Einsteinian gravity from BRST quantization of a topological action

In order to deduce Einsteinian gravity from a topological action, we start from the metric-free Pontrjagin invariant in four dimensions. Using the Becchi-Rouet-Stora-Tyutin antifield formalism with a double duality gauge fixing, we obtain a consistent quantization in spaces of double dual curvature. They correspond to classical instanton type solutions of a curvature-squared model of gravity, in the affine form proposed already by Weyl and Yang. However, the exact vacuum solutions with double duality properties exhibit a “vacuum degeneracy.” By modifying the duality of the curvature via scale breaking terms, we demonstrate that only Einstein’s equations with an induced cosmological constant of partially topological origin emerge for the macroscopic “background.”