A MacDowell-Mansouri type formulation for Einstein manifolds

We study a pure connection formulation plus algebraic constraints in four spacetime dimensions where the gauge group $G \supset SO(1, 3)$. We show that the action has, as particular cases, the MacDowell-Mansouri and the Stelle-West formulations for gravity. Also, under adequate specification of the constraint terms, we obtain Einstein manifolds, i.e., torsionless conformally flat manifolds.