies’ is an observational paper and as such can be read independently of Stacy McGaugh's preferred solution of MOND. I understood the observations to show a tight relation between baryonic mass and rotational velocity. It is surely meant to question the validity of dark matter as in order for dark matter theories to be compatible with these observations one has to invoke complex 'feed back' mechanisms. To my way of thinking any theory that can explain galaxy rotation velocities without dark matter will be compatible with these observations.
The feedback mechanisms are either there or they aren't. They shouldn't be dependent upon any unknown physics. Every aspect of these feedbacks should be measurable through a combination of observations and simulations. The only aspect of the feedbacks that relies upon unknown physics is the degree to which dark matter interacts (both with itself and with normal matter). Everything else just depends upon understanding in detail the normal matter within galaxies.
Research on feedeback reported in a paper newly submitted to the Monthly Notices of the Royal Astronomical Society has generated some interest,
https://arxiv.org/abs/1808.06634

The authors claim that dark matter is "heated up" by repeated bursts of star formation.These bursts produce a time-fluctuating gravitational potential to which the dark matter responds, giving dwarf galaxy core dark matter densities more in line with observations. No other types interactions are necessary, so the authors take is as evidence for collisionless cold dark matter.

A talk on this by one of the authors, Justin Read:

#### kimbyd

Gold Member
2018 Award
Research on feedeback reported in a paper newly submitted to the Monthly Notices of the Royal Astronomical Society has generated some interest,
https://arxiv.org/abs/1808.06634

The authors claim that dark matter is "heated up" by repeated bursts of star formation.These bursts produce a time-fluctuating gravitational potential to which the dark matter responds, giving dwarf galaxy core dark matter densities more in line with observations. No other types interactions are necessary, so the authors take is as evidence for collisionless cold dark matter.

A talk on this by one of the authors, Justin Read:

That's extremely fascinating!

#### ohwilleke

Gold Member
Research on feedeback reported in a paper newly submitted to the Monthly Notices of the Royal Astronomical Society has generated some interest,
https://arxiv.org/abs/1808.06634
The abstract concludes with the sentence: "Our results suggest that, to leading order, dark matter is a cold, collisionless, fluid that can be kinematically 'heated up' and moved around."

My intuition is that a "cold, collisionless, fluid" that can be kinemtically "heated" and moved around.", is almost trivially a contradiction of terms.

#### George Jones

Staff Emeritus
Gold Member
The abstract concludes with the sentence: "Our results suggest that, to leading order, dark matter is a cold, collisionless, fluid that can be kinematically 'heated up' and moved around."

My intuition is that a "cold, collisionless, fluid" that can be kinemtically "heated" and moved around.", is almost trivially a contradiction of terms.

Note that I put "heated up" in scare quotes in my post. The "heating up" is caused by a time-varying gravitational field, which in turn is caused by repeated bursts of star formation, not by other interaction (i.e., not by collisions).

"How certain is dark matter?"

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