A quantum reduction to Bianchi I models in loop quantum gravity

Understand

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.