Is the acceleration scale of the radial acceleration relation tracking the cosmic expansion rate?

Abstract

The MUSE-DARK survey has reported a highly significant increase of the radial acceleration relation (RAR) scale $a_0$ with redshift over $0.33<z<1.44$, parametrized linearly and described by its authors as phenomenological. We confront the same binned measurements with physically motivated scalings, using the continuous family $a_0(z)=A(1+z{)}^{\gamma }$ as the primary statistic. We find $\gamma =0.78\pm 0.15$ (statistical, plotted uncertainties read as $1\sigma$): a redshift-independent scale ($\gamma =0$) is excluded at $5.3\sigma$ by a nested test, and the matter-density scaling ($\gamma =3/2$) at $4.8\sigma$. Hubble tracking, $a_0(z)\propto H(z)$, with effective exponent $\gamma \simeq 1.10$, is consistent with the measurement within $2.1\sigma$ and is the information-criterion-preferred one-parameter description; its amplitude, $A=(1.40\pm 0.03)\times 10^{-10}$ m s${}^{-2}$, lies 17 per cent above the canonical SPARC value, within the latter's systematic-dominated uncertainty. The survey's remark that the evolution is 'faster than $H(z)$' is shown to be anchor-dependent: relative to a floating amplitude the binned growth is, if anything, mildly shallower than $H(z)$. All exponent-based conclusions are invariant under redshift-independent rescalings of $a_0$, and hence robust to common-mode stellar-mass systematics. At current precision, the long-noted coincidence $a_0\sim c{H}_0$ survives its first confrontation with direct kinematic measurements at intermediate redshift.

4 pages, 1 figure, 2 tables. Published in Monthly Notices of the Royal Astronomical Society 551(4), 2026

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