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 $a_0(z)=A(1+z)^γ$ as the primary statistic. We find $γ=0.78\pm0.15$ (statistical, plotted uncertainties read as $1σ$): a redshift-independent scale ($γ=0$) is excluded at $5.3σ$ by a nested test, and the matter-density scaling ($γ=3/2$) at $4.8σ$. Hubble tracking, $a_0(z)\propto H(z)$, with effective exponent $γ\simeq1.10$, is consistent with the measurement within $2.1σ$ and is the information-criterion-preferred one-parameter description; its amplitude, $A=(1.40\pm0.03)\times10^{-10}$ 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 $a_0\sim cH_0$ survives its first confrontation with direct kinematic measurements at intermediate redshift.