A new estimator of the deceleration parameter from galaxy rotation curves

The nature of dark energy may be probed by the derivative $Q={dq(z)\mathrm{/}dz\mid }_0$ at redshift $z=0$ of the deceleration parameter $q(z)$. It is probably static if $Q<1$ or dynamic if $Q>2.5$, supporting $\mathrm{\Lambda }$CDM or, respectively, $\mathrm{\Lambda }=(1-q)H^2$, where $H$ denotes the Hubble parameter. We derive $q=1-{\left(4\pi a_0\mathrm{/}cH\right)}^2$, 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 $V_c^4=A{M}_b$ 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.