2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/125662Einstein field equations with a cosmological constant are approximated to the second order in the perturbation to a flat background metric. The final result is a set of Einstein-Maxwell-Proca equations for gravity in the weak field regime. This approximation procedure implements the breaking of gauge symmetry in general relativity. A brief discussion of the physical consequences (Pioneer anomalous deceleration) is proposed in the framework of the gauge theory of gravity.11 pagesGeneral Relativity and Quantum Cosmologytext