Einsteinian gravity from a topological action

TL;DR

This paper derives a curvature-squared gravity model from a topological action in 4D, showing how Einstein's equations with a cosmological constant naturally emerge, with implications for dark energy and dark matter.

Contribution

It introduces a novel derivation of Einstein gravity from a topological invariant using BRST formalism and explores modifications leading to Einstein's equations with a cosmological constant.

Findings

Exact vacuum solutions exhibit vacuum degeneracy.

Modifying duality yields Einstein's equations with a cosmological constant.

Potential implications for dark energy and dark matter models.

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.