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.
