Galaxy rotation curves and the deceleration parameter in weak gravity

We present a theory of weak gravity parameterized by a fundamental frequency ${\omega }_0=\sqrt{1-q}H$ of the cosmoloogical horizon, where $H$ and $q$ denote the Hubble and, respectively, deceleration parameter. It predicts (i) a $C^0$ onset to weak gravity across accelerations $\alpha =a_{dS}$ in galaxy rotation curves, where $a_{dS}=cH$ denotes the de Sitter acceleration with velocity of light $c$, and (ii) fast evolution $Q(z)=dq(z)\mathrm{/}dz$ of the deceleration parameter by $\mathrm{\Lambda }={\omega }_0^2$ satisfying $Q_0>2.5$, $Q_0=Q(0)$, distinct from $Q_0\lesssim 1$ in $\mathrm{\Lambda }$CDM. The first is identified in high resolution data of Lellie et al.(2017), the second in heterogeneous data on $H(z)$ over $0<z<2$. A model-independent cubic fit in the second rules out $\mathrm{\Lambda }$CDM by $4.35\sigma$ and obtains $H_0=74.0\pm 2.2$ km s${}^{-1}$ Mpc${}^{-1}$ consistent with Riess et al. (2016). Comments on possible experimental tests by the LISA Pathfinder are included.