Einsteinian gravity from a topological action

Abstract

The curvature-squared model of gravity, in the affine form proposed by Weyl and Yang, is deduced from a topological action in 4D. More specifically, we start from the Pontrjagin (or Euler) invariant. Using the BRST antifield formalism with a double duality gauge fixing, we obtain a consistent quantization in spaces of double dual curvature as classical instanton type background. However, exact vacuum solutions with double duality properties exhibit a `vacuum degeneracy'. By modifying the duality via a scale breaking term, we demonstrate that only Einstein's equations with an induced cosmological constant emerge for the topology of the macroscopic background. This may have repercussions on the problem of `dark energy' as well as `dark matter' modeled by a torsion induced quintaxion.