Does the Galactic Acceleration Scale Track H(z)? A direct comparison of the a₀–H coincidence with the first measurements of RAR evolution

Abstract

The galactic acceleration scale a₀ ≈ 1.2 × 10⁻¹⁰ m s⁻² numerically satisfies a₀ ≈ cH₀/2π to within ~10%, a coincidence noted since Milgrom (1983) and still unexplained. Milgrom has long drawn the consequence: if the link is to the expansion rate rather than to Λ alone, a₀ is not constant but decreases with cosmic time, and in the deep-MOND regime rotation velocities scale as a₀^(1/4). For a ΛCDM expansion history this fixes a specific curve, a₀(z) ∝ H(z), rising by 76% at z = 1 and by a factor 3 at z = 2. Until recently that curve was untested at the required precision. It is no longer. Ciocan et al. (2026) have measured the radial-acceleration-relation bend scale for 79 star-forming galaxies over 0.33 < z < 1.44 and find a₀ increasing with redshift at high significance. This note confronts the hypothesis with that measurement, and separates two questions that must not be conflated: whether a₀(z) follows the shape of H(z), and whether its normalisation is c/2π. The measured evolution disfavours a constant a₀ under the published modelling and calibration, and a uniform baryonic-mass recalibration cannot by itself account for the reported redshift trend; both non-evolving interpretations are therefore disfavoured under those assumptions. The tracks-H shape is not visibly ruled out by the binned estimates, but it has not been decisively tested against them, and the note states what such a test requires. The strict normalisation A = cH₀/2π is disfavoured under the published calibration, which implies H₀ ≈ 95 km s⁻¹ Mpc⁻¹; it is not excluded, since on deep-MOND scaling a uniform baryonic-mass offset of roughly 0.13 dex — smaller than the molecular-gas systematic alone — would restore it. No mechanism is proposed, and no part of the scaling is new: the hypothesis, its adiabatic justification and the a₀^(1/4) response are Milgrom's. What this note contributes is the confrontation itself — the separation of the two claims, the amplitude they jointly require, and an argument for why the two verdicts have different robustness against the calibration that dominates the measurement.