Quote Of The Day

The sociology in the simulation community seems to be to assert complete success in explaining everything at all times until the next batch of simulations completes running, then point out all the improvements. Everything is explained all the time, only more so as time goes on.

- From Stacy McGaugh at Triton Station on June 18, 2026.

A Theoretically Innovative MOG Theory

Canadian physicist John Moffat's MOG modified gravity theory is a long standing tensor, vector, scalar modification of General Relativity (GR). As the link explains:

Scalar–tensor–vector gravity theory, also known as MOdified Gravity (MOG), is based on an action principle and postulates the existence of a vector field, while elevating the three constants of the theory to scalar fields. In the weak-field approximation, STVG produces a Yukawa-like modification of the gravitational force due to a point source. Intuitively, this result can be described as follows: far from a source gravity is stronger than the Newtonian prediction, but at shorter distances, it is counteracted by a repulsive fifth force due to the vector field.

STVG has been used successfully to explain galaxy rotation curves, the mass profiles of galaxy clusters, gravitational lensing in the Bullet Cluster, and cosmological observations without the need for dark matter. On a smaller scale, in the Solar System, STVG predicts no observable deviation from general relativity. The theory may also offer an explanation for the origin of inertia.

Yukawa forces are forces carried by massive mediator bosons (in contrast to the massless mediator boson of electromagnetism, the photon, which has an infinite range as a result), whose range is a function of the mediator mass. 

The most familiar example of a Yukawa force is the nuclear binding force (sometimes called the residual strong force) that holds photons and neutrons in atomic nuclei together, which is mediated by like composite mesons, especially pions (neutral pions have a mass of about 135 MeV, while charged ones have a mass of about 140 MeV) that have an effective range on the order of femtometers, which is similar to the size of an atomic nucleus.

In contrast, GR without a cosmological constant (including Deur's approach to explaining dark matter phenomena as gravitional) is a tensor theory, and GR with a cosmological constant is a tensor-scalar theory. Newtonian gravity is a scalar theory. Several of the main relativistic generalizations of MOND are also tensor, vector, scalar theories.

MOG, while not the subject of as much scholarship as MOND (Israeli physicist Mordehai Milgrom's 1983 non-relativistic toy model modification of Newtonian gravity that does a good job of replicating dark matter phenomena is almost near equilibrium systems of galaxy size or smaller), MOG is still one of the older modified gravity theories, has received considerable investigation from scientists other than its inventor, is relativistic, is more easily generalized to cosmology scale problems, and unlike MOND, models galaxy cluster phenomena often attributed to dark matter more successfully, at the cost of being somewhat less intuitive to understand.

Moffat's latest short paper formulates his MOG theory in a manner, that while essentially identical to the original, is easier to apply to cosmology scale questions.

We develop a Stueckelberg gauge-invariant formulation of modified gravity (MOG). 

The massive vector field is made gauge-invariant by introducing a compensating scalar field, without requiring a Higgs field, spontaneous symmetry breaking, or a vacuum expectation value to fix the effective Newtonian gravitational coupling. This separates the gauge-invariant origin of the vector mass from the cosmological evolution of the gravitational coupling. 

The formulation preserves the finite-range vector interaction of MOG, while allowing the effective gravitational coupling to be treated as an independent scalar or scale-dependent quantity. This distinction is important for cosmological tests, since early-universe constraints and late-time large-scale gravitational phenomena need not be tied to a symmetry-breaking vacuum. The Stueckelberg formulation provides a gauge-invariant framework for comparing MOG with nucleosynthesis, cosmic microwave background, large-scale structure, lensing, and distance data.

John W. Moffat, "Stueckelberg Gauge Invariant Formulation of MOG" arXiv:2606.26427 (June 4, 2026).

Another new MOG paper constrains the value of one of that theory's physical constants (to a value inconsistent with the range in the previous literature on the topic):

The scalar-tensor-vector-gravity (STVG), a prototype of modified gravity developed by Moffat, can correctly explain galaxy rotation curves, cluster dynamics, Bullet Cluster phenomena and cosmological data without invoking the observationally elusive general relativistic (GR) dark matter. Further, recent observations of neutron star masses are shown to defy some GR predictions, whereas STVG turns out to be more consistent with those observations. These successes indicate that STVG could be a potential candidate for a new theory of gravity. 

However, an important question concerns the possible range of values of the STVG dimensionless parameter α imposed by various physical scenarios. In the literature, the range 0.03 < α < 2.47 corresponding to different central source masses has been suggested. We show here that the α can be considerably constrained into the range 0 < α < 10^−5 assuming that the updated GPS fluctuation does not exceed the α-dependent correction to the terrestrial Sagnac delay.

R. Kh. Karimov, R. N. Izmailov, K. K. Nandi, "Terrestrial Sagnac delay in scalar-tensor-vector-gravity" arXiv:2606.27033 (June 25, 2026).

A footnote on f(R) gravity

Probably the other modified gravity theory with significant scholarship from multiple astrophysicists that is most often used to explain dark matter phenomena gravitationally is f(R) gravity (the image below is from this link), which like GR with a cosmological constant, and unlike MOG or some relativistic generalizations of MOND, is a tensor-scalar theory. The way f(R) gravity modifies GR is not with an extra vector field, but with a higher order derivative term. The standard Ricci scalar R in the Einstein-Hilbert action is replaced by a general function of R (e.g., R + (alpha)*R^2). Mathematically and dynamically, this higher-order derivative theory is exactly equivalent to standard General Relativity coupled to a single, dynamical scalar field (known as the scalaron), rather than only having the static scalar dark energy field that is equivalent to the cosmological constant.

Like MOG, f(R) gravity has a Yukawa correction to the gravitational potential, which (at least in part, it also has a time and scale dependent gravitational constant) is how it can explain some or all dark matter phenomena without dark matter particles.

The Modest Excess Higgs Boson Production Explained

The Standard Model is stochastic (i.e. probabilistic) and not deterministic. It doesn't say, if you do X then Y will happen. It says, if you do X, Y with happen Z percent of the time.

One of the many things that the Standard Model predicts is the Higgs boson production rate, as a probability distribution of the rate at which Higgs bosons are produced in given circumstances. The calculation is in the form of an infinite series of terms with leading order, next to leading order, next to next to leading order, etc. terms.

You haven't read much about the physics of Higgs boson production at this blog because its a lot less simple and intuitive than Higgs boson decays, which are much more straightforward and rely on simpler, less complicated processes and rules. This makes Higgs boson production harder to write good blog posts about than Higgs boson decays. Also, the experimental anomalies compared to Standard Model predictions for Higgs boson production have been less striking, with more uncertainty and not very striking discrepancies, even though the discrepancies in Higgs boson production rates have been quite persistent.

In practice, scientists calculate the Standard Model prediction for the Higgs production rate with as many terms as are practically feasible for them to calculate, and then they try to estimate the uncertainty arising from the omitted terms as best they can.

Usually, each slight incremental improvement in the accuracy of the calculation takes disproportionately more work to calculate than the amount of work that was necessary to make the previous improvement of that magnitude. 

But, now and then, scientists unexpectedly find a previous omitted term from their calculations that is really important, although figuring out which terms will be especially fruitful to include is still at a more art than science level right now. Research programs like the amplituhedron approach and related developments from it are trying to bring more science to that search, but we aren't quite there yet.

Experiments since 2012, when the Higgs boson was first discovered, have shown that Higgs production usually exceeds the rate calculated by the best available Standard Model prediction calculations, although either not by a statistically significant amount, or with only a mild statistical tension with the best available predicted value for the Standard Model Higgs boson production rate.

Initially, some scientists though that this could be because the Higgs boson was detected sooner than it would have been otherwise because of a statistical fluke of higher than expected Higgs production. At first, that was a plausible proposal.

But it has been 14 years now, so it probably wasn't that, because the slight bias towards higher the expected Higgs boson production rates hasn't completely gone away, as the sample size of Higgs bosons detected has surged and reduced statistical uncertainties (but not always systemic uncertainties in the measurements of the Higgs boson production rates). 

Of course, like every anomaly in high energy particle physics, some theorists have, instead, tried to explain this persistent, not very large anomaly, with beyond the Standard Model physics.

But, a new paper now explains most or all of what has been going on. It turns out that the Higgs boson that physicists have observed is behaving more like than Standard Model Higgs boson to higher precision than ever, once again.

The new paper recalculates the Standard Model predicted Higgs boson production rate and determines that some next to leading order terms contributing to the predicted Higgs boson production rate were more important than had been expected. It turns out that these omitted terms can led to up to 10% more Higgs bosons being produced than would have been predicted without them in some circumstances.

Including the omitted terms explains most or all of the excess of experimentally observed Higgs boson production over the old calculation of the SM predicted value. This also, by the way, tends to imply that the uncertainties in the old experimental measurements were probably overestimated, which is a common reality in electroweak physics (as opposed to QCD or astronomy where uncertainties are often underestimated).

This new discovery feels like a reprise of the comparisons between the experimentally measured values of muon g-2 and state of the art calculations of the Standard Model prediction. In both cases, the gap has been mostly bridged by improving the quality of the calculations of the Standard Model predictions with an immense amount of hard calculation work, rather than by improving experimental accuracy or discovery new beyond the Standard Model physics. And, like the muon g-2 discrepancies, the part of the Higgs boson production calculation that has impaired the accuracy of the Standard Model prediction has mostly been the very hard to calculate strong force/hadronic/quark based part of what is primarily an extremely precise electroweak calculation.

The new paper and its abstract are as follows:

We present the mixed QCD-electroweak corrections to Higgs boson pair production in the quark-antiquark channel. 

The virtual amplitudes are computed fully analytically using the method of differential equations. We determine the integration constants by matching our expressions to the large mass expansion limit of the canonical integrals. We implement the results in the POWHEG-BOX framework for phenomenological studies. 

The corrections are found to have a significant impact on the shapes of differential cross sections, reaching up to +10% for the invariant mass distribution of the Higgs boson pair near the production threshold. This channel has not been considered before in calculations of the next-to-leading order electroweak corrections to Higgs boson pair production.

Marco Bonetti, Gudrun Heinrich, Philipp Rendler, William J. Torres Bobadilla, "Electroweak corrections to Higgs boson pair production: The quark channel" arXiv:2606.25928 (June 24, 2026) (contribution to the proceedings of Loops and Legs in Quantum Field Theories 2026, Bayreuth, Germany).

The new paper above is a physics conference summary of a more detailed paper on the same topic released in January of this year.

Data On Galaxies

Are active galactic nuclei (AGNs) exceptions to the Tully-Fischer rule or are they just hard to measure?

Active galactic nuclei have sometimes been excluded from Tully-Fischer fits because the underlying data points have high uncertainties, due to their low inclinations relative to solar system based observers leading, in turn, to "large scatter" although the magnitude of the scatter really isn't all that high for fairly imprecise astronomy measurements of distant galaxies.

The small data set in a new paper doesn't really bely that but these may also be galaxies which are out of equilibrium or have non-gravitational forces (e.g., the massive nuclear forces involved in star formation) that are relevant and significant in their dynamics. The authors of a new paper note that:

While the samples used to calibrate the canonical TF relations did not explicitly flag AGNs for removal (Tully& Pierce 2000; Tully et al. 2008; Tully&Courtois 2012; Kourkchi et al. 2020a), the selection criteria generally exclude active galaxies. Primarily, all works above select spirals with inclinations greater than 45◦. As Type 1 AGNs have been observed to be preferentially hosted by face-on (<45◦) galaxies (Keel 1980; Maiolino & Rieke 1995; McLeod & Rieke 1995; Simcoe et al. 1997; Gkini et al. 2021), this criterion naturally excludes a significant amount of Seyfert 1 hosts. The nuclear flux from unobscured Type 1 AGNs represents the primary expected source of photometric scatter in TF relations, whereas the high levels of nuclear obscuration inherent in Type 2 systems are expected to largely mitigate such contamination.

Visually, their data set does show high AGN scatter but also shows big error bars largely consistent with the baryonic Tully-Fischer relation.

We present an investigation of the Tully-Fisher (TF) relation solely for galaxies hosting an active galactic nucleus (AGN). Using 22 galaxies with primary, z-independent distances, we find that active galaxies exhibit significantly larger scatter about all TF relations compared to each respective calibration for (largely) inactive galaxies. 

The larger scatter persists despite removal of the AGN contamination from the photometry of the Type 1 AGNs via 1) careful surface brightness decompositions or 2) employing SEDs to constrain the light contribution of the AGN. These results suggest that the influence of an AGN on its host galaxy's surface brightness may extend beyond the nucleus. 

We also calculate the percentage difference between TF and primary distances, and find that TF-based distances are biased towards overestimation of the primary distances to active galaxies by anywhere from 5-10 percent for the optical/near-infrared and approximately 15 percent for distances predicted from inverting the Baryonic TF (BTF) relation. As TF-based distances (especially the I-band) are relied on heavily for analysis and modeling of the local peculiar velocity (Vpec) field, we suggest that active galaxies be removed from future Vpec modeling samples.

Justin H. Robinson, et al., "On the Tully-Fisher Relation for Active Galaxies -- I: Evidence of Larger Scatter" arXiv:2606.22575 (June 21, 2026) (Accepted for publication in ApJ).

In one context, a new paper (which also has a small sample size) finds that inferred spherical dark matter halos aren't ruled out, although slightly flattened halos are still preferred.

Wide-field surveys like Euclid mark a new era of extragalactic stellar stream studies. With a large number of streams, it is now possible to constrain the dark matter halos of galaxies in a cosmological volume and draw comparisons to theoretical expectations for the geometry of dark matter halos. 

This study combines Euclid imaging with visual detection and segmentation annotations to analyse streams. We use projected stream morphologies to constrain the shape and centre-of-mass position (CoM) of each host galaxy's potential, jointly probing baryonic and dark matter distributions. These inferences complement weak lensing methods, with sensitivity to halo profile and geometry on sub-virial scales. The method enables both stacked, population-level constraints on halo flattening and CoM position, and constraints on these quantities for individual halos. 

We also present a novel method for transforming segmentation maps of stellar streams into smooth, curvature-preserving tracks optimised for fast and robust dynamical inference. This approach enables rapid modelling of stream morphology, supports a statistically rigorous combination of constraints across multiple streams within a single galaxy, and enables joint inference across galactic hosts. 

From our study of 13 galaxies with prominent tidal streams, we find agreement with spherical halos, albeit a mild preference for flattening with q=0.95+0.05−0.10 at 68% confidence. This is promising early agreement with ΛCDM predictions. 

With thousands more discovered streams expected across Euclid's mission, our programme will enable precise measurements of halo shapes and CoM positions across large samples and redshifts, offering constraints on the geometry of dark matter halos.

Euclid Collaboration, "Euclid Quick Data Release (Q1): The geometry of dark matter halos from extragalactic streams" arXiv:2606.21774 (June 19, 2026) (Submitted to A&A).

A Hot Hypothesis For Neptune And Uranus

Normally, I don't write much about planetary astronomy, not because there's anything wrong with the discipline, but because I'm concerned mostly with the quest to determine the fundamental laws of physics, and planetary astronomy is basically unrelated to that. But this paradigm shifting interpretation of the data regarding Uranus and Neptune deserves a mention.

Uranus and Neptune are commonly interpreted as volatile-rich "ice giants", an assumption that underpins most interior models. 

Here we show that their observed radii, bulk densities, gravitational harmonics, normalized moments of inertia, intrinsic luminosities, and key features of their atmospheric compositions are consistent with interiors comprising supercritical, hydrogen-rich magma oceans overlain by H2-rich envelopes. 

Our results, based on three fit parameters for each planet, provide a parsimonious explanation for the structures, thermal states, and atmospheric chemistries of Uranus and Neptune. We find that the Solar System's ice giants are better understood as magma-ocean giants, with origins parallel to those of sub-Neptune gas-dwarf planets. A continuum among gas dwarf planets permits Neptune and Uranus to serve as accessible, data-driven test cases for structure models and material properties used to understand sub-Neptunes.

Edward D. Young, Sarah P. Marcum, Aaron Werlen, Paula N. Wulff, "Ice Giants Revisited: Uranus and Neptune as Magma Ocean Worlds" arXiv:2606.18219 (June 16, 2026).

More Cosmology Limits On Neutrino Mass

In principle, the sum of the three neutrino masses and the number of neutrino types can be determined from astronomy observations in the context of a cosmology model. 

In practice, to a certain extent this determination is model dependent, although the estimates are consistently quite a bit less than 150 meV at the two sigma level. This is far less than the current 1410 meV lower bound (expected to be ultimately reduced to 660 meV) set by direct measurements of lightest of the three neutrino mass eigenstates in the Katrin experiment (currently 450 meV but expected to reach 200 meV once the experiment runs its course). 

Even fairly extreme tweaks to dark energy assumptions and a prior that the sum of the neutrino masses can't be less than the minimum established by neutrino oscillation experiments, in the paper below sets of cap of about 115 meV. So, the results are robust in the general vicinity of absolute neutrino masses, even if their specific limits vary by scores of meVs from each other.

Like other cosmology based absolute neutrino mass estimates, it doesn't absolutely rule out an inverted neutrino mass hierarchy, but it disfavors one in a statistically significant manner with fairly mild assumptions.

The effective number of neutrino types determined from cosmology measurements is more robust and overwhelming a fit to three types (plus an expected adjustment for radiation), ruling out additional sterile neutrinos with masses on the order of 10 eV or less (N(eff) is not sensitive to heavier neutrinos). 

This doesn't rule out seesaw neutrino mass models (which can involve very heavy sterile neutrinos) or sterile neutrino warm dark matter (which characteristically has keV scale masses), but it does seriously limit sterile neutrino explanations of anomalies in neutrino oscillation experiments (which tellingly are frequently inconsistent with each other).

We present a robust assessment of cosmological constraints on the sum of neutrino masses (∑mν) when relaxing the standard assumption of purely adiabatic primordial initial conditions. 

Allowing for a neutrino density isocurvature (NDI) component alongside the adiabatic mode, we analyse the latest CMB-SPA combination (Planck 2018, ACT DR6, and SPT-3G), DESI DR2 baryon acoustic oscillation data, and the DES Year 5 supernova sample. Within the ΛCDM model, the 95% upper limit weakens only marginally from ∑mν < 0.052 eV (purely adiabatic) to < 0.057 eV (including NDI), with the NDI amplitude consistent with zero. In the CPL dynamical dark energy model, the adiabatic limit is < 0.111 eV, shifting to < 0.115 eV with NDI, yet the isocurvature mode remains undetected. 

While these limits are robust against the inclusion of isocurvature perturbations, they are highly sensitive to both the assumed dark energy equation of state and the prior lower bound on ∑mν. Notably, the adiabatic ΛCDM limit of 0.052 eV lies below the minimum sum required by the normal neutrino mass hierarchy (0.05878 eV), indicating that this bound is an artifact of the statistical prior extending to zero. Imposing a physically motivated hierarchy-informed prior raises the limit to <0.092 eV. 

Our results demonstrate that current data show no evidence for NDI modes and that the inferred neutrino mass upper limit is robust against this extension, but a definitive, model-independent bound requires addressing prior dependencies and dark energy uncertainties. This work provides the first joint constraint on ∑mν and NDI using the full CMB-SPA+DESI DR2+DES dataset.

Hongsheng Hou, Sai Wang, Zhi-Chao Zhao, Xin Zhang, ""Constraints on the Sum of Neutrino Masses from ACT DR6 and DESI DR2 Considering Isocurvature Initial Conditions" arXiv:2606.17994 (June 16, 2026).

The Inferred Milky Way Dark Matter Distribution Isn't Spherical

Measuring matter dynamics outside the plane of spiral galaxies is critical 

Rotations curves of, and gravitational accelerations of, matter in the vicinity of spiral galaxies that is above or below the galactic plane where most of the ordinary matter in these galaxies is found, is critical to distinguishing between competing dark matter particle and gravity or fifth force based explanations of dark matter phenomena (or hybrids of the two paradigms like self-interacting dark matter).

These theories have been formulated and fine tuned to reproduce the dynamics of stars in the plane of spiral galaxies where they are much easier to observe and measure, and good data has been available for many decades. But because good data has not been available for the dynamics of stars outside the galactic plane of spiral galaxies, different models formulated to explain dark matter phenomena differ considerably in what they predict about that.

Measuring matter dynamics outside the plane of spiral galaxies is hard and has only recently become a viable possibility

But until very recently our astrophysical observations provided us with little data and limited accuracy outside the galactic plane of spiral galaxies with various kinds of "telescopes" for a variety of reasons. 

In the case of the Milky Way, the main problems have been that the density of stars to observe outside the galactic plane of the Milky Way is much lower than in or near the thin galactic disk where most of its stars are found, and the complication that as observers who are inside the Milky Way, the vantage point of our observations is obstructed by dense stars in the galactic plane or otherwise non-optimal.

In the case of other galaxies, one of the main problems have been that it is hard to determine if a particular star is in the galactic plane or above (or below) that plane unless we have a close to edge on view of the galaxy, that measuring rotation curves is hard with a true edge on view. Another problem is that the resolution of our view of a galaxy gets worse as the galaxy gets more distant which is especially a concern outside the plane of a spiral galaxy where the density of the stars we are trying to observe is low. And, when looking at another galaxy it is particularly hard to tell if a star outside the main plane of the galaxy is really part of the same gravitationally bound system, or is millions of megaparsecs away from it in the foreground of our observation of that galaxy.

Fortunately, we live in an era where we have an abundance of riches when it comes to astronomy observations, producing a torrent of data from extremely powerful telescopes like the Gaia space observatory (a telescope in orbit around Earth). The data from this space telescope is used by the Gaia collaboration's network of over 400 scientists and engineers funded by the European Space Agency (ESA) to build the most accurate 3D map of the Milky Way ever constructed.

As the paper below explains in its abstract, Gaia's measurement uncertainties are less than 5% for the vertical velocities of stars that it observes in the Milky Way, and are less than 20% for the vertical accelerations that it measures. 

These uncertainties may not seem all that great to someone unfamiliar with the details of galaxy scale astronomy observations. But in that subfield of astronomy,  uncertainties as low as 28% (i.e. 0.1 dex) are the considered good, and relative uncertainties on the order of 50%-100% are common place, so Gaia's measurements are gold standards of precision by comparison.

Comparing models

Both simple cold dark matter models (with their spherically symmetrical NFW dark matter particle halos) and MOND (even in its relativistic generalizations) predict dark matter phenomena are spherically symmetrical, which makes these theories mathematically much more tractable. 

Indeed, coming up with any kind of dark matter particle model without either (1) self-interactions more complex than a simple scalar field, or (2) interactions in excess of ordinary gravitational interactions with ordinary matter, that do not form spherical or nearly spherical dark matter halos, is extremely challenging and could very well be impossible (although I'm not aware of any analytically constructed "no go" theorem to that effect).

But not all explanations of dark matter phenomena predict spherically symmetric effects, and inferred dark matter halo shapes from prior observations have tended to favor non-spherical, rugby ball shaped inferred distributions of dark matter particles (even though theoretically, it has been challenging to come up with dark matter particle theories that reproduce these shapes).

Some gravity based explanations of dark matter phenomena, like the one described by Deur, also propose non-spherical dark matter phenomena in spiral galaxies. In Deur's approach dark matter phenomena arise from non-linear self-interactions within gravitational fields that manifest in, and only in, non-spherical matter distributions like those found in spiral disk disk galaxies. 

In Deur's analysis, in spiral galaxies, the pull of gravity towards the galactic center is stronger than the Newtonian expectation in the direction of rays from the galactic center in the galactic plane (especially at larger radii), while it is weaker than the Newtonian expectation in the vertical direction relative to the galactic plane (an effect which accounts, at least in part, for dark energy phenomena between galaxies).

Deur's analysis is also supported by another key data point that corroborates astronomy observations that infer non-spherical dark matter particle distributions in dark matter particle paradigms. He has observed that the relative proportion of matter in a galaxy that is made of luminous stars to inferred dark matter is strongly correlated in elliptical galaxies, with the extent to which the elliptical galaxy is not perfectly spherical.

New, high quality data shows that the Milky Way's inferred dark matter halo is not spherical 

Gaia has assembled new data with record breaking accuracy and sample sizes on the rotational velocities and accelerations of stars in the Milky Way based upon their polar coordinates (i.e. their distance from the Galactic center and their distance from the plane of the Milky Way spiral disk). This data, was compiled by the Gaia collaboration, and was analyzed and reported in a pre-print released today of an accepted for publication astronomy paper.

The new paper's analysis strongly favors inferred dark matter particle distributions which are not spherically symmetric. Instead, it strongly favors the inference in a dark matter particle paradigm of a flattened disk-like configuration around the ordinary matter of the Milky Way.

The Gaia data generically rules out all dark matter particle explanations of dark matter phenomena, gravity or fifth force based explanations,  and hybrid explanations (like self-interacting dark matter models), that predict spherically symmetric dark matter phenomena effects. 

This is a huge deal because most of the leading explanations of dark matter phenomena are spherically symmetric, and all of those models are now definitively ruled out.

The paper

We derive both the mid-plane and off-plane rotation curves, v(c)(R,z), and the vertical acceleration, a(z)(R,z), of the Milky Way (MW) using Gaia~DR3 data over the ranges of vertical heights z∈(−2,2) kpc and galactocentric distances R∈(8.5,14) kpc where the velocity components are determined with high precision, i.e., with an error <5%. In contrast, the vertical acceleration a(z)(R,z) is dominated by model-dependent systematics, with uncertainties of up to ∼20%. This level of accuracy allows us to place stringent constraints on the geometry of the MW's dark matter (DM) distribution, as the vertical gradients of the gravitational potential attain their maximum within this range of radial and vertical distances corresponding to the characteristic scales of the disk. 

We find that models including the observed stellar components together with a spherical DM halo fail to reproduce both the pronounced variation of v(c)(R,z) with height and the observed behavior of a(z)(R,z). 

In particular, spherical halos with a scale radius of rs∼15 kpc contribute negligibly to the off-plane rotation curve and vertical acceleration in the inner disk, leaving these features primarily determined by the stellar mass distribution. 

Conversely, models in which DM is confined to a flattened, disk-like configuration predict substantial contributions to both v(c)(R,z) and a(z)(R,z), resulting in a markedly better agreement with the data. We conclude that disk-like DM distributions are strongly favored over spherical halo models. 

Forthcoming Gaia data releases will enable even more stringent tests of the geometry and distribution of the MW's DM component.

Francesco Sylos Labini, Roberto Capuzzo-Dolcetta, "Constraining the Geometry of Galactic Dark Matter with Gaia Data Release 3" arXiv:2606.12548 (June 10, 2026) (accepted for publication in The Astrophysical Journal) (emphasis added in abstract).

The body text of the conclusion further explains that:

Our results show that the DM disk model provides a significantly better agreement with the data than the standard Navarro–Frenk–White (NFW) halo profile. 

In particular, spherical halos with characteristic scale radii of order ∼ 10 kpc contribute only marginally to the off-plane rotation curve and to the vertical acceleration within the inner disk, leaving these quantities predominantly determined by the distribution of the stellar mass. As a consequence, halo-based models systematically underestimate the measured vertical accelerations and fail to reproduce the observed decline of the rotation curve at intermediate heights. 

In contrast, models in which the DM is confined to a flattened, disk-like configuration predict substantial contributions to both the radial and vertical components of the gravitational field, leading to a markedly improved agreement with the observed trends of v(c)(R,z) and a(z)(R,z). This improvement is particularly evident at low to intermediate heights (|z| ≲ 2 kpc), where the vertical acceleration inferred from the data cannot be explained by the baryonic components alone. 

The success of the DM disk model arises from its geometry: a flattened mass distribution naturally enhances the vertical component of the gravitational potential without requiring an excessive total mass, and simultaneously reproduces the modest decline of the circular velocity with increasing z. These results strongly suggest that a significant fraction of the MW’s dark matter is distributed in a disk-like structure rather than in a quasi-spherical halo. 

Forthcoming Gaia data releases, offering improved statistics and reduced systematic uncertainties in stellar kinematics, will enable more stringent and spatially extended tests of the geometry of the Galaxy’s dark matter component, potentially allowing one to constrain its vertical and radial scale lengths with unprecedented precision. 

Standard Model Muon g-2 Calculation Closely Matches Experimental Data

The most accurate ever calculation of the Standard Model predicted value of muon g-2 matches the world average experimentally measured value to 0.7 sigma (with the prediction and the experimental measurement having a precision of 310 and 124 parts per billion, respectively).

The new theoretically calculated value for muon g-2 is: 

aμ = (116,592,052 ± 36) × 10−11.

The most precise available experimental measurement is as follows:

Fermilab (2025): (116,592,070.5 ± 14.8) × 10−11.

The difference is (18.5 ± 38.9) × 10−11

The relative experimental result has an uncertainty of 0.127 ppm. The new calculation of the Standard Model expected value has a relative uncertainty of 0.31 ppm.

The error weighted experimental world average, which has a relative uncertainty of 0.124 ppm is: 

(116,592,071.5 ± 14.5) × 10−11. 

This final result is recapped in an exhaustive final muon g-2 experimental data report at arXiv:2606.17323.

The difference between the world average and the new SM prediction calculation is 

(28.5 ± 38.8) × 10−11, which is 0.7 sigma (which is still closer than than one sigma expected by a random distribution of uncertainties if the results are identical).

This global test of the Standard Model (which implicates all three of its forces) at low energies passes with flying colors.

For 50 years, the standard model of particle physics has been very successful in describing subatomic phenomena. In the past quarter of a century, this was challenged by a mismatch between its predictions and precision measurements of the anomalous magnetic moment of the muon, a(μ). This disagreement was eventually reconciled, first through a determination in an ab initio lattice calculation of the most uncertain theoretical contribution, the leading-order hadronic vacuum polarization (LO-HVP), a(μ)^(LO-HVP) and subsequently by experimental results and updates of the reference standard-model predictions using lattice results for a(μ)^(LO-HVP).

Here we present a new calculation for this crucial quantity, obtaining 

. This reduces the uncertainty by a factor of 1.6 compared with our earlier computation. We use a hybrid approach that includes a small, long-distance contribution from experiments in a low-energy regime in which they all agree. Our approach combines the strengths of experimental and lattice data in different energy ranges, achieving better precision than with either alone. Our lattice quantum chromodynamics (QCD) simulations are performed on finer lattices . . . allowing for an even more accurate continuum extrapolation. 

Combined with the calculations of the other standard-model contributions . . . our result leads to a prediction that differs from the recent measurement of a(μ) by only 0.5 standard deviations. This provides a notable validation of the standard model to 11 digits.

A. Boccaletti, et al., "Hybrid calculation of hadronic vacuum polarization in muon g − 2 to 0.48%." 653 (8814) Nature 373 (April 22, 2026) (open access) DOI: 10.1038/s41586-026-10449-z

While the hadronic part of the calculation accounts for a fairly modest part of the total value, it is the source of almost all of the uncertainty in the calculation:

A Meta Post

Today is the 160th day of the year, and I am on track at 80 posts at this blog so far, the historically normal rate of about one post every two days. I have, however, had proportionately more physics posts and proportionately fewer non-physics posts, than usual, and my posts have had somewhat less depth than I'd ideally like them to, on average. There have been 2,981 posts at this blog over its entire duration.

The sister blog to this one, Wash Park Prophet, has 51 posts so far this year, which while far from being a dead blog, is the lowest posting rate there that I've had of all time (a bit more than 2.2 posts per week). I just can't maintain both blogs at my usual pace at my current job (and have shifted some of my output of hit and run posts to Facebook). I have made 9,696 posts at that blog since its inception.

I've made 12,677 posts at these two blogs combined since their inception.

Combined, I've made 131 posts in 160 days, a pace of about four posts every five days. Again, this is nothing to sniff at, but less than I've posted historically.

Cold Dark Matter Still Doesn't Work

The missing local baryon problem

Stacy McGaugh at Triton Station explores one of the many bits of empirical evidence, which he calls the missing local baryon problem, that really convincingly disfavors any kind of cold dark matter paradigm.

Basically, he utilizes a proof by contradiction. 

He assumes a standard cold dark matter model, analyzes the data on the share of the mass of galaxies and galaxy clusters that is made up of ordinary baryonic matter (which is about 15.7% in the cold dark matter paradigm), in line for the percentage for the whole universe in that paradigm. Then, he shows how the proportion of baryonic matter gets systemically lower in a very predictable manner as the absolute amount of baryonic matter in a galaxy falls.

The problem is that in the cold dark matter paradigm, galaxy clusters form as galaxies cluster together, and larger galaxies form from the merger of smaller galaxies. But this leaves open the question of how the proportion of baryonic matter in a pair of merged galaxies that form a larger galaxy can be systemically and precisely greater in a merged larger galaxy than it was in any of the smaller galaxies whose merger formed it.

Keep in mind that Standard Model physics demonstrates that in all but ultra-extreme circumstances (which haven't existed since the first few seconds after the Big Bang, at most) the total number of baryons in any system (less the total number of anti-baryons in any system) is constant (which has been experimentally confirmed to extreme precision), and that baryons profoundly outnumber anti-baryons in the universe (on the order of 10^10 to one), so there is no plausible physical mechanism by which new baryons are being created in galaxy mergers.

Indeed, even the proportion of the baryonic mass of the universe of each kind of atomic element, something that can only occur in nuclear fission and nuclear fusion reactions that happen mostly in mature stars, has changes only incrementally from the proportions of those atoms predicted to have been present fifteen minutes after the Big Bang, and even then, in amounts and by mechanisms mostly associated with the nuclear physics of stars, that are reasonably well understood. This strongly reinforces the idea that the new baryons aren't being created in galaxy mergers.

So, the shortfall of baryons in a dark matter particle paradigm, that is present in every system smaller than a galaxy cluster, would have to come from the intergalactic medium (IGM) of cold interstellar gas between galaxies and the circumgalactic medium (CGM) of cold interstellar gas in the dark matter halos of galaxies.

Fig. 1 of McGaugh et al. (2026): Conceptual elements of a galaxy: the stars (yellow/blue) and atomic gas (green) of NGC 6946 (Spitzer 3.6µ and 21 cm data: F. Walter et al. 2008) are shown embedded in an extended dark matter halo (black). The dark matter density decreases continuously with radius so the halo has no hard edge, but for convenience we adopt the common convention that the radius r200 marks the boundary of the dark matter halo and the dividing line between the circumgalactic medium (CGM) and the intergalactic medium (IGM; orange). The stars and atomic gas illustrated here appear within r < 20 kpc while r(200) ≈ 220 kpc (not shown to scale).

One kpc (i.e. kiloparsec) equals 32,600 light years.

But while this is the only possible solution to the local missing baryon problem in essentially all galaxies (but especially the smaller ones) in the dark matter particle paradigm, there is basically no way to make this work.

Therefore, cold dark matter models are inconsistent with what we observe.

CDM predicts excessive dwarf galaxy masses

Another example demonstrates that in the Local Group that includes the Andromeda galaxy and the Milky Way, one of its minor galaxies should have more mass than its two biggest galaxies and even more mass than the Local Group as a whole, which is contrary to the kinetic dynamics of the system as a whole and contrary to the conservation of matter. As McGaugh explains:

One signature of this misfit is the occurrence of very large V(200) for dwarf galaxies with small V(f). Taken literally, this would mean that some of the smallest dwarf galaxies reside in dark matter halos that outweigh those of giants like the Milky Way. This seems absurd, and it is. For example, by this approach, the dwarf galaxy NGC 3109 residing just outside the Local Group outweighs the Local Group and both its giants, Andromeda and the Milky Way, put together. But it is pretty clear from the local velocity field that the entire Local Group is not orbiting this little dwarf.

Real galaxies rarely have NFW halo distributions 

In dark matter particle paradigms, inferred dark matter halos have a "pseudo-isothermal" distribution, while collisionless cold dark matter must theoretically have, as an inexorable consequence of a very simple statistical mechanics style calculation that applies to dark matter particle with these very simple properties, what is called an NFW distribution, which is a very poor fit to the vast majority of galaxies.

Figure 2 from McGaugh et al. (2026): The observed flat velocity V(f) as it relates to the fitted V(200) for pseudo-isothermal (left panel) and NFW (right panel) halos (Li et al. 2020). Filled points have formal uncertainties < 20% in V(200); open points are less accurate fits. The solid line shows V(f) = V(200). The gray line in the right panel shows Equation (2a) of Katz et al. (2019), which corresponds roughly to f(v) ≈ 1.4.

V(f) is the rotational velocity of a galaxy at about a 65,000 light year radius, V(200) is the velocity of a galaxy at about 715,000 light year radius, and f(v) is equal to V(200)/V(f). 

The bottom line is that pseudo-isothermal dark matter halo distributions are a decent fit to what is observed with f(v) approximately equal to 1 and little scatter in the data (and scatter mostly associated with data points that have high uncertainties), while an NFW dark matter halo distribution has f(v) approximately equal to 1.4 with a great deal of scatter in the data.

This is a problem for the dark matter paradigm because coming up with a dark matter candidate with properties the naturally form pseudo-isothermal halos (for a candidate that isn't excluded by other data) is a challenging enterprise. Indeed, pseudo-isothermal dark matter halo density distributions aren't even theoretically stable.

CDM predicts the wrong slope for the Tully-Fischer scaling law

In a cold dark matter paradigm, the baryonic Tully-Fischer relationship (which roughly speaking related galaxy size to the speed of its flat rotation) has a slope of four when the observed relationship has a slope of three. 

When your power law exponent is a power of three rather than a predicted power of four, you have a seriously flawed functional form for your model.

Gravity based solutions compared

Toy-model MOND has challenges of its own (especially in galaxy clusters, although the intra-cluster medium of cold interstellar gas that was recently estimated makes the discrepancy smaller), but it is much more descriptive of the data, and predictive, than the cold dark matter paradigm. It even fits clusters reasonably well also with a tweak to just one of its parameters, rather than to the model as a whole. 

Deur chalks up the different gravitational behavior of galaxy clusters and galaxies to the different geometries of the mass distributions involved.

Data Combinations For Neutrion Oscillations

The PMNS matrix with non-zero CP conservation and a normal ordering of neutrino masses is still a good description of all of the available raw data from four leading neutrino experiments (without the need for right handed or otherwise sterile neutrinos, or non-standard neutrino interactions, or Majorana neutrino mass). 

This is hardly breaking news but provides yet another confirmation, independent of the major neutrino physics collaborations that this fairly simple model of neutrino physics works.

We present the first combined oscillation analysis of multiple atmospheric neutrino datasets, featuring data from Super-Kamiokande, IceCube-DeepCore, and KM3NeT/ORCA together with reactor data from Daya Bay. 

Such combinations have long been considered infeasible outside experimental collaborations; we demonstrate that a unified physics model can simultaneously describe all datasets with no significant parameter tensions. 

Fitting 839,048 events across 1536 bins with 91 parameters, our combined analysis yields competitive measurements of the neutrino mixing parameters, disfavors CP conservation, and prefers the Normal over the Inverted Mass Ordering.

Philipp Eller, "Atmospheric Neutrino Oscillations: the Full Picture" arXiv:2606.09714 (June 8, 2026).

The body text notes that:

We disfavor the absence of CP violation at ∆χ2 = 8.06 and the Inverted Ordering at ∆χ2 = 9.11.

These preferences are statistically significant at a more than 95% confidence level.

The preference for normal ordering is about three sigma (roughly a 99% confidence level). 

This preference is also corroborated by an independent statistically significant preference for a normal ordering from cosmology data that strengthens that preference when cosmology data is combined with terrestrial experimental data. But quantifying the cosmology data preference is challenging because it is cosmology model dependent (see also here). 

Cosmology data does, however, consistently favor a lightest neutrino mass eigenstate far less massive than the Katrin direct neutrino mass measurement experiments (by two or three orders of magnitude).

Neutrinoless beta decay experiments (which imply Majorana neutrino mass limits) aren't yet powerful enough to make meaningful statements about neutrino masses relative to other data sources for neutrino masses.

A Preon Model

There are lots of issues with preon models that model at least some of the Standard Model fundamental particles as composite (experimental limits on compositeness are strict and naively rule them out for simpler models). But this is a more interesting one than most.

We build a framework for Regge trajectories from the Nambu-Goto action. We compute the 6-preon Regge trajectory in a preon model, include the worldsheet conformal anomaly, and build the parameter-free Veneziano amplitude. The amplitude has s-channel poles matching the spectrum to 0.5%, and at fixed-angle scattering decays exponentially with a negative Gross-Mende coefficient, realized numerically to 0.03%. 

This is a soft, genuinely non-perturbative ultraviolet completion of the preon model - and thereby of the Standard Model, which emerges as its low-energy limit.

Risto Raitio, "Soft UV Completion of a Preon Model" arXiv:2606.06541 (June 4, 2026).

The model used in this case is spelled out in the introduction:

Quarks and leptons arise as three-preon composites bound at the metacolor scale Λ(cr); the three fermion generations emerge not as a postulated multiplicity but as dynamical excitations of these composites; and the chiral, anomaly-free matter content of one Standard Model family is reproduced from a small set of preon charges. In this picture the Standard Model is the low-energy limit of a confining metacolor gauge theory, much as hadronic physics is the low-energy limit of QCD.

More Higgs Boson Properties Measured

The experimental data is still strongly consistent with the observed Higgs boson being the Standard Model Higgs boson.

A study of the structure of the coupling between the Higgs boson and the top quark is performed using events from tt¯H and tH production in the H→γγ decay channel, with 164 fb−1 of proton-proton collision data at a center-of-mass energy of s√ = 13.6 TeV collected by the ATLAS detector at the LHC. 

The cross section of the tt¯H process times the Higgs to diphoton decay branching ratio is measured to be 1.46+0.40−0.35=1.46+0.34−0.32(stat.)+0.22−0.13(sys.) fb, corresponding to 1.13+0.33−0.28 times the Standard Model prediction. 

An observed 95% confidence level limit on the tH production cross section times the Higgs to diphoton decay branching ratio is set at 6.2 times the Standard Model prediction, compared to an expected limit of 4.4 times, constituting the most stringent tH upper limit achieved in a single measurement to date. 

The results are combined with 140 fb−1 of proton-proton collision data collected at s√ = 13 TeV in the same production and decay channel, and a CP-mixing angle of |α|>38∘ is excluded at the 95% confidence level, with a purely CP-odd Higgs-top Yukawa coupling excluded at the level of 5.8 standard deviations, providing the most stringent direct constraints on the CP structure of the Higgs-top Yukawa interaction to date.

ATLAS Collaboration, "Probing the Higgs-top Yukawa interaction in the tt¯H and tH processes using H→γγ with the ATLAS detector" arXiv:2606.04855 (June 3, 2026) (Phys. Rev. Lett.) (the paper is 36 pages long including a 20 pages long list of authors).

Dark Matter Phenomena Free Dwarf Galaxies

MOND explains these galaxies with the external field effect. Dark matter particle theories rely upon a tidal stripping hypothesis. More data about these galaxies helps explore and evaluate hypotheses like these. 

Also, to be clear, the distances in the abstract below are from Earth, not from the giant NCG 1052 galaxy (which is the relevant data point for the external field effect and tidal striping hypotheses).

NGC 1052-DF2 and DF4 are two ultra-diffuse galaxies deficient in dark matter (DM), and reported as part of a remarkable linear trail of dwarf galaxies in the NGC 1052 field. 

Recently, NGC 1052-DF9 has been identified as the third galaxy missing DM along the trail. This structure may have been formed in a high-velocity head-on collision between two gas-rich dwarfs, known as the "bullet-dwarf" scenario. However, the trail overlaps in projection with a foreground system, the NGC 1035 group at ∼13 Mpc, raising suspicions that the trail is an artifact of this superposition. 

DF2 and DF4 have been found to be at distances of 21.7±1.2 and 20.0±1.6 Mpc, respectively, using the tip of the red giant branch (TRGB) method with deep Hubble Space Telescope (HST) imaging, but the distances to other trail dwarfs remain unknown. 

In this Letter, we use HST imaging to obtain surface brightness fluctuation (SBF) distance estimates for eight candidate trail dwarfs, as well as for the giant galaxies NGC 1052 and NGC 1035. We find that the dwarfs are all at ∼20 Mpc, and are not associated with the foreground NGC 1035 group. However, for DF2, we derive an SBF distance of 17.7±1.4 Mpc, inconsistent with the published HST TGRB distance (21.7±1.2 Mpc). Meanwhile, James Webb Space Telescope (JWST) observations of DF2 offer a second, and potentially more accurate, TRGB distance of 17.6±0.6 Mpc. While this value matches our SBF result, it is clear that uniform JWST imaging of the remaining trail dwarfs is critically needed.

Yimeng Tang, Gagandeep S. Anand, Aaron J. Romanowsky, Pieter G. van Dokkum, Kevin A. Bundy, "New Measurements of Distances to Galaxies in the NGC 1052 Field with the Hubble and James Webb Space Telescopes: Testing the Bullet-Dwarf Origin of the Trail" arXiv:2606.05144 (June 3, 2026) (Accepted for publication in ApJ Letters).

A Novel GUT

There is virtually no chance that this grand unification theory reflects reality, but it is a quite unusual approach that combines a mishmash of ideas. 

We present an SU(12)×SU(2)(L)×U(1)(R) model unifying SU(9) quark color-flavor with SU(3) lepton flavor as a flavorful alternative to conventional theories of unification. We begin in the ultraviolet with a single yukawa shared by the unified up-type quarks and neutrinos, and no further new fermions. We show that gauged quark color-flavor and lepton flavor instantons dynamically generate the bottom and tau yukawas, which implements a massless quark solution to the strong CP problem and sets up a flavored type-I seesaw mechanism. Only two new scalar irreps are needed for the symmetry-breaking steps, which include quark color-flavor deconstruction and then infrared reunification, and the Standard Model gauge group in this theory emerges as

 

 

 

 

 

where Γ∈{1,ℤ(2)} is the electroweak global structure and there is a discrete gauge symmetry X=B−3(L(i)+L(j)−L(k)) which brings additional ℤ(3) global structure to the SM. This gauge symmetry acts as a flavorful upgrade of the ℤ(18)^(B+L) anomaly-free global symmetry of the SM and stabilizes the proton absolutely. Non-invertible chiral symmetry-breaking is crucial to our model, and we discuss the rich spectrum of emergent generalized symmetries and topological defects appearing at various stages. In the infrared, the novel shared quotient between continuous and discrete groups links the one-form and two-form global symmetries of the Standard Model.

Antonio Delgado, Seth Koren, "Quark-Lepton Color-Flavor Unification" arXiv:2605.30413 (May 28, 2026).

All About MOND And Dark Matter

MOND still works.

The baryonic Faber-Jackson relation (BFJR) links the baryonic mass of pressure-supported systems to their mean velocity dispersion. For elliptical galaxies, the BFJR is thought to be a projection of the fundamental plane (FP), which includes the stellar half-mass radius as a third variable. We study the BFJR and FP across eight orders of magnitude in baryonic mass, encompassing galaxy groups, ellipticals, dwarf ellipticals, and dwarf spheroidals. We compile and homogenize data for 1400 pressure-supported systems and measure their mean internal baryonic acceleration ⟨gbar⟩. 

We find that the properties of the BFJR and FP systematically depend on the internal acceleration of the sampled systems, with a transition around the acceleration scale a(0) ≃ 1.2 × 10^10 m*s^−2. For low-acceleration systems with ⟨gbar⟩ < 0.6 a(0) (dwarf galaxies and galaxy groups), the BFJR relation takes the form log(10)(M(bar)/M⊙) = (4.19 ± 0.10) log(10)(σ(los)/km*s^−1) + (2.55 +0.16 −0.16) with an orthogonal intrinsic scatter of 0.11±0.01 dex [ed. about ± 29% which is low for astronomy observations].

The FP expected from the Newtonian virial theorem is followed by high-acceleration systems (massive ellipticals with ⟨gbar⟩ ≳ 6a(0)), whereas low-acceleration systems deviate from the FP at both low masses (dwarf galaxies) and high masses (galaxy groups). 

Our results generally agree with the expectations of MOND: high-acceleration systems follow the Newtonian virial theorem in which a radial variable explicitly appears (the FP), while low-acceleration systems follow the MOND virial theorem in which the radial dependence disappears (the BFJR). On average, the MOND external field effect seems to play a secondary role in dwarf galaxies in galaxy groups and clusters.

Yong Tian, Federico Lelli, Marcel S. Pawlowski, Stacy McGaugh, Yi Duann, Kyu-Hyun Chae, Enrico Di Teodoro, Konstantin Haubner, Meng Hua Kuo, Chung-Ming Ko, "The Baryonic Faber-Jackson Relation and Fundamental Plane of Galaxy Groups, Elliptical Galaxies, and Dwarf Galaxies" arXiv:2605.26965 (May 26, 2026) (A&AL in press).

But there are dissenters, who conclude that MOND is disfavored, albeit, with a much smaller sample size, and based upon a "cored halo" model that there is not produced by any underlying dark matter physics model. 

Dwarf galaxies have long been recognised as important testing grounds for models of dark matter. For instance, it is here where the cusp-core problem is most apparent. 

In this work we select two dwarf galaxy samples: LITTLE THINGS and dwarf galaxies in SPARC. We use these to examine whether there are preferences for MOND or dark matter halos in these objects. Notably, our analysis employs the latest developments in Hamiltonian Monte Carlo sampling methodology and robust model comparison via ELPD differences. 

Our findings suggest a > 4σ preference for cored halo models over MOND. However, this relies on significant preferences from 7 out of 19 SPARC galaxies and 11 of 18 from LITTLE THINGS (few of which are overwhelming). It is notable that only a single galaxy prefers MOND over a cored halo. 

Thus, this evidence is suggestive, but does not conclusively decide against MOND. We also test for evidence of a MOND external field effect, and find weak evidence against its presence. 

Despite these statistical preferences, most SPARC galaxies remain compatible with a universal MOND scale. In LITTLE THINGS, a free MOND model is preferred to a universal value at ∼8σ, but this is of doubtful physical significance. 

For MOG, the story is different, here we find ≳8σ preferences for all halos (or MOND) against universal MOG models with significant exclusions in individual galaxies across both samples. Thus, a proposed universal rotation curve model derived from MOG is quite strongly disfavoured.

Geoff Beck, "For modified gravity, it's the LITTLE THINGS that matter" arXiv:2605.27217 (May 26, 2026).

And then, there is this attempt to explain dark matter phenomena:

We review recent results showing that, within the framework of quantum field theory in curved spacetime, the semiclassical energy-momentum tensor of the neutrino flavor vacuum fulfills the equation of state of dust and cold dark matter. By considering spherically symmetric spacetimes in the weak field approximation, the flavor vacuum is shown to contribute as a Yukawa correction to the Newtonian potential. We discuss how this modified potential provides a mechanism to account for the flat rotation curves of spiral galaxies. In this perspective, neutrino mixing is presented as a viable contributing factor to the dark matter content of the universe.

Antonio Capolupo, Salvatore Capozziello, Gabriele Pisacane, Aniello Quaranta, "Particle Physics in Curved Spacetime and Dark Matter" arXiv:2605.26134 (May 21, 2026).