[podiki]

After a little more of a skim: the paper seems mostly to be about reproducing an equation like that of MOND (modified Newtonian dynamics). Which, fine, some people are fans of MOND (not most, and for good reason from the theoretical which this might address, to the practical like previous comment), but there's a whole lot more than just the dynamics of rotating galaxies to consider. Without even going into that (bullet cluster, lensing, n-body simulations, galaxy formation, etc.) it doesn't (yet?) replace anything.

[sigmoid10]

Most important is still the CMB. Back then everything was ionized and yet we have extremely good evidence of matter that only contributed gravitationally to density perturbations and not via the ordinary electromagnetic path. There is no way to explain this merely by modifying the law of gravity. So even if MOND or similar approaches turn out to be correct, they can never explain all aspects of dark matter. Only particles can.

[raattgift]

Sure, but the origin of this preprint is in the stochastic-classical/uncertain-quantum "postquantum-classical" theory the Oppenheim group is working on. Their theory is premised on a weakening of the gravitational interaction at short distances (it's "asymptotically free" and thus renormalizable) compared to perturbative quantum gravity (which is non-renormalizable by power counting). However, they discovered that the gravitational interaction in their theory can be too strong. More technically, in their diffusion limit they extract a different scalar potential than from GR's weak field limit, with the former growing (statistically) stronger with increasing radius. This in practice means even with a highly similar source, their theory predicts significantly different geodesics compared to General Relativity.

Rather than abandon the theory or complicate it such that it becomes compatible with fully classical GR, they solved a Schwarzschild-de Sitter (static spherical symmetry and an expansion term which "washes out" the extra-strength gravitational potential before it gets too strong) spacetime with a galactic mass (described simply and with some restrictions) and found that the geodesics are within a standard deviation or so of stable circular MONDian orbits. That result would relieve some of the immediate concern that their theory is unphysical, and drive them towards further study of its large-length-scale behaviour.

(In fact their result is better than some earlier attempts to make a generally covariant MOND by adding auxiliary gravitational fields to GR (see the overview by Famaey & McGaugh 2012). Postquantum-classical gravity was on a relativistic footing from the start, although exactly how diffeomorphism invariance and manifest covariance of formulations works in postquantum-classical gravity is really interesting, see <https://arxiv.org/abs/2402.17844> if you want details)

It would be interesting to see how their theory does does -- it would have to be studied numerically -- with any sort of CDM halo. Various stellar binaries are also an obvious place to look, since for sufficiently wide ones, you can't "wash out" the extra strength of the scalar potential with an expansion term. (Wide binaries are really rough on MOND too, for comparable reasons).

> it doesn't (yet?) replace anything

The authors know that. From just after Eqn (23) in the preprint <https://arxiv.org/abs/2402.19459>:

"While this study demonstrates that galactic rotation curves can undergo modification due to stochastic fluctuations, a phenomenon attributed to dark matter, it is important to acknowledge the existence of separate, independent evidence supporting ΛCDM. In particular, in the CMB power spectrum, in gravitational lensing, in the necessity of dark matter for structure formation, and in a varied collection of other methods used to estimate the mass in galaxies"