A Covariant Viscoelastic Spacetime Framework with Gravitational Memory

We propose a covariant gravitational framework in which spacetime exhibits viscoelasticproperties and retains memory of past stress-energy configurations. The theory introducesa dynamical memory sector characterized by a relaxation timescale τ = C/H, leading toa nonlocal gravitational response at low accelerations while recovering general relativity inhigh-acceleration regimes.In the weak-field limit, the model predicts an enhanced gravitational response arisingfrom spacetime relaxation effects, naturally reproducing the observed flattening of galacticrotation curves without invoking non-baryonic dark matter. The framework also yieldsthe observed radial acceleration relation and the baryonic Tully–Fisher scaling as directconsequences of the memory response.At cosmological scales, the memory sector contributes an effective stress-energy component that modifies the expansion history. We test the model against cosmic microwavebackground observations and We show that the model can reproduce the qualitative acoustic peak structure of the Planck 2018 observations. Parameter constraints obtained fromMarkov Chain Monte Carlo analysis indicate that the viscoelastic parameters remain compatible with current observations without requiring fine tuning.