Galaxy Rotation Curves from Cumulative Background Effects in General Relativity

This record serves as an archival reference for a phenomenological study examining galaxy rotation curves within the framework of general relativity. The manuscript explores whether a slowly evolving cosmological background, motivated by the structure of the Friedmann equations, can contribute cumulatively to the effective dynamics of disk galaxies. Within an effective-potential description, such a background contribution can reproduce the flat features of observed galaxy rotation curves without invoking dark matter or modifying the local gravitational law. An earlier phenomenological formulation examined a general power-law scaling to characterize the cumulative background contribution. In the present version, the cosmological constant is treated explicitly as a constant parameter, consistent with general relativity, and the phenomenological description is reformulated in terms of a cumulative background kernel. Physical consistency considerations indicate that a scaling close to $n=2$ provides a smooth and well-behaved contribution at galactic scales. Version 2 clarifies the interpretive role of the background term without altering the physical content, numerical results, or illustrative figures. No new observational claims are introduced. This record is maintained for archival and timestamping purposes as part of an ongoing research program.