Self-similar behavior in galaxy dynamics and distributions of dark matter
Radial accelerations in galaxy dynamics are now observed over an extended range in redshift that includes model calculations in $\Lambda$CDM. In a compilation of data of the {\em Spitzer} Photometry and Accurate Rotation Curves (SPARC) catalogue, the recent sample of Genzel et al.(2017) and the McMaster Unbiased Galaxy Simulations 2, we report on self-similarity expressed in the variable $\zeta = a_N/a_{dS}$, given by the Newtonian acceleration $a_N$ based on baryonic matter content over the de Sitter scale of acceleration $a_{dS}=cH$, where $c$ is the velocity of light and $H$ is the Hubble parameter. At $\zeta=1$, smooth galaxy dynamics in $\Lambda$CDM models is found to be discrepant from the observed $C^0$ galaxy dynamics, marking the transition to anomalous dynamics in weak gravity $(\zeta<1)$ from Newtonian gravity ($\zeta\ge1$) by baryonic matter content. At a level of confidence of $6\sigma$, this poses a novel challenge to cold dark matter distributions on galactic scales models, here identified with a causality constraint on inertia imposed by the cosmological horizon.