Self-similar galaxy dynamics below the de Sitter scale of acceleration

Radial accelerations $\alpha$ in galaxy dynamics are now observed over an extended range in redshift that includes model calculations on galactic distributions of cold dark matter (CDM) 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 effective self-similarity 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. SPARC, MUG2 and theory satisfy ${a_N}/{\alpha} \simeq 2.1\,\zeta^\frac{1}{2}$ $(\zeta <<1)$. At $\zeta=1$ in transition to Newtonian gravity ($\zeta>>1$), however, there is a $6\sigma$ gap between SPARC and MUGS2. This poses a novel challenge to CDM in $\Lambda$CDM against the apparent $C^0$ galaxy dynamics observed in SPARC. We attribute the latter to reduced inertia below the de Sitter scale of acceleration $(\zeta < 1)$, based on a causality constraint imposed by the cosmological horizon ${\cal H}$.