径向加速度关系的加速度尺度是否追踪宇宙膨胀速率？
Is the acceleration scale of the radial acceleration relation tracking the cosmic expansion rate?
AI总结：
该研究检验MUSE-DARK巡天中径向加速度关系尺度随红移的演化，发现其与哈勃膨胀率一致，而非红移无关或物质密度标度，并确认$a_0\sim cH_0$的巧合在中介红移处成立。
AI中文摘要：
MUSE-DARK巡天报告了在0.33<z<1.44范围内径向加速度关系（RAR）尺度$a_0$随红移高度显著的增长，该增长被参数化为线性形式，并被其作者描述为唯象结果。我们将相同的分箱测量与物理动机的标度关系进行对比，采用连续族$a_0(z)=A(1+z)^{\gamma}$作为主要统计量。我们发现$\gamma=0.78\pm0.15$（统计误差，图中不确定性读作$1\sigma$）：红移无关的尺度（$\gamma=0$）被嵌套检验以$5.3\sigma$排除，物质密度标度（$\gamma=3/2$）以$4.8\sigma$排除。哈勃追踪，即$a_0(z)\propto H(z)$，其有效指数$\gamma\simeq1.10$，在$2.1\sigma$内与测量一致，并且是信息准则偏好的单参数描述；其振幅$A=(1.40\pm0.03)\times10^{-10}$ m s$^{-2}$，比标准SPARC值高17%，处于后者系统主导的不确定度范围内。该巡天关于演化“快于$H(z)$”的评论被证明依赖于锚点：相对于浮动振幅，分箱增长即使有，也只是略浅于$H(z)$。所有基于指数的结论在红移无关的$a_0$重新标度下不变，因此对共模恒星质量系统效应具有鲁棒性。在当前精度下，长期注意到的巧合$a_0\sim cH_0$在中介红移处首次与直接运动学测量的对抗中幸存下来。
英文摘要：
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.
