A Covariant Viscoelastic Spacetime Framework with Gravitational Memory (no Figure)

Galaxy rotation curves have long revealed a discrepancy between the observed gravitational acceleration in galaxies and that predicted from the distribution of baryonic matteralone. Traditionally, this discrepancy has been interpreted as evidence for dark matter halossurrounding galaxies. However, extensive observational studies have uncovered a remarkably tight correlation between the baryonic acceleration and the observed total acceleration,known as the radial acceleration relation (RAR). The universality and small scatterof this relation suggest the existence of a fundamental acceleration scale governing galacticdynamics.In this work we propose that this acceleration scale emerges from a viscoelastic response of spacetime itself. In the proposed framework spacetime behaves as a mediumwith a finite relaxation timescale determined by cosmological expansion. The relaxation timeis given byτ = κ/H,where H is the Hubble parameter and κ is a dimensionless constant characterizing theviscoelastic properties of spacetime. This relaxation leads to a delayed gravitational responsethat manifests as an additional acceleration component at galactic scales.Within this framework a characteristic acceleration scale naturally arises,amem = κcH0/2π ,which links galactic dynamics directly to the cosmic expansion rate. We show that thismechanism simultaneously reproduces three key observational relations in disk galaxies: theradial acceleration relation (RAR), the shapes of galaxy rotation curves, and the baryonicTully–Fisher relation (BTFR). These results suggest that the observed galactic accelerationscale may originate from a fundamental dynamical property of spacetime rather than fromparticle dark matter