A Covariant Viscoelastic Spacetime Origin of the Galactic Acceleration Relation (A Single-Parameter Model of Gravitational Memory in Spacetime)

We propose a macroscopic framework in which spacetime behaves as a viscoelastic mediumpossessing causal gravitational memory. Gravitational dynamics depend not only on the instantaneous distribution of mass–energy but also on accumulated spacetime deformation. Themodel is governed by a single universal relaxation timescale τ = C/H. We construct a covariantextension of general relativity incorporating a memory stress–energy tensor and demonstraterecovery of Einstein gravity in the short-memory limit. The framework reproduces flattenedgalaxy rotation curves, modifies cosmological expansion, and predicts scale-dependent structureformation using a single parameter. We present observational tests using galaxy rotation curvesand discuss implications for cosmology and gravitational lensing.