Understand
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 $H(z)=H_0\sqrt{1+\omega_m(6z+12z^2+12z^3+6z^4+(6/5)z^5)}/(1+z)$ 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.