Does the galactic acceleration scale follow the cosmic age? A registered prediction, a0 ∝ 1/t, confronted with rotation curves at z = 1-2

Abstract

The radial acceleration relation of disc galaxies has one scale, a0 ≈ 1.2 × 10⁻¹⁰ m s⁻², numerically close to cH0/2π. This record fixes one law for its evolution before the comparisons reported here (the data sets were already known): CT1, a0(z)/a0(0) = t0/t(z), with t the cosmic age computed from the expansion history of MM 2.32 (8896 samples). CT1 predicts a0 larger by 2.35 at z = 1 and 4.18 at z = 2; the same clock in ΛCDM differs by 0.35 % at z = 2, so the test concerns the clock, not the MM cosmology. Alternatives on the same background: a constant a0 and a0 ∝ H. Four published data sets are used. RC100 (Nestor Shachar et al. 2023) at z ≥ 2: the dark-matter fraction at the effective radius predicted from the kinematics is 0.24 with a constant a0 and 0.63 with CT1, against 0.26 published. MUSE-DARK II (z ≈ 1): no evolution of the baryonic Tully-Fisher zero point (0.00 ± 0.06 dex), where CT1 predicts −0.26 to −0.32 dex in the low-acceleration regime assumed. KMOS3D: the zero point rises by +0.17 ± 0.06 dex from z ≈ 0.9 to 2.3, which the fixed-regime model does not reproduce for any law. MUSE-DARK III (four bins at z = 0.5-1.3, read from the published figure): a0 grows with redshift and a constant a0 is the worst law; with the local calibration frozen, CT1 has a better nominal statistic than a0 ∝ H, but its growth is steeper than that of the bins (1.75 against 1.36 between the last and first bin). CT1, as registered, is in tension with the first three comparisons: the mass shift that minimises its nominal χ² for RC100 at z ≥ 2 is about half the adopted baryonic mass, below the stellar mass at the central values for 26 galaxies out of 41, while gas measurements in similar populations point the other way. The tension is conditional on the published mass models; no joint likelihood with covariances has been built, and CT1 is not claimed to be excluded. The data sets are themselves in tension (RC100 at z ≈ 2 against the growth of MUSE-DARK III); their different mass normalisations are a possible explanation, not one isolated here. Protocols were written and hashed before each calculation; one registered expectation did not hold and one protocol contains an arithmetic error, both reported. The author is not a professional physicist; the framework and its premises are his. Computations were done with AI assistants (Claude and Codex); the second assistant reviewed the draft twice before publication and the corrections are listed in the package. All code is included; the five programs were re-run from scratch before deposit and reproduce the reference outputs identically.