**A Dark Matter Particle Oriented Astronomer Acknowledges The Need For A New Paradigm**

The nearly collisionless dark matter of the lambda CDM model is inconsistent with the extremely tight fit of inferred dark matter distributions with the visible luminous matter in galaxies.

A major new review paper strains to find a different kind of dark matter to address the problem, but a gravity modification that captures the insights of MOND while addressing its flaws, still makes more sense as a solution.

The distribution of the non-luminous matter in galaxies of different luminosity and Hubble type is much more than a proof of the existence of dark particles governing the structures of the Universe. Here, we will review the complex but well-ordered scenario of the properties of the dark halos also in relation with those of the baryonic components they host. Moreover,we will present a number of tight and unexpected correlations between selected properties of the dark and the luminous matter. Such entanglement evolves across the varying properties of the luminous component and it seems to unequivocally lead to a dark particle able to interact with the Standard Model particles over cosmological times.This review will also focus on whether we need a paradigm shift, from pure collisionless dark particles emerging from "first principles", to particles that we can discover only by looking to how they have designed the structure of the galaxies.

Paolo Salucci, "The distribution of dark matter in galaxies" (November 21, 2018) (60 pages, 28 Figures ~220 refs. Invited review for The Astronomy and Astrophysics Review).

Consider, for example, this quote from the review article at page 52:

The latest post at Triton Station also underlines this point with pointed examples. While Self-Interacting Dark Matter (SIDM) models can reproduce the rotation curve fits predicted by MOND, they do so with two extra parameters, a couple of which are degenerate, and plain old cold dark matter models simply can't accomplish this feat.

The post demonstrates that because MOND has fewer degrees of freedom than SIDM it is sensitive to measurement errors (nuisance parameters) that SIDM models just absorb in their fits, allowing MOND to distinguish, for example, between erroneous and true distances of galaxies for Earth and errors in measuring the inclination angle of the galaxy relative to Earth, that SIDM models cannot.

I continue to think that the gravitation based solution worked out by Alexandre Deur (a professional physicist whose primary work is in QCD) is the most promising explanation of the data, since it solves pretty much all of the (acknowledged) short fallings of the toy model MOND theory. In particular, his approach is fully relativistic, fits cluster data including colliding cluster data in addition to galaxies, explains a feature of large elliptical galaxies not explained by MOND, isn't ruled out by neutron star-black hole merger data because it involves only a single kind of massless graviton, has (in principle if not in practice) one less free parameter than MOND, explains some or all dark energy phenomena without the cosmological constant, and has a solid theoretical quantum gravity effect motivation that is reality checked by parallels to its predictions for gravity in mathematically similar QCD. In his approach, both dark matter phenomena and dark energy phenomena are basically weak field consequences of the distinctions between quantum gravity and classical general relativity that arise from the interactions of gravitons with other gravitons.

He makes his approach mathematically tractable by using a scalar (i.e. spin-0) graviton approximation which he credibly shows would be very similar in the relevant respects to a full fledged spin-2 graviton theory which is mathematically insurmountable because a massless spin-2 graviton cannot be described by a theory that we know how to renormalize, following a mathematical strategy used to manage the difficult math involved in describing spin-1 gluons in QCD.

Alas, this approach hasn't yet attracted enough interest from full time gravity theorists to receive a really thorough independent vetting, even though several of Deur's articles on the subject have been published in peer reviewed journals.

Unlike pure collisionless dark matter models (which don't work), SIDM models (which can produce rotation curves similar to those of MOND), clearly fail Occam's Razor relative to Deur's gravity based explanations of dark matter, because, in addition to having four more free parameters, it also introduces not just a new beyond the Standard Model dark matter fermion, but also a fifth force governing interactions between dark matter particles and other dark matter particles and also with baryonic matter with a carrier boson of its own, and also some sort of boson to explain dark energy, in addition to the graviton present in quantum gravity formulations of both theories. Deur's approach actually has one less fundamental parameter than general relativity with a cosmological constant.

If I had a few million dollars, I'd spend it on a research program to more comprehensively develop and evaluate Deur's work, because, in my opinion, his work presents the most promising work on quantum gravity with phenomenological applications of anything done by anyone in physics. Indeed, I don't think that I am overstating the case to say that his work rivals that of Einstein's in overall importance. Quantum gravity is the Holy Grail of fundamental physics, and his work gets you 90% of the way there. Since I don't have that kind of money, however, the best that I can do is to get out the word to people whom might have those resources.

One important feature to develop, in particular, in any gravitation based solution to the dark matter problem is its early universe cosmology, because no gravitationally based approach to explaining dark matter has yet received serious attention as a means of explaining the cosmic microwave background (CMB) radiation's third peak that is explained by cold dark matter. This doesn't rule out these approaches, however, because this is only true because nobody knows what these theories predict at all, rather than because observation falsifies these theories. There is theoretical work out there, however, that demonstrates that it is possible in principle to replicate the CMB background of dark matter with a theory somewhere in the parameter space of the scalar graviton simplifications of quantum gravity used by Deur, although the details of such a theory are not well developed.

Consider, for example, this quote from the review article at page 52:

Remarkably, the situation much simplifies when we express the circular velocity V (r) 12 in the double-normalized form: V (r/Ropt)/V (Ropt) TContinuing at pages 54-55:he profiles of the RCs emerge as a function of just one parameter, at choice among the above six, plus Vopt, Mvir and the angular momentum for unit mass j (see Lapi et al. 2018). Remarkably,this occurs independently on whether a galaxy is dark matter or luminous matter dominatedfor R < Ropt.The emerging evidence is that structural quantities deeply rooted in the luminous sector, like the disk length scales, tightly correlate with structural quantities deeply rooted in the dark sector, like the DM halo core radii.

In spirals, dwarf disks and LSBs there are extraordinary multiple connections between the dark and the luminous components. This occurs over many orders of magnitudes in halo masses and over the whole ranges of galaxies morphology and luminosity. The “standard” explanation relates to a dynamical evolution of the galaxies, in particular, of their DM halo densities, caused by powerful baryonic feedbacks.Although this scenario is far than being rejected, it seems, however, unable to cope with the intriguing wealth of correlations between quantities deep-rooted in opposite dark/luminous worlds that we have presented in this review.More in detail, while we cannot completely rule out the possibility that astrophysical phenomena can be responsible for the above intriguing scenario, on the other hand, what emerges in galaxies allow us to propose a shift of paradigm, according to which, the nature of dark matter is not given to us by convincing theoretical arguments, but must be searched in the various properties of the DM halos and stellar disks.

**More Confirmation**The latest post at Triton Station also underlines this point with pointed examples. While Self-Interacting Dark Matter (SIDM) models can reproduce the rotation curve fits predicted by MOND, they do so with two extra parameters, a couple of which are degenerate, and plain old cold dark matter models simply can't accomplish this feat.

The post demonstrates that because MOND has fewer degrees of freedom than SIDM it is sensitive to measurement errors (nuisance parameters) that SIDM models just absorb in their fits, allowing MOND to distinguish, for example, between erroneous and true distances of galaxies for Earth and errors in measuring the inclination angle of the galaxy relative to Earth, that SIDM models cannot.

**The End Game**I continue to think that the gravitation based solution worked out by Alexandre Deur (a professional physicist whose primary work is in QCD) is the most promising explanation of the data, since it solves pretty much all of the (acknowledged) short fallings of the toy model MOND theory. In particular, his approach is fully relativistic, fits cluster data including colliding cluster data in addition to galaxies, explains a feature of large elliptical galaxies not explained by MOND, isn't ruled out by neutron star-black hole merger data because it involves only a single kind of massless graviton, has (in principle if not in practice) one less free parameter than MOND, explains some or all dark energy phenomena without the cosmological constant, and has a solid theoretical quantum gravity effect motivation that is reality checked by parallels to its predictions for gravity in mathematically similar QCD. In his approach, both dark matter phenomena and dark energy phenomena are basically weak field consequences of the distinctions between quantum gravity and classical general relativity that arise from the interactions of gravitons with other gravitons.

He makes his approach mathematically tractable by using a scalar (i.e. spin-0) graviton approximation which he credibly shows would be very similar in the relevant respects to a full fledged spin-2 graviton theory which is mathematically insurmountable because a massless spin-2 graviton cannot be described by a theory that we know how to renormalize, following a mathematical strategy used to manage the difficult math involved in describing spin-1 gluons in QCD.

Alas, this approach hasn't yet attracted enough interest from full time gravity theorists to receive a really thorough independent vetting, even though several of Deur's articles on the subject have been published in peer reviewed journals.

Unlike pure collisionless dark matter models (which don't work), SIDM models (which can produce rotation curves similar to those of MOND), clearly fail Occam's Razor relative to Deur's gravity based explanations of dark matter, because, in addition to having four more free parameters, it also introduces not just a new beyond the Standard Model dark matter fermion, but also a fifth force governing interactions between dark matter particles and other dark matter particles and also with baryonic matter with a carrier boson of its own, and also some sort of boson to explain dark energy, in addition to the graviton present in quantum gravity formulations of both theories. Deur's approach actually has one less fundamental parameter than general relativity with a cosmological constant.

If I had a few million dollars, I'd spend it on a research program to more comprehensively develop and evaluate Deur's work, because, in my opinion, his work presents the most promising work on quantum gravity with phenomenological applications of anything done by anyone in physics. Indeed, I don't think that I am overstating the case to say that his work rivals that of Einstein's in overall importance. Quantum gravity is the Holy Grail of fundamental physics, and his work gets you 90% of the way there. Since I don't have that kind of money, however, the best that I can do is to get out the word to people whom might have those resources.

One important feature to develop, in particular, in any gravitation based solution to the dark matter problem is its early universe cosmology, because no gravitationally based approach to explaining dark matter has yet received serious attention as a means of explaining the cosmic microwave background (CMB) radiation's third peak that is explained by cold dark matter. This doesn't rule out these approaches, however, because this is only true because nobody knows what these theories predict at all, rather than because observation falsifies these theories. There is theoretical work out there, however, that demonstrates that it is possible in principle to replicate the CMB background of dark matter with a theory somewhere in the parameter space of the scalar graviton simplifications of quantum gravity used by Deur, although the details of such a theory are not well developed.

## 13 comments:

Is it possible that classical general relativity through its nonlinearity has graviton-graviton interactions built in and thus if properly solved for cosmological scales will deliver the same results as Deur? I feel I hsve seen hints of this in Deur's papers. Otherwise, I am with you although I do not care for comparisons with historic figures. Time will tell on that.

Is there a rigorous derivation of these claimed results, including MOND and cc, from first principles of his proposal?

@jd His papers purport to simply follow from GR, but in the manner in which Einstein's equations are applied in conventional GR today, the same results are not reached. My intuition is that this is because gravitational energy is not treated as an input in the stress-energy tensor, even though gravitational energy is not ignored entirely in Einstein's equations. His papers do, however, make very vanilla assumptions about a graviton's properties.

@neo Basically, what he does is start with what the Lagrangian for a full spin-2 graviton for quantum gravity should be naively (which can't be solved mathematically), then simplifies to the scalar case, and then demonstrates (basically using numerical methods) that the terms in the infinite series beyond the first several can be safely ignored, and then solves this simplified Lagrangian from first principles to get a MOND-like result (his equation for spiral galaxy rotation curves is in the form of a generic Yukawa force), and then, rather than calculate the constants from first principles (which should be possible in principle using this method) he fits the constant in the resulting equation to the data derived in MOND papers. He then derives solutions in the case of elliptical galaxies and galactic clusters from the same truncated scalar graviton Lagrangian.

Does this count as derived from first principles? Basically yes, it does so at least to the same extent that perturbative QCD is derived from the properties of a three color, six quark flavor quark-gluon interaction from first principals. The full first principles equation isn't used in either case, but the equation used is explicitly derived from a first principles equation and simplified using methods whose impact can be qualitatively and quantitatively described (e.g. a scalar graviton theory is basically a static case version of full GR).

Is his derivation rigorous? Not really. But, this is pretty normal in physics. For example, renormalization was used for almost half a century before the validity of this methodology was demonstrated rigorously. Still, one thing that more resources and attention are needed for is to confirm his barebones analysis more rigorously.

Still, one of the real attractions of this approach is that it has a solid theoretical basis in very ordinary assumptions found in any quantum gravity theory (e.g. that gravitons are massless and couple to other particles, including other gravitons, with a strength proportionate to their mass-energy).

Also he is able to make this breakthrough because of the "sneak preview" that QCD provides strongly suggesting approaches to take mathematically that have been proven and confirmed experimentally in closely analogous systems. Indeed, one of the reasons that he was able to see this when so many others in the GR community did not, is his deep understanding, applied on a daily basis of the mathematical methods used in QCD which most GR specialists while vaguely familiar with, do not know from memory like the back of their hands. Collectively, almost none of them, all of whom are trained in more or less the same way, have the right tools in their regular toolbox to solve the problem. Also, because Deur lacks sufficient familiarity with GR to know some of the possibilities that have been rigorously ruled out in GR as conventionally formulated, and is instead simply applying the general axioms of GR to the quantum gravity context without being unduly worried about whether his formula corresponds exactly to classical GR in the limit (it doesn't), he was able to effectively take blinders that everybody else is wearing off. The biggest difference between his approach and classical GR as currently applied, it appears to me, is that the equations of classical GR fail to properly capture the self-interactions of the gravitational field (classical GR doesn't have gravitons, of course) that its axioms claim that these equations do.

More @neo I have set up a permanent page on Deur's work that I can update over time so that people looking at it always get the most current information, which contains links to all of the papers setting forth his analysis and a powerpoint presentation that explains the gist of those papers in an easier to read format. Feel free to click through to the papers and confirm that my summary in the comment above is correct.

@neo Specifically:

The gravitational Lagrangian that he develops is as follows:

ℒGR=[∂ψ∂ψ]+√G[ψ∂ψ∂ψ]+G[ψ2∂ψ∂ψ]+ΣGn/2[ψn∂ψ∂ψ]+√ψμνTμν

This is derived by expanding the ℒGR in term of tensor gravity field ψμν by developing gμν around the Minkowsky metric: gμν~ημν+G1/2ψμν+...

This compared to the QCD Lagrangian:

ℒQCD=[∂ψ∂ψ]+√4παs[ψ2∂ψ]+ 4παs[ψ4]

The first terms of each are Newtonian gravity and perturbative QCD respectively (in the static case). The next two terms of the respective Lagrangians are field self-interaction terms.

How strong are the gravitational self-interaction terms?

This is a function, roughly speaking, of system mass and system size:

Near a proton GMp/rp=4×10-38 with Mp the proton mass and rp its radius. ==>Self-interaction effects are negligible:

ℒGR=[∂ψ∂ψ]+√G[ψ∂ψ∂ψ]+G[ψ2∂ψ∂ψ]+... the stricken terms --> zero.

For a typical galaxy: Magnitude of the gravity field is proportionate to GM/sizesystem which is approximately equal to 10-3.

Basically, the more thinly spread the mass is in space, the stronger the self-interaction terms are relative to the Newtonian term of the Lagrangian. For gravitons, the profoundly weak strength of the Newton's constant means that self-interaction terms are only significant at immense distances where the mass is spread thinly.

In QCD, by comparison, the profoundly greater strength of the QCD coupling constant allows the self-interaction terms to be significant even at tiny distances on the order of 10-15 meters, despite the fact that the color charges are not spread thin.

More @neo

If the mass is confined to a disk, the self-interactions cause the system to reduce from a three dimensional one to a two dimensional one, causing the force to have a 1/r form that we see in the MONDian regime of spiral galaxies.

In the geometries where Deur's approach approximate's MOND, the following formula approximate's the self-interaction term:

FG = GNM/r2 + c2(aπGNM)1/2/(2√2)r

where FGis the effective gravitational force, GN is Newton's constant, c is the speed of light, M is ordinary baryonic mass of the gravitational source, r is the distance between the source mass and the place that the gravitational force is measured, and a is a physical constant that is the counterpart of a0 in MOND (that should in principle be possible to derive from Newton's constant) which is equal to 4*10−44 m−3s2.

Thus, the self-interaction term that modifies is proportionate to (GNM)1/2/r. So, it is initially much smaller that the first order Newtonian gravity term, but it declines more slowly than the Newtonian term until it is predominant.

thanks for these posts. have you thought about getting Sabine Hossfelder or Stacy McGaugh interested on their respective blogs?

I have implored both to look into it a couple of times each, with non-committal but also not dismissive responses, but have not gone so far as to be irritating. If I had the money I would put both of them on the dream team to investigate it further.

ever been in touch with deur?

IMO, the fact mond ao is close to cc/3 is significant, in that i think that ao codes behavior of gravity (or inertia) in the cc regime

Yes. He'd like to do more in this area, but doesn't have the funding and needs his day job as a QCD physicist.

I think that the fact mond ao is close to cc/3 is a coincidence.

Lee Smolin's paper https://arxiv.org/abs/1704.00780 takes the opposite approach, that MOND is a regime of the cc. and to his credit he's got 15 cites

his paper offers a derivation of ao from cc.

i know you read Deur's paper years before Smolin, but

what if you encountered Smolin's paper years before Deur's.

From Stacy McGaugh at the lastest Triton Station post:

" I do disagree with the assertion that I often see, and remains a widespread misconception among scientists, that MOND does not do a good job of explaining cosmic phenomena. I’ve been through all that, and it is simply incorrect to say dark matter is always better outside of galaxies. Sure, it has shortcomings, but often dark matter only appears to be better because it declines to make a comparably testable prediction. Clusters of galaxies are a great example: MOND is off by a factor of 2 in mass (20% in velocity). Dark matter makes no prediction. Anything over the luminous mass is OK. The rest is dark. It doesn’t matter if that’s a factor of 2 or 5 (the modern value) or 6 (the cosmic value) or ~100 (Zwicky’s value). Being a factor of 2 off only sounds bad because there is a definite prediction! With dark matter we don’t care what that factor is because we have no prediction – at least, not one that can not be fudged.

Still, MOND itself is incomplete. I think we are left with two primary options: (i) MOND is pointing to some deeper theory of dynamics (a change in the law of inertia a possibility; it doesn’t have to be gravity) that has MOND as an approximation in the appropriate limit, or (ii) some kind of dark matter that interacts directly with baryons in a way that gives rise to MOND-like phenomenology. I spent a lot of time over many years trying to invent such stuff, without success. More recent efforts like Blanchet’s dipolar dark matter or Khoury’s superfluid dark matter are viable possibilities that others have invented. SIDM does not fall in this category. It interacts with itself, not the baryons, so my reaction when it was reintroduced in 2000 was that it was dead on arrival: it is constructed to ignore the real problem. I’m less certain now as the math does have a term that involves the baryons, albeit not obviously the right term, so I give it a [very] outside chance that it might work out. What does not have a realistic chance is what the vast majority of my colleagues seem to favor: that the observed phenomenology will somehow emerge from feedback during galaxy formation in the conventional context of cold dark matter. This strikes me as a form of magical thinking. If MOND-like phenomenology were so natural to simulations of galaxy formation, why did it never emerge from such simulations before I told them the answer? I have no doubt that if can be *made* to emerge from such simulations, as simulators are very clever and have an endless number of knobs to twiddle. It then becomes a separate question whether the universe really works like that, with all the knobs turned Just So."

Another comment to the same hypothesis testing thread at Triton station by someone else sums up the cc argument: "As for your Option 1, Dr. Hossenfelder has an equation that relates MOND acceleration scale and the cosmological constant (see video)

http://backreaction.blogspot.com/2018/11/modified-gravity-demystified-video.html

Here’s my MOND=CC hypothesis where I derive MOND acceleration scale g = 1.2 e-10 m/s^2 from the cosmic acceleration (a) of the expansion of the universe. Age of universe (t) = 13.8 billion years. Without cosmic acceleration, the radius of universe would be 13.8 billion lightyears. But the radius to cosmic horizon R = 46.5 billion ly. Thus the scale factor s = 46.5/13.8 = 3.37 is due to cosmic acceleration

MOND=CC hypothesis postulates that all space must expand by a factor of 3.37. However, space within galaxies is prevented from expansion by galactic gravitational field, which is stronger than the anti-gravitational field (repulsive force) of cosmic expansion. At the outer radii of galaxies, gravitational field is weaker than anti-gravity. Thus this region of space should expand by the scale factor. I prove mathematically that this gravitational field threshold is equivalent to MOND acceleration scale.

From kinematic equations:

R = v t + ½ a t^2 where v = c = speed of light

Solving for a = cosmic acceleration

a = 2 (R – v t) / t^2 = 3.27 e-9 m/s^2

Since a > g = MOND acceleration scale, space should expand. It already did. I calculate the galactic radius before expansion and show cosmic acceleration (a) approximately equals MOND acceleration scale (g)

From Newtonian mechanics:

g = G M / r^2 where: G = gravitational constant, M = mass of galaxy, r = radius of galaxy

We reduce r by the scale factor s = 3.37 to get radius before space expansion

g’ = G M / (r/3.37)^2 = 11.36 G M/r^2 where g’ = gravitational acceleration before expansion

Hence: g’ = 11.36 g

Equating g’ and a:

a = g’ = 11.36 g

a/g = 2.4

Therefore, cosmic acceleration (a) approximately equals MOND acceleration scale (g) by a factor of 2.4. This is pretty close considering estimates of the mass of our galaxy vary by a factor of 5. MOND=CC hypothesis predicts the deviation of galactic orbital speed from Newtonian dynamics will not exceed the scale factor s = 3.37"

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