• DOI:10.1103/PhysRevD.91.081502
• Corpus ID: 119266197

Quantum reduction to Bianchi I models in loop quantum gravity

@article{Bodendorfer2014QuantumRT,
  title={Quantum reduction to Bianchi I models in loop quantum gravity},
  author={Norbert Bodendorfer},
  journal={Physical Review D},
  year={2014},
  volume={91},
  pages={081502}
}

• N. Bodendorfer
• Published 21 October 2014
• Physics
• Physical Review D

We propose a quantum symmetry reduction of loop quantum gravity to Bianchi I spacetimes. To this end, we choose the diagonal metric gauge for the spatial diffeomorphism constraint at the classical level, leading to an $\mathbb{R}_{\text{Bohr}}$ gauge theory, and quantise the resulting theory via loop quantum gravity methods. Constraints which lead classically to a suitable reduction are imposed at the quantum level. The dynamics of the resulting model turn out to be very simple and manifestly coincide with those of a polymer quantisation of a Bianchi I model for the simplest choice of full theory quantum states compatible with the Bianchi I reduction. In particular, the "improved" $\bar{\mu}$ dynamics of loop quantum cosmology can be obtained by modifying the regularisation of the Hamiltonian constraint with similar ideas, in turn yielding insights into the full theory dynamics.