Predicted Value Of Neff Refined

A new calculation of the predicted value of the observable N(eff) (for the effective number of neutrinos) from cosmology data when there are exactly three neutrino flavors predicts that N(eff) = 3.0439 ± 0.0006. 

The commonly quoted value determined with a somewhat less precise model is 3.045 which is consistent with the new value at the two sigma level.

Astronomy observations are consistent with these predicted values. We know that there are at least three neutrino flavors, but astronomy observations rule out the possibility of four or more neutrino flavors at high significance. This measure of the number of neutrino flavors would include sterile neutrinos that oscillate with the three ordinary active neutrinos up to about 1-10 eV of mass (which is far more massive than any of the active neutrino masses). But a sterile neutrino that is much more massive than that would not impact the value of the N(eff) observable.

W and Z boson decays rule out a fourth generation active neutrino up to masses of about 45.6 GeV.

Archaic Hominins Crossed The Wallace Line Long Ago

Stone tools dated with related animals remains show that archaic hominins had crossed the Wallace line by 1.26 ± 0.22  million years ago. 

Presumably, these archaic hominins would have been Homo erectus although there are no associated hominin bones past the Wallace line to confirm that this was the case.

The Standard Model Constants Are Constant

The available evidence constrains changes in the strong force coupling constant over time (implicitly, through the quantum chromodynamics energy scale lambda QCD) to a value consistent with zero to high precision, from a robust set of four different sets of data going all of the way back to Big Bang Nucleosynthesis which happens about fifteen minutes after the Big Bang. 

The constraint from atomic clocks of 3.2 ± 3.5 parts per 10^17 per year, when the age of the universe is about 1.38 x 10^10 years, implying a maximum difference of 230 ± 250 parts per billion over the entire age of the universe. The constraint from a natural nuclear reactor on Earth that started to react 1.8 billion years ago is slightly more strict at less than 72 parts per billion over the entire age of the universe. A proposed extension of the paper would tighten that constraint by four orders of magnitude.

Of course, the strong force coupling constant, like all of the other experimentally determined Standard Model constants, run with energy scale, so when the universe was very hot, not so long after the Big Bang, its value at the prevailing temperature of the universe would have been smaller, because the strong force coupling is weaker at higher energies. The relationship between energy-scale and the strength of the strong force coupling constant is known exactly in the Standard Model and has been corroborated by particle accelerator experiment data.

This is also what efforts to determine the electromagnetic force coupling constant (i.e. the Fine Structure Constant) and electron and quark mass ratios, using astronomy to determine those ratios at high redshifts, has found.

Laboratory and astrophysical tests of ''constant variation'' have so far concentrated on the dimensionless fine-structure constant α and on the electron or quark mass ratios Xe,q=me,q/ΛQCD, treating the QCD scale ΛQCD as unchangeable. 

Certain beyond Standard Model frameworks, most notably those with a dark matter or dark energy scalar field ϕ coupling with the gluon field, would make ΛQCD itself time dependent while leaving α and the electron mass untouched. Under the minimal assumption that this gluonic channel is the sole ϕ interaction, we recast state-of-the-art atomic clock comparisons into δΛQCD/ΛQCD=(3.2 ± 3.5) × 10^−17 yr^−1 limits, translate the isotope yields of the 1.8-Gyr-old Oklo natural reactor into a complementary geophysical limit of |δΛQCD/ΛQCD| < 2 × 10^−9 over that time span, corresponding to the linear drift limit |δΛQCD/ΛQCD| < 1 × 10^−18 yr^−1, and show that the proposed 8.4 eV 229Th nuclear clock would amplify a putative ΛQCD drift by four orders of magnitude compared with present atomic clocks. We also obtain constraints from quasar absorption spectra and Big Bang Nucleosynthesis data.

V. V. Mansour, A. J. Mansour, "Constraints on the Variation of the QCD Interaction Scale ΛQCD" arXiv:2508.07266 (August 10, 2025) (derivatives in the abstract above are shown with sigma notation rather than in the original superscript dot notation, because dot notation is hard to render in the blogger interface).

Tau Lepton g-2 And Electric Dipole Moment

The substance of a new paper considering new physics that could arise in the tau lepton anomalous magnetic moment (g-2) and electric dipole moment (EDM) is purely ill-motivated speculation and doesn't deserve any discussion here. 

But the introduction to the paper (PDF) conveniently recaps the current state of experimental measurements of these properties (that are established to high precision in electrons and muons), and the Standard Model predictions for these quantities (which have been confirmed for electrons and muons):

The SM contributions to the electron and muon g−2 are precisely calculated and compared with experiments. On the other hand, a nonzero EDM requires CP violation which arises predominantly from the phase in the Cabibbo-Kobayashi-Maskawa (CKM) matrix within the SM, resulting in extremely suppressed predictions for charged lepton EDMs. Therefore, the discovery of a nonzero EDM indicates the existence of physics beyond the SM. 

In fact, precise measurements of the electron EDM [ed. the absolute value of which is currently experimentally limited to not more than 4.1 * 10^-30 ecm] already put stringent constraints on a wide range of new physics models [ed. especially supersymmetry]. While the current upper limit on the muon EDM [ed. the absolute value of which is currently experimentally limited to not more than 1 * 10^-19 ecm] hardly gives a constraint by itself, the projected experiments will reach the sensitivity to explore new physics at the electroweak scale. 

The dipole moments of the tau lepton are currently much less constrained than those of the electron and muon due to the tau’s short lifetime, but they will provide a valuable window into new physics effects that scale with lepton mass. 

The SM contribution to the tau g −2 is precisely calculated and found as a(SM)(τ) = (117717.1 ± 3.9) × 10^−8 [ed. i.e. 0.001177171(39)], including updates of the hadronic vacuum polarization contributions. On the other hand, its measurements at the Large Hadron Collider (LHC) are still not as precise: 

ATLAS: −0.057 < a(τ) < 0.024 (95% C.L.), (1.4) 

CMS: −0.0042 < a(τ) < 0.0062 (95% C.L.). (1.5) 

The SM contribution to the tau EDM is tiny. At the quark level, the leading contribution is given at the four-loop level, dSM τ = O(10^−47) ecm, while the hadron level long distance effect enhances the contribution to dSM τ ≃ −7.32 × 10^−38 ecm. 

The current experimental upper limits are:

−1.85 × 10^−17 ecm < Re(dτ) < 0.61 × 10^−17 ecm (95% C.L.), (1.6)

−1.03 ×10^−17 ecm < Im(dτ) < 0.23 × 10^−17 ecm (95% C.L.), (1.7) 

|dτ| < 2.9 × 10^−17 ecm (95% C.L.).  (1.8) 

Note that the complex form of the limits is due to the off-shell photon in the e+e− → τ+τ− process. 

There is also an indirect limit on |dτ| from the electron EDM constraint via the three-loop light-by-light mechanism, which is

 |dτ| < 1.1 ×10^−18 ecm for |de| < 1.1 × 10^−29 ecm, 

 |dτ| < 4.1 ×10^−19 ecm for |de| < 4.1 × 10^−30 ecm (1.9) 

providing a stronger constraint compared with the direct bounds. 

Although measurements of the tau g − 2 and EDM remain experimentally challenging, we can expect improved sensitivities for these observables by ongoing and projected experiments such as the Belle II experiment, Beijing Electron-Positron Collider (BEPCII) and Circular Electron-Positron Collider (CEPC). They will reach the sensitivities of |aτ| ∼ 10^−5 and |dτ| ∼ 10^−19 ecm.

Thus, the ongoing and projected experiments, which improve upon the status quo by about two orders of magnitude each, should show a tau g-2 consistent with 0.00118(1) and a tau EDM that is experimentally indistinguishable from zero. 

A different result would suggest new physics, which there is no good reason to suspect, or serious systemic errors in the experiments.

Previous discussion of the tau lepton's properties can be found in posts at this blog on May 28, 2024 and May 23, 2023. 

The Koide's rule predicted value for the tau lepton mass is 1776.96894(7) MeV.

The Particle Data Group's world average of the tau lepton mass is 1776.93 ± 0.09 MeV which is a precision of slightly under one part per 20,000. 

The experimentally measured mass of the tau lepton is consistent with the Koide's rule prediction made in 1981 at the 0.4 sigma level, even though the relevant masses were known much less precisely in 1981, and the experimental value has grown closer to the predicted value over time. 

There are dozens of lepton decay modes with a branching fraction of more than 1% in addition to many more less common decay modes. About 85% of those decay modes involve a decay to an electron or muon, plus one or more neutral particles (such as neutrinos, neutral pions, and/or neutral kaons).

More Constraints On Primordial Black Holes

A new study, that doesn't rely on the micro-lensing and Hawking radiation exclusions which are the primary methods for constraining primordial black hole frequency, places very strict limitations on the maximum potential abundance of "supermassive" primordial black holes. 

It limits them to less than 0.1% of dark matter in a dark matter particle hypothesis for "supermassive" primordial black holes (i.e. primordial black holes that are 10,000 times more massive than the Sun or more). This had already been ruled out long ago, albeit not quite so strictly. 

The main focus on primordial black holes as a dark matter candidate has been on asteroid sized primordial black holes in the range of 3.5 × 10^−17 to 4 × 10^−12 solar masses (i.e. twelve to seventeen orders of magnitude smaller in mass than the Sun), which by definition cannot arise from stellar collapse. Non-detection of Hawking radiation (which is a net emission for primordial black holes up to about 10^-8 solar masses), and micro-lensing, has largely ruled out larger primordial black holes as a significant component of dark matter (if it exists). 

Also, while the paper frames its constraints in terms of primordial black holes, it would seem to apply to any dark matter candidate in that mass range, such as ordinary black holes and MACHOs (massive compact halo objects).

We present updated constraints on the abundance of primordial black holes (PBHs) dark matter from the high-redshift Lyman-α forest data from MIKE/HIRES experiments. Our analysis leverages an effective field theory (EFT) description of the 1D flux power spectrum, allowing us to analytically predict the Lyman-α fluctuations on quasi-linear scales from first principles. Our EFT-based likelihood enables robust inference across redshifts z = 4.2−5.4 and down to scales of 100 kpc, within previously unexplored regions of parameter space for this dataset. 

We derive new bounds on the PBH fraction with respect to the total dark matter fPBH, excluding populations with fPBH≳10^−3 for masses MPBH ∼ 10^4−10^16 M⊙. This offers the leading constraint for PBHs heavier than 10^9 M⊙ and highlights the Lyman-α forest as a uniquely sensitive probe of new physics models that modify the structure formation history of our universe.

Mikhail M. Ivanov, Sokratis Trifinopoulos, "Effective Field Theory Constraints on Primordial Black Holes from the High-Redshift Lyman-α Forest" arXiv:2508.04767 (August 6, 2025).

Another recent study (from August 11, 2025) reaches the same conclusion.

Additional Context

The Ordinary Matter Budget Of The Universe

Most of the ordinary matter in the universe is found in stars (about half) and the intergalactic/interstellar medium (mostly interstellar gas and dust) which is also about half, with planets and asteroids accounting for less than 1% of the total amount of ordinary mass in the universe. 

Stellar-mass black holes (formed from dying stars) account for not more than about 0.1% of the universe's ordinary matter, and supermassive black holes, found at the centers of galaxies, account for not more than about 0.01% of the universe's ordinary matter. 

Contributions to the mass-energy of the universe from photons and neutrinos are also very small (even though both kinds of particles are extremely numerous).

Planets, Asteroids, and Comets

Self-gravity forces planet-like objects of more than 0.5 x 10^21 kg (about one four billionth of the mass of the Sun) and more than 400 km in radius, to become approximately spherical, and this is the lower floor for dwarf planets, regular planets, and planet-sized moons. The mass of the Earth is about 3 x 10^-6 solar masses.

Objects smaller than this (but larger than dust or interstellar gas) tend to form non-spherical asteroids and comets, although some are approximately spherical due to random chance.

Star and Brown Dwarves

As an aside, anything other than a star or a black hole, can't have more than about 1.24% of the mass of the Sun (i.e. 13 Jupiter masses), because then gravity causes unstable nuclear fusion to commence in its core, turning it into a "sub-brown dwarf" although NASA conservatively assumes that planets could be as large as 30 Jupiter masses (about 2.86% of the mass of the Sun). In ideal conditions, a sub-brown dwarf can form at masses as low as one Jupiter mass (about 1/1024th of the mass of the Sun). Sub-brown dwarves and true brown dwarves, which range from 13 to 80 Jupiter masses (i.e. up to about 7.8% of the mass of the Sun) fill a liminal space between true planets with no gravity induced nuclear fusion and the smallest "main-sequence" stars. 

While brown dwarves are an order of magnitude or two heavier than large gas giant planets, like Jupiter and Saturn, they aren't much larger: "most brown dwarfs are slightly larger in volume than Jupiter (15–20%), but are still up to 80 times more massive due to greater density." Jupiter's radius is 11 times that of Earth, and the Sun's radius is 10 times that of Jupiter.

The theoretical maximum mass of a star is on the order of 200 solar masses. Of the billions and billions of stars that astronomers have observed, only 11 of them are potentially more than 150 solar masses, and only 5 of them have an upper end of their two sigma mass range (given the uncertainty of the mass measurement) above 200 solar masses. Only 2 stars have a best fit mass estimate above 200 solar masses, and realistically, given the uncertainty in these mass measurements (which is stated for one of the two and is not stated for the other), a mass of 200 solar masses of less is probably within the two sigma uncertainty range of the observation for both cases (particularly if one considers look elsewhere effects which are significant given the very large number of star masses measured).

The theoretically largest radius star is about 1700 times the radius of the Sun (by comparison, the orbit of Saturn is about 2,048 times the radius of the Sun). The largest radius star ever observed has a radius of 1530 ± 370 times the radius of the Sun.

Thus, any compact object with a mass of more than about 2 * 10^2 solar masses, or a radius more than about 1700 times the radius of the Sun (the Sun has a radius of about 700,000 km) is a supermassive black hole.  

Black Holes

An ordinary stellar collapse black hole has a minimum mass which is more than two times the mass of the Sun, but this minimum mass is a bit under three times the mass of the Sun. This mass, in the non-spinning case is called the Tolman-Oppenheimer-Volkoff limit.  In theory, this threshold mass may vary modestly based upon the spin of the neutron star. The mass limit is 18%-20% higher for a very rapidly spinning neutron star that is on the brink of becoming a black hole. A stellar mass black hole has an event horizon radius  (i.e. Schwarzschild radius radius) of about 6-9 km to 300 km.

The maximum density of anything ever observed in astronomy or high energy physics or nuclear physics is a neutron star/black hole right at the high end of the Tolman-Oppenheimer-Volkoff limit.

Pinning down the exact threshold more precisely is a matter of ongoing astronomy research. The least massive object definitively classified as a black hole has a mass of 3.04 ± 0.06 solar masses. A handful of observations of objects close to the limit have suggested a limit somewhere on the order of 2.01 to 2.9 solar masses.

Between stellar mass black holes (many of which have been indirectly observed) and supermassive black holes at the core of galaxies (many of which have been indirectly observed) are intermediate-mass black holes, which were first observed with gravitational wave telescopes:

An intermediate-mass black hole (IMBH) is a class of black hole with mass in the range of one hundred to one hundred thousand (10^2–10^5) solar masses: significantly higher than stellar black holes but lower than the hundred thousand to more than one billion (10^5–10^9) solar mass supermassive black holes.

An intermediate-mass black hole has an event horizon radius of 300 km to 300,000 km (which is smaller than the radius of the Sun). 

In theory, it would have been possible shortly after the Big Bang and predominantly in the first second after the Big Bang, for matter to be dense enough to form a black hole with less mass than necessary to form an ordinary stellar collapse black hole (even though the density needed to form a black hole increases as the mass which collapses into a black hole gets smaller).  These hypothetical black holes are called primordial black holes. 

But no primordial black holes have ever been observed, despite the fact that they are predicted to emit intense Hawking radiation (a.k.a. Bekenstein-Hawking radiation after Jacob Bekenstein, who died at age 68 in 2015, and Stephen Hawking, who died at age 76 in 2018, who both proposed it) which has never been detected:

Depending on the model, primordial black holes could have initial masses ranging from 10^−8 kg (the so-called Planck relics) to more than thousands of solar masses. However, primordial black holes originally having masses lower than 10^12 kg would not have survived to the present due to Hawking radiation, which causes complete evaporation in a time much shorter than the age of the Universe. . . . Primordial black holes are also good candidates for being the seeds of the supermassive black holes at the center of massive galaxies, as well as of intermediate-mass black holes.

The smaller the black hole, the more rapidly it evaporates due to Hawking radiation. A primordial black hole which initially had the mass of the Sun (2 * 10^30 kg) would now have a mass of something on the order of 10^23 kg (about one 10,000,000th the mass of the Sun) due to Hawking radiation (although accretion of new matter could counteract Hawking radiation and slow down the rate at which a primordial black hole's mass declines).

A hypothetical stable mass primordial black hole has an event horizon radius of at least 24 meters. Evaporating primordial black holes would have a smaller event horizon radius. An asteroid sized black hole would have an event horizon radius of about 0.03 millimeters to 3 meters and would emit significant Hawking radiation.

For black holes formed by stellar mass collapse (about 3 solar masses) or more, the mass loss due to Hawking radiation would be almost completely offset by accretion of mass-energy from its absorption of cosmic background radiation alone, setting aside interstellar dust and other objects that could fall into the black hole. Specifically:

Since the universe contains the cosmic microwave background radiation, in order for the black hole to dissipate, the black hole must have a temperature greater than that of the present-day blackbody radiation of the universe of 2.7 K. The relationship between mass and temperature for Hawking radiation then implies the mass must be less than 0.8% of the mass of the Earth [i.e. about 2.4 * 10^-8 solar masses]. This in turn means any black hole that could dissipate cannot be one created by stellar collapse. Only primordial black holes might be created with this little mass.

The theoretical maximum size of a black hole (with maximal spin) is 2.7 x 10^11 solar masses, and the most massive black hole ever observed has an estimated mass of up to 1 x 10^11 solar masses. The largest theoretically possible black hole has an event horizon radius of about 800 billion (i.e. 800,000,000,000) km.

New Precise Determinations Of Three Quark Masses

A new paper makes some of the most precise determinations ever of the b, c, and s quark masses. The new paper takes into account quantum electrodynamics (QED) corrections (which is ignored in most quark mass determinations), and the unequal u quark v. d quark masses. It disregards, however, the vacuum polarization contribution of the b quark in its c and s quark mass determinations.

The determined b quark pole mass of 4.1911(62) GeV in the new paper compares to a Particle Data Group world average value of 4.1830(40) GeV which is consistent at the 1.1 sigma level. This should slightly pull up the PDG world average.

The new paper's c quark and s quark mass determinations in the abstract are at the unconventional 3 GeV energy scale in a 4 flavor QCD determination (which ignores b quark effects since the energy scales in question are below the b quark mass). These are m(c) = 0.9808(33) GeV, and m(s) = 83.34(26) MeV, which are lower than the values at the conventional energy scales, because the running of the quark masses with higher energies is towards smaller masses. 

Normally, the c quark mass is quoted as a pole mass with the Particle Data Group world average c quark pole mass of 1.2730(28) GeV. The beta function of this experimentally determined Standard Model constants from 3 GeV to the pole mass, give an c quark pole mass in the new paper of 1.2712(82) GeV which is consistent at the 0.2 sigma level. This should slightly pull down the PDG value.

The s quark mass is  normally quoted at 2 GeV with the Particle Data Group world average s quark mass at 2 GeV of 93.50(80) MeV.  The beta function of this experimentally determined Standard Model constants from 3 GeV to 2 GeV, gives an s quark mass at the 2 GeV energy scale in the new paper of 92.32(42) MeV which is consistent at the 1.3 sigma level and about twice as precise as the current world average from only a single determination. This should significantly pull down the PDG value. This also confirms definitively (at 32 sigma) that the s quark is less massive than the muon (which is 105.6583755(23) MeV), something that has only been definitively established in the last few years.

Each of the new measurements (but especially the s quark mass determination) should lower the uncertainty in the world average (although the c and s quark mass estimates from the PDG already adjust up the uncertainty in their sources that go into their inverse error weighted averages by 1.2 and 1.1 respectively).

We extend an earlier lattice QCD analysis of heavy-quark current-current correlators to obtain new values for the MS masses of the b, c, and s quarks. The analysis uses gluon configurations from the MILC collaboration with vacuum polarization contributions from u, d, s, and c quarks (nf = 4), and lattice spacings down to 0.032 fm. We find that m(b)(m(b), nf = 5) = 4.1911(62) GeV, m(c)(3 GeV, nf = 4) = 0.9808(33) GeV, and m(s) (3 GeV, nf = 4) = 83.34(26) MeV. 

These results are corrected for QED by including (quenched) QED in the simulations. They are among the most accurate values by any method to date. We give a detailed analysis of finite lattice-spacing errors that shows why the HISQ discretization of the quark action is particularly useful for b-quark simulations even for lattices where am(b) ≈ 1. We also calculate QED and isospin corrections to the (fictitious) η(s)-meson mass, which is used to tune s-quark masses in lattice simulations.

HPQCD Collaboration, "New high-precision b, c, and s masses from pseudoscalar-pseudoscalar correlators in nf = 4 lattice QCD" arXiv:2508.02862 (August 4, 2025).

My Confidence In Various Physics Hypotheses

There are various unresolved questions in physics about which I have an opinion. I'm not 100% sure of any of them, but more sure of some than others.

In this post, I give my subjective probabilities for various possibilities, in numbers rounded to avoid spurious accuracy and to increments not less than 1% (even if the true probability expressed as 1% is a bit less than 0.5%):

1. Dark matter phenomena:

* Dark matter phenomena are explained by general relativity or subtle modifications or quantum gravity, that only discernible in weak gravitational fields: 90%

* Dark matter phenomena are explained by a 5th force or a singlet ultralight dark matter boson: 6%

* Dark matter phenomena are explained by dark matter particles of micro-eV to TeV mass: 3%

* Dark matter phenomena are explained by dark matter particles of greater than TeV mass (including composite dark matter candidates such as MACHOs, primordial black holes, and stable heavy hadrons in addition to heavy fundamental particles): 1%

2. Dark energy phenomena:

* Dark energy phenomena are an emergent result of the same gravitational effects that give rise to dark matter phenomena (and do not violate mass-energy conservation): 60%

* Dark energy phenomena are equivalent to the cosmological constant of general relativity: 15%

* Dark energy phenomena exist and are fundamental and not just a side effect of dark matter phenomena, but dark energy is not a constant: 15%

* Dark energy phenomena are a result of flawed astronomy methods and don't really exist: 10%

3. The Lambda CDM model:

* The Lambda CDM model is deeply flawed (even though it may be a useful crude first order approximation): 95%

* The Lambda CDM model is basically correct (although it may omit some minor factors like neutrino masses): 5%

4. Cosmological inflation:

* Cosmological inflation did not happen: 85%

* Some form of cosmological inflation happened: 15%

5. Quantum gravity:

* Gravity is fundamentally a quantum phenomena involving gravitons in Minkowski space: 65%

* Gravity arises from a discrete or quantum space-time (whether or not it also has gravitons): 15% 

* Gravity is emergent from Standard Model forces: 10%

* Gravity is fundamentally a classical and deterministic phenomena: 10%

6. Universe scale asymmetry:

* The universe is not homogeneous and isotropic at the largest possible scales: 65%

* At the largest possible scales, the universe is homogeneous and isotropic: 35%

7. Maximum density:

* There is no physical constraint on maximum mass-energy density: 65%

* There is a maximum mass-energy density greater than the mass-energy density of a minimum mass stellar black hole (such as a Planck scale limitation): 20%

* There is a maximum mass-energy density close to the mass-energy density of a minimum mass stellar black hole: 15%

8. Supersymmetry:

* There is no version of supersymmetry that exists: 99%

* Some version of supersymmetry exists: 1%

9. String Theory:

* Reality is not fundamentally described by string theory: 98%

* Reality is fundamentally described by string theory: 2%

10. Fundamental fermions:

* The Standard Model includes all of the fundamental particles that are fermions: 95%

* The Standard Model omits up to five fundamental fermions (none of which are additional generations of existing Standard Model fundamental fermions) such as a dark matter particle(s) or right handed neutrinos or supersymmetric partners of Standard Model bosons: 4%

* The Standard Model omits at least one additional generation of Standard Model fermions, and/or omits more than five additional fundamental fermions: 1%

11. Fundamental bosons:

* The Standard Model includes all of the fundamental particles that are bosons other than a possible massless spin-2 graviton: 85%

* The Standard Model omits additional fundamental particles that are bosons beyond a massless spin-2 graviton (e.g. additional Higgs bosons, dark matter bosons, dark matter self-interaction bosons, X17 bosons, bosons involved in neutrino mass generation, bosons involved in cosmological inflation and/or dark energy, fifth force carrying bosons, scalar or vector gravitons, massive gravitons, leptoquarks, supersymmetric partners of Standard Model fermions): 15%

12. Sphalerons:

* Sphaleron interactions are physically possible: 50%

* Sphaleron interactions are not physically possible: 50%

13. Stable heavy hadrons:

* There are no stable or metastable hadrons other than the proton and neutron: 95%

* There are stable or metastable hadrons other than the proton and neutron: 5%

14. Stable heavy elements:

* There are no chemical elements with an atomic number in excess of 118 with a half-life of more than 30 seconds: 65%

* There are chemical elements in "islands of stability" with an atomic number in excess of 118 with a half-life of more than 30 seconds: 35%

15. Neutrino mass:

* Neutrinos have Majorana mass: 10%

* Neutrino mass arises from a see-saw mechanism with one or more heavy right handed neutrinos: 5%

* Neutrino mass arises from some other mechanism not yet widely considered: 85%

16. Sterile neutrinos:

* Right handed sterile neutrinos with the same mass as left handed neutrinos exist: 1%

* One or more sterile neutrinos that oscillate or interact with left handed neutrinos, and masses not identical to left handed neutrinos, exist: 2%

* The three left handed neutrinos of the Standard Model are the only neutrinos that exist: 97%

17. Neutrino mass hierarchy:

* The neutrino masses have a "normal" hierarchy: 95%

* The neutrino masses have an "inverted" hierarchy: 5%

18. CP Violation by neutrinos:

* The PMNS matrix exhibits maximal CP violation: 8%

* The PMNS matrix exhibits near maximal CP violation: 85%

* The PMNS matrix exhibits low levels of CP violation: 5%

* The PMNS matrix does not allow for CP violation in neutrino oscillation: 2%

19. Non-standard neutrino interactions:

* There are no non-standard neutrino interactions (i.e. interactions beyond neutrino oscillations and weak force interactions) to be discovered: 90%

* There are some non-standard neutrino interactions: 10%

20. Lepton number and baryon number violation:

* Lepton number and baryon number are always conserved: 50%

* Lepton number and baryon number are only violated in sphaleron interactions: 45%

* Lepton number and baryon number are violated in non-sphaleron interactions (such as neutrinoless double beta decay, proton decay, flavor changing neutral currents, etc.): 5%

21. LP & C:

* The sum of the squares of correctly defined masses of the fundamental particles is equal to the sum of the Higgs vacuum expectation value: 60%

* The sum of the squares of correctly defined masses of the fundamental particles is not equal to the sum of the Higgs vacuum expectation value: 40%

22. Koide's Rule:

* Koide's rule for the masses of charged leptons is true to at least one part per 100,000: 90%

* Koide's rule for the masses of charged leptons is violated by more than one part per 100,000: 10%

23. An extended Koide's rule for quarks:

* The quark masses obey some extended version of Koide's rule: 70%

* The quark masses do not obey some extended version of Koide's rule: 30%

24. The physics desert:

* There are no beyond the Standard Model high energy physics to be discovered between the highest energy scale reached by the Large Hadron Collider (about 10^4 GeV), and energy scales a billion times greater than the highest energy scale reached by the Large Hadron Collider  (about 10^13 GeV): 85%

* There are new high energy physics to be discovered between the highest energy scale reached by the Large Hadron Collider (about 10^4 GeV), and energy scales a billion times greater than the highest energy scale reached by the Large Hadron Collider  (about 10^13 GeV): 15%

25. Planet Nine:

* Planet Nine exists: 65%

* Planet Nine does not exist: 35%

Predictions About Planet Nine

A new preprint sums up some of the expected properties of a hypothetical Planet Nine, which has been inferred from the orbits of other solar system object.

Evidence suggests the existence of a large planet in the outer Solar System, Planet Nine, with a predicted mass of 6.6 +2.6 / -1.7 Earth masses (Brown et al., 2024). Based on mass radius composition models, planet formation theory, and confirmed exoplanets with low mass and radius uncertainty and equilibrium temperature less than 600 K, we determine the most likely composition for Planet Nine is a mini-Neptune with a radius in the range 2.0 to 2.6 Earth radii and a H-He envelope fraction in the range of 0.6 percent to 3.5 percent by mass. Using albedo estimates for a mini-Neptune extrapolated from V-band data for the Solar Systems giant planets gives albedo values for Planet Nine in the range of 0.47 to 0.33. Using the most likely orbit and aphelion estimates from the Planet Nine Reference Population 3.0, we estimate Planet Nines absolute magnitude in the range of -6.1 to -5.2 and apparent magnitude in the range of +21.9 to +22.7. Finally, we estimate that, if the hypothetical Planet Nine exists and is detected by upcoming surveys, it will have a resolvable disk using some higher resolution world class telescopes.

David G. Russell, Terry L. White, "The Radius, Composition, Albedo, and Absolute Magnitude of Planet Nine Based on Exoplanets with Te(q) less than 600 K and the Planet Nine Reference Population 3.0" arXiv:2507.22297 (July 30, 2025).

Improving Top Quark Mass Measurements

Determining the top quark mass precisely is quite important to evaluating many theoretical proposals regarding the source of the experimentally measured mass constants in the Standard Model (equivalently, the pattern to the Higgs Yukawas). 

A new proposal would largely eliminate one of the main sources of systemic error in that measurement, which currently has a combined uncertainty from all sources in an inverse error weighted global average of ± 300 MeV or so. The W boson mass is known to about ± 12 MeV. And, the sources of uncertainty when measuring their masses in collider experiments are highly correlated. So, if the ratio of the top quark mass to the W boson mass can be determined precisely, then the uncertainty in the top quark mass measurement can be greatly reduced.

The top quark mass is a key parameter of the standard model, yet measuring it precisely at the Large Hadron Collider (LHC) is challenging. Inspired by the use of standard candles in cosmology, we propose a novel energy correlator-based observable, which directly accesses the dimensionless quantity 𝑚(𝑡)/𝑚(𝑊). We perform a Monte Carlo study to demonstrate the feasibility of the top mass extraction from Run 2, 3, and High-Luminosity LHC datasets. Our resulting 𝑚(𝑡) can be defined in a well-controlled short-distance mass scheme and exhibits remarkably small uncertainties from nonperturbative effects, as well as insensitivity to parton distribution functions, outlining a roadmap for a record precision measurement at the LHC.

Jack Holguin, et al., "Using the 𝑊 Boson as a Standard Candle to Reach the Top: Calibrating Energy-Correlator-Based Top Mass Measurements" Phys. Rev. Lett. 134, 231903 (13 June, 2025).

Minimal Gravitational Fields

Gravity is an infinite range force. In isolated circumstances, gravitational pulls from opposite directions can cancel out. But, the vast majority of the time, there is at least some small net gravitational pull in one direction or another.

Stacy McGaugh at Triton Station digs into this observation, in both a Newtonian approximation and MOND, to determine that the minimum gravitational acceleration in deep space in MOND (in light of new data about the percentage of baryons that are in deep space) is about 2% of Milgrom's constant a(0).

This is important in MOND in a way that it isn't in conventional general relativity, because "MOND breaks the strong equivalence principle (but not the weak or Einstein equivalence principle)" with its external field effect.

Can Gravity Help Explain Some Standard Model Constants?

An interesting short paper (five pages) argues that the difference between the CKM matrix parameters and those of the PMNS matrix can be explained with an asymptotically safe gravity extension of the Standard Model.

The quark mixing (CKM) matrix is near-diagonal, whereas the lepton mixing (PMNS) matrix is not. We learn that both observations can generically be explained within an ultraviolet completion of the Standard Model with gravity. 

We find that certain relations between CKM matrix elements should hold approximately because of asymptotically safe regimes, including |Vud|^2+|Vus|^2 ≈ 1 and |Vcd|^2+|Vcs|^2 ≈ 1. Theoretically, the accuracies of these relations determine the length of the asymptotically safe regimes. Experimental data confirms these relations with an accuracy of 10^−5 and 10^−3, respectively. This difference in accuracies is also expected, because the ultraviolet completion consists in a fixed-point cascade during which one relation is established already much deeper in the ultraviolet. This results in |Vub|^2 < |Vcb|^2 and translates into measurable properties of B-mesons. 

Similar results would hold for the PMNS matrix, if neutrino Yukawa couplings were large. The ultraviolet complete theory therefore must -- and in fact can -- avoid such an outcome. It contains a mechanism that dynamically limits the size of neutrino Yukawa couplings. Below an upper bound on the sum of Dirac neutrino masses, this allows the PMNS matrix to avoid a near-diagonal structure like the CKM matrix. Thus, large neutrino mixing is intimately tied to small Dirac neutrino masses, ∑mν ≲ (1) eV and a mass gap in the Standard Model fermion masses.

Astrid Eichhorn, Zois Gyftopoulos, Aaron Held, "Quark and lepton mixing in the asymptotically safe Standard Model" arXiv:2507.18304 (July 24, 2025).

Unsolved Physics Problems

 

I would add at least a couple more. 

There are false problems that ask "why doesn't the universe act like I think (for no good reason) that it should?" This includes the hierarchy problem, the strong CP problem, the baryon asymmetry of the universe, and all research invoking the concept of "naturalness."

And, there are contradictory data problems, where one asks why multiple measurements of the same thing (in your current theory) are producing irreconcilable results. These have included the proton radius puzzle, the data based calculation of muon g-2, the measurement of the mean lifetime of unbound neutrons, the reanalysis of CDF data to determine the W boson mass that produced an anomalous result, and the Hubble tension. Usually, in these cases, the answer is that somebody screwed up in one or both of the experiments (at a minimum by overstating the uncertainty in the result), or the theoretical analysis involved, but sometimes, the theory that said the measurements should be the same was wrong.

BSM Physics Constraints In Light Of Muon g-2

The confirmation that the Standard Model prediction for muon g-2 matches the experimental result greatly constrains beyond the Standard Model physics. But how much? 

A new preprint engages with that question.

We review the role of the anomalous magnetic moment of the muon a_mu as a powerful probe of physics beyond the Standard Model (BSM), taking advantage of the final result of the Fermilab g-2 experiment and the recently updated Standard Model value. This review provides both a comprehensive summary of the current status, as well as an accessible entry point for phenomenologists with interests in dark matter, Higgs and electroweak or neutrino and flavour physics in the context of a wide range of BSM scenarios. It begins with a qualitative overview of the field and a collection of key properties and typical results. It then focuses on model-independent, generic formulas and classifies types of BSM scenarios with or without chiral enhancements. A strong emphasis of the review are the connections to a large number of other observables -- ranging from the muon mass and the muon--Higgs coupling and related dipole observables to dark matter, neutrino masses and high-energy collider observables. Finally, we survey a number of well-motivated BSM scenarios such as dark photons, axion-like particles, the two-Higgs doublet model, supersymmetric models and models with leptoquarks, vector-like leptons or neutrino mass models. We discuss the impact of the updated Standard Model value for a_mu and of complementary constraints, exploring the phenomenology and identifying excluded and viable parameter regions.

Peter Athron, Kilian Möhling, Dominik Stöckinger, Hyejung Stöckinger-Kim, "The Muon Magnetic Moment and Physics Beyond the Standard Model" arXiv:2507.09289 (July 12, 2025) (Invited review for Progress in Particle and Nuclear Physics; 274 pages, 50 figures).

A Hubble Tension Recap

The Hubble tension has, for whatever reason, been treated as a more serious challenge to the LambdaCDM "standard model of cosmology", which contrary to the statement highlighted below in the abstract, actually has many other serious discrepancies with astronomy observations. A new preprint examines its implications for the model.

Differences in the values of the Hubble constant obtained from the local universe and the early universe have resulted in a significant tension. This tension signifies that our understanding of cosmology (physical processes and/or cosmological data) is incomplete. Some of the suggested solutions include physics of the early Universe. 

In this paper we aim to investigate common features of various early universe solutions to the Hubble constant tension. The physics of the early universe affects the size of the sound horizon which is probed with the Cosmic Microwave Background (CMB) data. Within the standard model, the size of the horizon (within limits of current measurements) is affected by processes that could occur between (approximately) 1 day after the Big Bang and the last scattering instant. We focus on simple extensions incorporating Early Dark Energy (EDE) and show how such a model affects the inferred values of the Hubble constant. We compare this model to LambdaCDM models using MCMC analysis, likelihoods over the parameter space and Bayesian evidence. The MCMC analysis shows that EDE leads to a decrease in the size of the sound horizon that is consistent with H0 = 73.56 km/s/Mpc but we also show that MCMC analysis favours increasing redshift and proportion of EDE. The Bayesian evidence favours our EDE model for very narrow, finely-tuned parameter space. 

The LambdaCDM model used for comparison has good evidence across a wide parameter space. We interpret this as an indication that more sophisticated models are required. We conclude that if the Hubble tension were to be related to the physics of the early universe, EDE could be used as a window to explore conditions of the early universe and extend our understanding of that era.

Gawain Simpson, Krzysztof Bolejko, Stephen Walters, "Beyond LambdaCDM: How the Hubble tension challenges early universe physics" arXiv:2507.08479 (July 11, 2025).

The History And Prehistory Of Human Disease

A new paper in Nature concludes from ancient DNA that while infectious diseases were common in humans since the hunter-gatherer era, that there was a real surge, not at the time of the Neolithic Revolution, but when steppe herders started to invade and conquerer farmers, and hunter-gatherers, possibly because they lived more closely with their animals and because the diseases that they carried helped facilitate their conquests. The New York Times also discusses the paper.

Infectious diseases have had devastating effects on human populations throughout history, but important questions about their origins and past dynamics remain. To create an archaeogenetic-based spatiotemporal map of human pathogens, we screened shotgun-sequencing data from 1,313 ancient humans covering 37,000 years of Eurasian history. We demonstrate the widespread presence of ancient bacterial, viral and parasite DNA, identifying 5,486 individual hits against 492 species from 136 genera. Among those hits, 3,384 involve known human pathogens, many of which had not previously been identified in ancient human remains. Grouping the ancient microbial species according to their likely reservoir and type of transmission, we find that most groups are identified throughout the entire sampling period. Zoonotic pathogens are only detected from around 6,500 years ago, peaking roughly 5,000 years ago, coinciding with the widespread domestication of livestock. Our findings provide direct evidence that this lifestyle change resulted in an increased infectious disease burden. They also indicate that the spread of these pathogens increased substantially during subsequent millennia, coinciding with the pastoralist migrations from the Eurasian Steppe

Martin Sikora, et al., "The spatiotemporal distribution of human pathogens in ancient Eurasia" Nature (July 9, 2025).

All the GUTs Worth Considering

A fairly short new paper (five pages plus seven pages of footnotes and an appendix) tries to list most or all of the possible Grand Unified Theories a.k.a. GUTs (i.e. theories the unify the three Lie groups of the Standard Model, but not gravity, into a single unified mathematical structure; unified theories that also include gravity are called Theories of Everything a.k.a. TOEs) that could include the Standard Model of Particle Physics, or an extension of it. 

There aren't all that many possibilities that are promising, and several decades of attempts to fit the Standard Model into one in a way that provides useful theoretical insight has not been very fruitful. While this line of inquiry isn't as troubled as supersymmetry (which is a dead man walking) or string theory (which is almost as troubled), it isn't very "hot" either.

Many potential GUTs, including the most minimal SU(5) GUT, would (1) imply violations of baryon number and/or lepton number conservation that aren't observed (e.g. proton decay, flavor changing neutral currents, and neutrinoless double beta decay), (2) lack some fundamental particles that are observed in the Standard Model, or (3) imply the existence of new fundamental particles beyond the Standard Model that haven't been observed (and in some cases, these particles have been ruled out to quite high energies). 

As a general rule, the bigger the Lie group of the unifying GUT, the more likely it is that it will imply far more new fundamental particles than there is any good reason to think that even a many particle dark sector should contain. Theoretical physicists prefer GUTs that imply as minimal an extension of the Standard Model as possible. Moreover, GUTs with certain kinds of new fundamental particles, such as those that imply more than three generations of fundamental Standard Model fermions, are strongly disfavored.

The experimental constraints on baryon number violating and lepton number violating processes (outside sphaleron interactions which are predicted in the Standard Model at extremely high energies but have not been observed) like proton decay, flavor changing neutral currents, and neutrinoless double beta decay are both very strict and very robust (i.e. they have been tested in multiple, independent ways). The exclusions of new fundamental particles are generally up to masses of several hundred to many thousands of GeVs, which is less strict, and the possibility of beyond the Standard Model fundamental particles is also strongly motivated (although not compelled) by the existence of dark matter phenomena. 

In the early days of GUT theories, a much sought after GUT property was that the three Standard Model forces unify at high enough energies in a manner that echos electroweak unification theory (which was one of the very attractive features of supersymmetry theory). But this has also been elusive. 

The Standard Model beta functions of the three Standard Model forces (electromagnetism, the weak force, and the strong force), which govern how the strength of these forces change with energy scale, extrapolated to arbitrarily high energy scales, based upon data all of the way up to the energy scales that can be reached by the Large Hadron Collider a.k.a. LHC (the highest energy scale high energy physics experiment every conducted), never unify. So, if a GUT the unifies the three Standard Model forces exists is some high energy scale, this must be due to new physics at energy scales above those that can be experimentally probed so far that is outside the domain of applicability of the Standard Model. 

Basically, given the energy scales that have already been reached by the LHC, energies at which the three Standard Model force could possibly unify haven't been present anywhere in the universe since some fraction of a second elapsed after the Big Bang. Of course, it is entirely possible that the three Standard Model forces simply don't unify at any energy scale that has ever existed or ever could exist.

Under a reasonable set of ab-initio assumptions, we define and chart the atlas of simple gauge theories with families of fermions whose masses are forbidden by gauge invariance. We propose a compass to navigate the atlas based on counting degrees of freedom. When searching for Grand-unification Theories with three matter generations, the free energy singles out the SU(5) Georgi-Glashow model as the minimal one, closely followed by SO(10) with spinorial matter. The atlas also defines the dryland of grand-unifiable gauge extensions of the standard model. We further provide examples relevant for gauge dual completions of the standard model as well as extensions by an additional SU(N) gauge symmetry.

Giacomo Cacciapaglia, Aldo Deandrea, Konstantinos Kollias, Francesco Sannino, "Grand-unification Theory Atlas: Standard Model and Beyond" arXiv:2507.06368 July 8, 2025).

The final paragraph of the conclusion of the main paper also enumerates some limitations on this paper serving as a truly comprehensive list of possibilities:

We have not considered yet scalar fields, as their mass cannot be prevented by any symmetry. Including spontaneous symmetry breaking of the gauge symmetry and generation of Yukawa couplings could imprint further constraints on the atlas, providing a phenomenological compass to navigate us towards the optimal high-energy theory. In our analysis, asymptotic freedom plays a crucial role in counting the degrees of freedom of each theory.

Non-Linear Cosmology Dynamics

Assuming the data has a Gaussian distribution (i.e. is distributed in a "normal" probability curve) is often reasonable, since this is what happens when data comes from independent simple percentage probability events. And, it is a convenient assumption when it works, because mathematically it is much easier to work with Gaussian distributions than most other probability distributions. But, sometimes reality is more complicated than that and this assumption isn't reasonable. 

The supernova data used to characterize dark energy phenomena isn't Gaussian. 

Trivially, this means that statistical uncertainty estimates based upon Gaussian distributions overestimate the statistical significance of observations in the fat tailed t-distribution. 

Non-trivially, this means that the underlying physics of dark matter phenomena are more mathematically complex than something like Newtonian gravity (often assumed for astronomy purposes as a reasonable approximation of general relativity) or a simple cosmological constant. Simple cosmology models don't match the data. 

This paper estimates dark energy parameters for more complex dark energy models that can fit the data.

Type Ia supernovae have provided fundamental observational data in the discovery of the late acceleration of the expansion of the Universe in cosmology. However, this analysis has relied on the assumption of a Gaussian distribution for the data, a hypothesis that can be challenged with the increasing volume and precision of available supernova data. 

In this work, we rigorously assess this Gaussianity hypothesis and analyze its impact on parameter estimation for dark energy cosmological models. We utilize the Pantheon+ dataset and perform a comprehensive statistical, analysis including the Lilliefors and Jarque-Bera tests, to assess the normality of both the data and model residuals. 

We find that the Gaussianity assumption is untenable and that the redshift distribution is more accurately described by a t-distribution, as indicated by the Kolmogorov Smirnov test. Parameters are estimated for a model incorporating a nonlinear cosmological interaction for the dark sector. The free parameters are estimated using multiple methods, and bootstrap confidence intervals are constructed for them.

Fabiola Arevalo, Luis Firinguetti, Marcos Peña, "On the Gaussian Assumption in the Estimation of Parameters for Dark Energy Models" arXiv:2507.05468 (July 7, 2025).

Steppe Ancestry In Italy

Blonde hair percentages, at a population statistics level, is a good proxy for Indo-European steppe ancestry levels (it's not as good as autosomal DNA, but the sample size and amount of fine grained geographic detail is much better). You'd need an estimate for the amount of steppe ancestry in Italians to calibrate this litmus test, however.

The first farmers of Europe had essentially 0% blonde hair, much like modern Sardinians, who are their closest genetic match. Blonde hair in Europe arrived more or less exclusively via steppe migration in late Neolithic to early Bronze Age from an ultimate homeland in the vicinity of modern Ukraine, although plenty of migration happened within Europe after this migration and not all steppe migrants had blonde hair. It is also possible to have very little steppe ancestry while still having the blonde hair gene. 

The chart shows the percentage of blond haired people in the regions shown on the map in (or near) Italy. Overall, about 8% of Italians are naturally blonde (another estimate suggests 15%). It suggests that Indo-European migration to Italy was largely north to south (with exceptions for urban centers) and reached southern Italy in far smaller proportions than northern Italy, although it is hard to know how much of the migration was modern, how much was medieval, how much was from the Roman era, and how much dates to pre-history.

Until the late 1870s, Italy was not a unified country, with Southern Europe belonging to the poorer Kingdom of the Two Sicilies with a more agricultural economy, and Northern Europe belonging to a number of smaller and more prosperous states with more mercantile economies, which could have impacted migration patterns by increasing migration from areas with more blonde people. 

From Reddit.

In the medieval era Northern Europeans, including the Normans and Vikings and Germanic tribes, had greater interactions with Northern Italy than with Southern Italy, as well. 

In the Roman era, migration to the Roman capital and its major cities from North Africa, Egypt, and the Levant might have diluted the percentage of people with steppe ancestry.

Shortly before the classical Roman era, there were a number of Greek colonies in Italy, which could be reflected in the purple regions on the map (about 4% of Greeks are naturally blonde), with some blurring out due to admixture with regions near former Greek colonies.

From Wikipedia.

A New Strong Force Coupling Constant Determination

The Particle Data Group value for the strong force coupling constant is 0.1180 ± 0.0009. This new determination, based upon earlier runs of LHC dijet data and lower energy HERA data, is consistent with the PDG value at the 0.1 sigma level. 

The strong force coupling constant is pervasively important in almost all high energy physics calculations, but it known much less precisely (with just one part per 131 parts precision) than most other Standard Model or fundamental physical constants. So, pinning this down more precisely is always big deal.

The beta function that describes how the strong force coupling constant runs with energy scale is an exact theoretical prediction of the Standard Model, with no experimental uncertainties. The conference presentation's confirmation that the strong force coupling constant runs with energy scale just as predicted in the Standard Model, over four orders of magnitude of energy scale, is arguably an even more important confirmation of the Standard Model, because there are fewer experimental confirmations of this in the literature.

In this talk we present a determination of the strong coupling constant αs and its energy-scale dependence based on a next-to-next-to-leading order (NNLO) QCD analysis of dijet production. 

Using the invariant mass of the dijet system to probe αs at different scales, we extract a value of αs(mZ) = 0.1178 ± 0.0022 from LHC dijet data. 

The combination of various LHC datasets significantly extends the precision and scale reach of the analysis, enabling the first determination of αs up to 7 TeV. By incorporating dijet cross sections from HERA, we further probe αs at smaller scales, covering a kinematic range of more than three orders of magnitude. Our results are in excellent agreement with QCD predictions based on the renormalization group equation, providing a stringent test of the running of the strong coupling across a wide energy range.

João Pires, "Precision determination of αs from Dijet Cross Sections in the Multi-TeV Range" arXiv:2507.01670 (July 2, 2025) (Contribution to the 2025 QCD session of the 59th Rencontres de Moriond).

A New Relativistic Generalization Of MOND (And More)

This six page article is just a conference paper summary of a much more involved modified gravity theory and its implications. The abstract is silent on how well it handles galaxy cluster physics, which deviate (in a quite systemic way) from simple toy-model MOND theories, or the Hubble tension.

We propose an alternative scalar-tensor theory based on the Khronon scalar field labeling a family of space-like three-dimensional hypersurfaces. This theory leads to modified Newtonian dynamics (MOND) at galactic scales for stationary systems, recovers GR plus a cosmological constant in the strong field regime, and is in agreement with the standard cosmological model and the observed cosmic microwave background anisotropies.

Luc Blanchet, Constantinos Skordis, "Khronon-Tensor theory reproducing MOND and the cosmological model" arXiv:2507.00912 (July 1, 2025) (Contribution to the 2025 Gravitation session of the 59th Rencontres de Moriond).

A fuller explanation of the theory can be found here.

Another lengthy paper by P. S. Bhupal Dev et al., examines the constraints dark matter-neutrino interactions which are very strict.

We present a comprehensive analysis of the interactions of neutrinos with the dark sector within the simplified model framework. We first derive the exact analytic formulas for the differential scattering cross sections of neutrinos with scalar, fermion, and vector dark matter (DM) for light dark sector models with mediators of different types. We then implement the full catalog of constraints on the parameter space of the neutrino-DM and neutrino-mediator couplings and masses, including cosmological and astrophysical bounds coming from Big Bang Nucleosynthesis, Cosmic Microwave Background, DM and neutrino self-interactions, DM collisional damping, and astrophysical neutrino sources, as well as laboratory constraints from 3-body meson decays and invisible Z decays. 

We find that most of the benchmarks in the DM mass-coupling plane adopted in previous studies to get an observable neutrino-DM interaction effect are actually ruled out by a combination of the above-mentioned constraints, especially the laboratory ones which are robust against astrophysical uncertainties and independent of the cosmological history. 

To illustrate the consequences of our new results, we take the galactic supernova neutrinos in the MeV energy range as a concrete example and highlight the difficulties in finding any observable effect of neutrino-DM interactions. 

Finally, we identify new benchmark points potentially promising for future observational prospects of the attenuation of the galactic supernova neutrino flux and comment on their implications for the detection prospects in future large-volume neutrino experiments such as JUNO, Hyper-K, and DUNE. We also comment on the ultraviolet-embedding of the effective neutrino-DM couplings.