Galaxy dynamics probes weak gravity at accelerations below the de Sitter scale of acceleration a _ { dS } = cH , where c is the velocity of light and H is the Hubble parameter .
Low and high redshift galaxies hereby offer a novel probe of weak gravity in an evolving cosmology , satisfying H ( z ) = H _ { 0 } \sqrt { 1 + \omega _ { m } ( 6 z + 12 z ^ { 2 } +12 z ^ { 3 } +6 z ^ { 4 } + ( 6 / 5 ) z ^ { 5 } ) } / ( 1 + z ) with baryonic matter content \omega _ { m } sans tension to H _ { 0 } in surveys of the Local Universe .
Galaxy rotation curves show anomalous galaxy dynamics in weak gravity a _ { N } < a _ { dS } across a transition radius r _ { t } = 4.7 \mbox { kpc } M _ { 11 } ^ { 1 / 2 } ( H _ { 0 } / H ) ^ { \frac { 1 } { 2 } } in galaxies of mass M = 10 ^ { 11 } M _ { \odot } M _ { 11 } , where a _ { N } is the Newtonian acceleration based on baryonic matter content .
We identify this behavior with a holographic origin of inertia from entanglement entropy , that introduces a C ^ { 0 } onset across a _ { N } = a _ { dS } with asymptotic behavior described by a Milgrom parameter satisfying a _ { 0 } = \omega _ { 0 } / 2 \pi , where \omega _ { 0 } = \sqrt { 1 - q } H is a fundamental eigenfrequency of the cosmological horizon .
Extending an earlier confrontation with data covering 0.003 \lesssim a _ { N } / a _ { dS } \lesssim 1 at redshift z \sim 0 in Lellie et al .
( 2016 ) , the modest anomalous behavior in the Genzel et al .
sample at redshifts 0.854 \leq z \leq 2.282 is found to be mostly due to clustering 0.36 \lesssim a _ { N } / a _ { dS } \lesssim 1 close to the C ^ { 0 } onset to weak gravity and an increase of up to 65 % in a _ { 0 } .