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 a0 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 a0(z)=A(1+z)γ as the primary statistic. We find γ=0.78±0.15 (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, a0(z)∝ H(z), with effective exponent γ≃1.10, is consistent with the measurement within 2.1σ and is the information-criterion-preferred one-parameter description; its amplitude, A=(1.40±0.03)×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 a0, and hence robust to common-mode stellar-mass systematics. At current precision, the long-noted coincidence a0∼ cH0 survives its first confrontation with direct kinematic measurements at intermediate redshift.
Versions
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BibTeX
@misc{alcock2026acceleration,
title = {{Is the acceleration scale of the radial acceleration relation tracking the cosmic expansion rate?}},
author = {G. T. Alcock},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.38796},
eprint = {2609.38796},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.38796},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Is the acceleration scale of the radial acceleration relation tracking the cosmic expansion rate?
AU - G. T. Alcock
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.38796
UR - https://arxiv.org/abs/2609.38796
AB - 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±0.15 (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)∝ H(z), with effective exponent γ≃1.10, is consistent with the measurement within 2.1σ and is the information-criterion-preferred one-parameter description; its amplitude, A=(1.40±0.03)×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∼ cH_0 survives its first confrontation with direct kinematic measurements at intermediate redshift.
ER -