Galaxy Rotation Curves and the Radial Acceleration Relation in Viscoelastic Spacetime Gravity

rkably tight correlation between baryonic matter and the observed gravitationalacceleration in galaxies. In the standard cosmological framework these phenomena areinterpreted as evidence for dark matter halos. In this work we investigate an alter-native explanation based on the viscoelastic spacetime framework with gravitationalmemory.In this theory spacetime behaves as a macroscopic viscoelastic medium whose re-laxation time is governed by the cosmological expansion rate, τ = κ/H. The delayedrelaxation of accumulated curvature strain generates an additional gravitational re-sponse in quasi-static systems such as galaxies.We show that the effective gravitational acceleration in galaxies can be describedby an emergent relation of the formgeff = gbar + √gbaramem exp−r gbaramem,where amem is a characteristic acceleration scale set by cosmology. This relationis not introduced as an empirical interpolation formula but emerges as the macro-scopic nonlinear limit of the modified Poisson equation associated with the viscoelasticmemory sector of spacetime.We compare the predictions of this framework with the observed radial accelera-tion relation and with galaxy rotation curves from the SPARC dataset. The resultsshow that the viscoelastic spacetime model naturally reproduces the observed scalingrelations without invoking particle dark matter halos.