Finite Relaxation Geometry: Spacetime Relaxation as the Origin of Dark-Sector Phenomena

Modern cosmology faces several persistent challenges, including the physical origin of dark matter, the nature of dark energy, and empirical regularities observed in galactic dynamics. These phenomena are commonly interpreted through additional matter components or modifications of gravitational theory.

In this work we develop Finite Relaxation Geometry (FRG), a theoretical framework in which spacetime curvature responds to matter with a finite relaxation timescale rather than instantaneously. This dynamical response introduces geometric memory into spacetime and modifies gravitational behavior in weak-field and cosmological regimes.

Within this framework, several phenomena traditionally attributed to the dark sector acquire a unified geometric interpretation. MOND-like galactic dynamics and empirical relations observed in galaxies can emerge from geometric relaxation in low-acceleration regimes, while galactic halos may reflect accumulated curvature memory. On cosmological scales, the observed acceleration of the Universe appears as a large-scale limit of geometric relaxation.

Finite Relaxation Geometry therefore provides a dynamical spacetime framework in which multiple dark-sector phenomena can arise from the finite relaxation of spacetime geometry itself.