On the Effect of Hubble Expansion on Wide Binary and Spiral Galaxy Rotation Flattening During and After Cosmic Deceleration-to-Acceleration Crossover

The discovery of cosmic acceleration advances space-time theory and serves to resolve the tension between dark matter and modified gravity. An initial advance from the discovery is the inward-infinite light-speed stipulation within the Hubble expansion that reveals increasing lookback-time dilation which, upon rotation into epochal space-time, gives agreement with observed cosmic acceleration in the local universe. The present work helps resolve the DM vs modified gravity tension by more deeply deriving, to leading order, a relativistic inverse-radius (subfield) gravitation in a spiral galaxy—by joining the lookback and Schwarzschild time-dilations within the Lorentz transformation—thereby determining the asymptotic/flattened rotation speed for comparison with the Tully-Fisher relation. In the first of two derivations, subfield gravity is derived within the deceleration-to-acceleration crossover, wherein the crucial H(r)=r₀H₀/r relation is justified and employed. The same equation is derived in the current universe, starting with the lookback-time equation and again evoking the Lorentz transformation to neglect order (rH/c)² terms. Far field orbital-speeds for spiral galaxies agree with the Tully-Fisher relation, and accord with observations of wide-binary rotation speeds.