Is Milgrom's Constant Really Constant?

Reductionist physicists always like to derive physical constants, rather than than simply measure them. This paper proposes a way to do so for modified gravity in a MOND-like theory, expanding the theory's domain of applicability to galaxy clusters while sacrificing the universality of Milgrom's constant, a(0). 

It also hints, as Deur explicitly concludes, that MOND-like effects may be influenced by the extent to which a matter distribution is (or is not) spherically symmetric, and provides a mechanism to explain why MOND-like effects arise.

Modified Newtonian Dynamics (MOND) generally resolves the need for dark matter in galaxy rotation curves introducing a single new constant of acceleration a(0). It is well known that increasing a(0) by a factor of a few can alleviate the residual mass discrepancies that MOND leaves in galaxy clusters. 

Within a parameter-free Machian interpretation of MOND, in which a(0) ∼ GM(u)/R(u)^2 arises from the scalar sum of inverse-square distance gravitational mass contributions in the universe, we promote a(0) to a variable influenced by mass external to a locally enclosed region in the spherically symmetric case. 

Instead of a boost of a(0) in terms of gravitational potentials as in EMOND, we show that a boost in terms of this directionless inverse-square field roughly amounts to the boost needed to accommodate the mass discrepancies of MOND in galaxy clusters. We conclude by beginning to generalize the proposed formulation beyond spherical symmetry.

Manuel Uruena Palomo, Juan David Santander, "Machian MOND: a variable a0 in galaxy clusters" arXiv:2608.04894 (August 5, 2026) (published version in International Journal of Modern Physics D).

Cloud-9

A hydrogen gas cloud, called Cloud-9, that has been observed in deep space in the radio wave frequency, which cannot be seen in the visible light spectrum provides a way to distinguish between different dark matter hypotheses and while the paper below doesn't consider it, between modified gravity theories and dark matter hypotheses.

Starless gas clouds provide a new way to test gravitational dynamics and this is just the first examination of many to come.

Between cold dark matter and self-interacting dark matter, the observations strongly favor self-interacting dark matter, although neither hypothesis is a great fit.

Recently, the Five-hundred-meter Aperture Spherical Telescope discovered a gas-rich hydrogen cloud near M94 in the 21cm band. Lacking an optical counterpart, this object, dubbed Cloud-9, has been identified as a compelling Reionization Limited H Cloud (RELHIC). RELHICs provide exceptionally clean laboratories for probing dark matter, free from the baryonic complexities associated with star formation and feedback. 

We show that the observed hydrogen column density profile of Cloud-9 is consistent with a gas cloud embedded in either a cuspy halo predicted by the standard cold dark matter (CDM) model or a cored halo produced by self-interacting dark matter (SIDM). 

In both cases, the halo must have an unusually diffuse central density. The best-fitting CDM halo lies around 7σ below the cosmological concentration--mass relation, whereas SIDM core-forming halos reduce the tension to only around 3σ. 

We further identify Cloud-9 analogs in the Concerto suite of cosmological zoom-in simulations with velocity-dependent SIDM, demonstrating that RELHICs provide a promising new probe of dark matter self-interactions.

Morgan Ohana, Xingyu Zhang, Hai-Bo Yu, "Cold Dark Matter and Self-Interacting Dark Matter Interpretations of Cloud-9" arXiv:2608.04362 (August 5, 2026).

Meanwhile, another new paper finds that the tight relationship between the distribution of baryonic matter and galactic rotation curves has held true for as far back as at least z=0.42 (i.e. 4.4 billion years ago) with astronomy data.

The Baryonic Tully-Fisher relation (BTFR) is one of the tightest scaling relations for disk galaxies in the local Universe, and therefore is an important tool for studying the fomation and evolution of galaxies. . . . 

A random forest classifier is used to investigate the origin of the outlier component. We find that low signal significance and inaccurate inclinations are the key factors that contribute to the outlier population, indicating that observational effects are the dominant origin. 

Evolutionary trends are examined in three different redshift bins. Both the slope and zero point show consistency within 1-σ uncertainty in the two low redshift bins, indicating no significant evolution.