
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 accel- eration, a0 = c 2 √Gρc = 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) re- duce 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 (rs = 144.3 Mpc, ℓA = 301.7). We are explicit about the bound- aries: 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= gext/a0(z) ∝ 1/E(z), distinct f
COSMOLOGY, MOND
COSMOLOGY, MOND
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