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.

14 pages

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• Tests of the Gravitational Inverse-Square Law below the Dark-Energy Length Scale
• String-inspired Gauss-Bonnet gravity reconstructed from the universe expansion history and yielding the transition from matter dominance to dark energy
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• Unification of gravity, gauge fields, and Higgs bosons
• Graviweak Unification, Invisible Universe and Dark Energy
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• Gravi-Weak Unification and Multiple Point Principle
• Graviweak Unification in the Visible and Invisible Universe and Inflation from the Higgs Field False Vacuum
• False Vacuum Higgs Inflation and the Graviweak Unification