In the context of the equivalence principle, we resolve the lack of full correspondence in the behavior of light paths between accelerating and stationary gravitational frames. As a consequence, we postulate a moving `Acceleration Field Space’ (AFS), complementary to general relativity’s metric space. Free-falling objects that are mathematically considered as coming from infinity and travel along geodesics can be regarded as `stationary' in AFS, while the space itself moves past metric-stationary objects. Light always travels at the vacuum speed $c$ with respect to AFS. Clock recordings for light events are aligned in both the AFS and metric spaces, although spatial distances differ. We demonstrate that AFS behaves as a medium that influences redshift through its acceleration, distinguishing it from the ether concepts of the pre-relativity era. We also show that AFS is independent of arguments relying on the behavior of light. Unlike equal length paths in the metric description, in AFS, upward radial light path distances are greater than downward. We demonstrate that within AFS, gravitational time dilation can be interpreted as equivalent in mechanism to the cosmological redshift effect. This allows AFS to unify two previously distinct phenomena under a single theoretical construct: gravitational redshift, and cosmological redshift. We make a prediction linking black holes, dark matter and all gravitating bodies in the universe, to the density of dark energy. The proposed framework revises our understanding of spacetime structure and provides a single conceptual foundation for all three forms of the equivalence principle. We discuss the theoretical implications and testable predictions of the AFS model. Our results highlight the potential of AFS to enhance the metric space description, providing an intuitive understanding of gravitational phenomena, while remaining consistent with experimental results.