A new estimator of the deceleration parameter from galaxy rotation curves

The nature of dark energy may be probed by the derivative $Q=\left.dq(z)/dz\right|_0$ at redshift $z=0$ of the deceleration parameter $q(z)$. It is probably static if $Q<1$ or dynamic if $Q>2.5$, supporting $\Lambda$CDM or, respectively, $\Lambda=(1-q)H^2$, where $H$ denotes the Hubble parameter. We derive $q=1-\left(4\pi a_0/cH\right)^{2}$, enabling a determination of $q(z)$ by measurement of Milgrom's parameter $a_0(z)$ in galaxy rotation curves, equivalent to the coefficient $A$ in the Tully-Fisher relation $V^4_c=AM_b$ between rotation velocity $V_c$ and baryonic mass $M_b$. We infer that dark matter should be extremely light with clustering limited to the size of galaxy clusters. The associated transition radius to non-Newtonian gravity may conceivably be probed in a free fall Cavendish type experiment in space.