This is another possible explanation for dark matter phenomena. It makes some big claims. It will take time and some examination to determine if these claims about this novel approach hold up to further scrutiny (it probably doesn't). It also purports to explain dark energy phenomena.

We first briefly review the adventure of scale invariance in physics, from Galileo Galilei, Weyl, Einstein, and Feynman to the revival by Dirac (1973) and Canuto et al. (1977).

We then gather concrete observational evidence that scale-invariant effects are present and measurable in astronomical objects spanning a vast range of masses (0.5 M⊙< M <10^14 M⊙) and an equally impressive range of spatial scales (0.01 pc < r < 1 Gpc).

**Scale invariance accounts for the observed excess in velocity in galaxy clusters with respect to the visible mass, the relatively flat/small slope of rotation curves in local galaxies, the observed steep rotation curves of high-redshift galaxies, and the excess of velocity in wide binary stars with separations above 3000 kau found in Gaia DR3.**

Last but not least, we investigate the effect of scale invariance on gravitational lensing. **We show that scale invariance does not affect the geodesics of light rays as they pass in the vicinity of a massive galaxy. However, scale-invariant effects do change the inferred mass-to-light ratio of lens galaxies as compared to GR. **As a result, the discrepancies seen in GR between the total lensing mass of galaxies and their stellar mass from photometry may be accounted for. This holds true both for lenses at high redshift like JWST-ER1 and at low redshift like in the SLACS sample.

**Of note is that none of the above observational tests require dark matter or any adjustable parameter to tweak the theory at any given mass or spatial scale.**

Andre Maeder, Frederic Courbin, "A Survey of Dynamical and Gravitational Lensing Tests in Scale Invariance: The Fall of Dark Matter?" arXiv:2410.21379 (October 28, 2024) (accepted in "Symmetry").

Sabine Hossenfelder, at her blog, give the paper a thumbs down:

From what I gather from Maeder’s list of publications, he’s an astrophysicist who recently had the idea to revolutionize cosmology by introducing a modification of general relativity. The paper which now makes headlines studies observational consequences of a model he introduced in January and claim to explain away the need for dark matter and dark energy. Both papers contain a lot of fits to data but no consistent theory. Since the man is known in the astrophysics community, however, **the papers got published in ApJ, one of the best journals in the field.**

**For those of you who merely want to know whether you should pay attention to this new variant of modified gravity, the answer is no. The author does not have a consistent theory. The math is wrong.**

For those of you who understand the math and want to know what the problem is, here we go.

Maeder introduces a conformal prefactor in front of the metric. You can always do that as an ansatz to solve the equations, so there is nothing modified about this, but also nothing wrong. He then looks at empty de Sitter space, which is conformally flat, and extracts the prefactor from there.

He then uses the same ansatz for the Friedmann Robertson Walker metric (eq 27, 28 in the first paper). Just looking at these equations you see immediately that they are underdetermined if the conformal factor (λ) is a degree of freedom. That’s because the conformal factor can usually be fixed by a gauge condition and be chosen to be constant. That of course would just give back standard cosmology and Maeder doesn’t want that. So he instead assumes that this factor has the same form as in de Sitter space.

Since he doesn’t have a dynamical equation for the extra field, my best guess is that this effectively amounts to choosing a weird time coordinate in standard cosmology. If you don’t want to interpret it as a gauge, then an equation is missing. Either way the claims which follow are wrong. I can’t tell which is the case because the equations themselves just appear from nowhere. Neither of the papers contain a Lagrangian, so it remains unclear what is a degree of freedom and what isn’t. (The model is also of course not scale invariant, so somewhat of a misnomer.)

Maeder later also uses the same de Sitter prefactor for galactic solutions, which makes even less sense. You shouldn’t be surprised that he can fit some observations when you put in the scale of the cosmological constant to galactic models, because we have known this link since the 1980s. If there is something new to learn here, it didn’t become clear to me what.

Maeder’s papers have a remarkable number of observational fits and pretty plots, which I guess is why they got published. He clearly knows his stuff. He also clearly doesn’t know a lot about modifying general relativity. But I do, so let me tell you it’s hard. It’s really hard. There are a thousand ways to screw yourself over with it, and Maeder just discovered the one thousand and first one.

Please stop hyping this paper.

Her concerns are duly noted and are probably correct.