Scaling MOND with Z

The MOND acceleration scale as the cosmic dynamical acceleration: a scaling–MOND cosmology and its bridges to the dark sector

We examine the proposal that the Milgromian acceleration scale is the cosmic dynamical acceleration, a₀ = c²√(Gρ_c) = cH(z)/Z with Z = 2√(8π/3) ≈ 5.789. The evolving‑scale hypothesis itself is Milgrom's (2014); our contribution is an explicit covariant realization of it and a proof of its CMB‑safety. Algebraically a₀ = cH/Z re‑expresses the long‑known coincidence a₀ ≈ cH₀ through the Friedmann relation; its coefficient‑free consequence is that the scale evolves, a₀(z) = a₀(0) E(z). Fitting a₀ ∝ E(z)^p to the recent compilation (SPARC; Vărăşteanu 2025; MUSE–DARK III 2026) gives p = 0.80 ± 0.17; constant a₀ is excluded at 5σ in the nominal fit, but a jackknife and an inter‑method systematic (the 1.7σ discrepancy between the two near‑coincident local anchors) reduce this to ≈ 2σ, so we treat the trend as a suggestive hint, not a detection. Working from the Aether–Scalar–Tensor (AeST) action we promote the scale to the aether expansion, a₀ = cθ/(3Z), and show by order‑counting—reinforced by the identity δq⁰⁰ = 0 that survives perturbing the aether itself—that a₀ is absent from the linear cosmological perturbations; the running therefore leaves the linear CMB and P(k) exactly invariant, which we confirm by direct integration of the Einstein–Boltzmann system (r_s = 144.3 Mpc, ℓ_A = 301.7). We are explicit about the boundaries: the O(1) coefficient Z is a posit; the Standard‑Model constants do not follow; and the apparent‑a₀ evolution is itself reproduced by ΛCDM hydrodynamic simulations, so the amplitude alone does not discriminate. The one prediction that does—a redshift‑weakening external field effect, η = g_ext/a₀(z) ∝ 1/E(z), distinct from both ΛCDM and constant‑a₀ MOND—is forecast to require a dedicated z ≳ 4 campaign.