Vacuum-Energy-Driven Repulsive Gravity on a Detuned Randall–Sundrum Brane: An Effective-Mass Analysis

We examine a self-consistent interpretation of dark-energy-inducedrepulsive gravity in a Randall–Sundrum-type braneworld. The original Randall–Sundrum construction contains a negative five-dimensionalbulk vacuum energy; an accelerating four-dimensional brane insteadrequires a positive effective four-dimensional cosmological constant.Starting from a five-dimensional Einstein–Hilbert action with a positivetension brane, we demonstrate that an upward detuning of the branetension generates a positive induced cosmological constant and permits a de Sitter brane geometry. In the low-energy regime, wherehigh-energy and projected Weyl corrections are negligible, the induced equations reduce to Einstein gravity with a cosmological constant. A positive vacuum energy EΛ in a sphere has the positivemass equivalent MΛ = EΛ/c2, but its negative pressure yields anactive gravitational mass −2MΛ. Consequently, the outward acceleration at radius r may be written in the Newtonian-looking formFrep = 2G4mMΛ(r)/r2 = Λ4c2mr/3. The inverse-square representation is exact within its stated assumptions, although MΛ(r) ∝ r3;hence it is not a new universal inverse-square two-body force. For fixedpositive central mass and positive cosmological constant, attractionand repulsion have equal magnitudes at exactly one balance radius,not at every separation; that radial balance is unstable. We specify theconditions under which the effective description applies, distinguish itfrom genuinely new bulk-gravity predictions, and discuss observationaltests and theoretical limitations. The minimal framework reproduces1known Einstein–Λ behavior and does not by itself constitute an experimentally established new interaction