A quantum reduction to Bianchi I models in loop quantum gravity

Abstract

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.

5 pages. v2: partly rewritten to clarify derivation, gauge group enlarged from U(1) to R_Bohr, relation to old and new LQC dynamics discussed, previous results unchanged. v3: journal version, minor clarifications

References in corpus (7)

• Quantum Nature of the Big Bang: Improved dynamics
• Quantum Nature of the Big Bang: An Analytical and Numerical Investigation
• Spherically Symmetric Quantum Geometry: States and Basic Operators
• Towards Spinfoam Cosmology
• Relating loop quantum cosmology to loop quantum gravity: Symmetric sectors and embeddings
• Loop Quantum Cosmology from Loop Quantum Gravity
• A quantum reduction to spherical symmetry in loop quantum gravity

Cited by in corpus (3)

• An elementary introduction to loop quantum gravity
• Loop quantization of the Gowdy model with local rotational symmetry
• Bianchi I effective dynamics in Quantum Reduced Loop Gravity