Unified brane gravity: Cosmological dark matter from a scale dependent Newton constant

We analyze, within the framework of unified brane gravity, the weak-field perturbations caused by the presence of matter on a 3-brane. Although deviating from the Randall-Sundrum approach, the masslessness of the graviton is still preserved. In particular, the four-dimensional Newton force law is recovered, but serendipitously, the corresponding Newton constant is shown to be necessarily lower than the one which governs Friedmann-Robertson-Walker cosmology. This has the potential to puzzle out cosmological dark matter. A subsequent conjecture concerning galactic dark matter follows.