Emergent Cosmic Acceleration from Viscoelastic Spacetime Relaxation

This work proposes a cosmological framework in which spacetime behaves as a viscoelastic medium possessing gravitational memory and relaxation dynamics. In this picture, the response of spacetime to the evolving matter distribution is not instantaneous but occurs with a finite relaxation timescale given byτ = κ / H,where H is the Hubble expansion rate and κ is a dimensionless relaxation constant characterizing the viscoelastic response of spacetime.The delayed relaxation of spacetime introduces an effective dynamical contribution to the cosmological expansion history. As a result, the observed accelerated expansion of the Universe can emerge naturally without invoking a fundamental cosmological constant or dark energy component. Numerical integration of the modified cosmological equations shows that the resulting expansion history closely follows the standard ΛCDM model at early times while producing late-time acceleration.An important consequence of this framework is the emergence of a direct connection between galactic dynamics and cosmology. The characteristic acceleration scale observed in galaxy rotation curves arises naturally from the cosmological expansion rate through the relationa₀ = κ c H₀ / (2π).The model predicts a present cosmic age of approximately 15–16 Gyr and provides a unified interpretation linking cosmic expansion, galactic acceleration relations, and the relaxation dynamics of spacetime within a single theoretical framework.