Approximation to the Second Order Approximation of Einstein Field   Equations with a Cosmological Constant in a Flat Background
  Einstein 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. 
Clovis Jacinto de Matos