Geodesics in quantum gravity Missing Link

[kodama]

TL;DR

a quantum mechanical reason

​

what do you think of the relationship between the cosmology constant and MOND ao, coincidence that they are close or a quantum mechanical reason​

Sabine Hossenfelder, think that

Physicists Find Missing Link Between Quantum Mechanics and Gravity​

reference

Physical Review D​

Geodesics in quantum gravity​

Benjamin Koch1,2,3,*, Ali Riahinia1,2,†, and Angel Rincon4,‡
Phys. Rev. D 112, 084056 – Published 22 October, 2025

DOI:https://doi.org/10.1103/w1sd-v69d

could explain why

comment ?

 

[PeterDonis]

what do you think of the relationship between the cosmology constant and MOND ao, coincidence that they are close or a quantum mechanical reason

It's one of many quantum gravity speculations that are open areas of research. It's much too early to be able to give any definite opinion on how any such speculations will turn out.

 

[ChrisF]

● The closeness of a₀ and Λ-derived quantities isn't coincidence — it's been noted explicitly in the literature. Milgrom himself pointed out that a₀ ~ cH₀, which connects MOND's critical acceleration directly to the cosmological
expansion rate. Since in ΛCDM the cosmological constant satisfies Λ ~ 3H₀²/c², both a₀ and Λ trace back to the same cosmological scale H₀. The "coincidence" is really two phenomena sharing a common origin in whatever sets H₀.

The interesting question is whether that shared origin is dynamical or fundamental. If H₀ is just a boundary condition of this particular universe, then the Λ-a₀ relationship is environmental. If H₀ is set by something deeper — vacuum
properties, quantum geometry — then both Λ and a₀ are expressions of that deeper thing and their ratio should be derivable rather than tuned.

The Koch et al. geodesic paper is relevant here. If quantum corrections to geodesic motion generate effective acceleration terms at scales ~ c²√Λ, that would naturally produce a₀-scale physics from Λ without any separate MOND
postulate. That's a genuine structural connection, not a numerical coincidence.

Whether it's quantum mechanical in origin is the real question and the answer depends entirely on what sets Λ. That's unsolved.

 

[PeterDonis]

which connects MOND's critical acceleration directly to the cosmological
expansion rate.

By $H_0$ do you mean the present expansion rate? Or the "expansion rate" derived from the estimated value of $\Lambda$? In the literature $H_0$ usually means the former, but you seem to be using it as though it referred to the latter.

 

[ChrisF]

By $H_0$ do you mean the present expansion rate? Or the "expansion rate" derived from the estimated value of $\Lambda$? In the literature $H_0$ usually means the former, but you seem to be using it as though it referred to the latter.

The measured present value — Milgrom's original observation is a₀ ~ cH₀ using the observed expansion rate. The connection to Λ is then one step indirect: in flat ΛCDM, Λ = 3H_Λ²/c² where H_Λ = H₀√Ω_Λ ≈ 0.84 H₀. So a₀ ~ cH₀ implies a₀
~ c√(Λ/3) to within that same factor. The coincidence holds either way but you're right that they're not the same quantity — H₀ is the cleaner statement since it's directly observed rather than derived from a model-dependent Λ estimate.

 

[PeterDonis]

The measured present value

Then the connections you are talking about are only valid now; they're not generally true.

The connection to Λ is then one step indirect

If you want to look at it that way. But the more important point is that it's only valid now; it's not generally true. $H$ changes with time, but $H_\Lambda$ does not.

 

[ChrisF]

Then the connections you are talking about are only valid now; they're not generally true.


If you want to look at it that way. But the more important point is that it's only valid now; it's not generally true. $H$ changes with time, but $H_\Lambda$ does not.

That's a fair and important distinction. You're right — within ΛCDM, H(t) is time-varying and Λ is not, so any relationship built on H₀ specifically is epoch-dependent, not fundamental. Milgrom noted the numerical coincidence but the problem you're identifying — why now? — is real and known in the literature as the MOND coincidence problem.

The cleaner version of the connection, if one exists, would have to be a₀ ~ c√(Λ/3), which IS constant since Λ doesn't evolve. That's numerically similar to cH₀ right now — since H_Λ = H₀√Ω_Λ ≈ 0.84H₀ today — but the two diverge over cosmic time. Whether a₀ is actually tied to Λ directly rather than to the present H is an empirical question: if a₀ tracks H(t) as the universe evolves, it's dynamical. If it stays fixed while H changes, it points to Λ or something equally constant as the underlying quantity.