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)/dz|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 ΛCDM or, respectively, Λ = (1 − q)H, where H denotes the Hubble parameter. We derive q = 1 − (4πa0/cH), enabling a determination of q(z) by measurement of Milgrom’s parameter a0(z) in galaxy rotation curves, equivalent to the coefficient A in the Tully-Fisher relation V 4 c = AMb between rotation velocity Vc and baryonic mass Mb. 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.