An embedding of loop quantum cosmology in (b, v) variables into a full theory context

TL;DR

This paper embeds loop quantum cosmology in (b, v) variables into a full quantum gravity framework, clarifying how symmetry reduction and dynamics emerge from the full theory using similar variables and quantization techniques.

Contribution

It introduces a method to embed (b, v) loop quantum cosmology into a full quantum gravity theory, connecting reduced models with the full theory via specific variables and constraints.

Findings

Symmetry reduction characterized by vanishing phase space functions.

Loop quantum cosmology dynamics derived from the full theory Hamiltonian.

Application to spherical symmetry with similar reduction results.

Abstract

Loop quantum cosmology in (b, v) variables, which is governed by a unit step size difference equation, is embedded into a full theory context based on similar variables. A full theory context here means a theory of quantum gravity arrived at using the quantisation techniques used in loop quantum gravity, however based on a different choice of elementary variables and classical gauge fixing suggested by loop quantum cosmology. From the full theory perspective, the symmetry reduction is characterised by the vanishing of certain phase space functions which are implemented as operator equations in the quantum theory. The loop quantum cosmology dynamics arise as the action of the full theory Hamiltonian on maximally coarse states in the kernel of the reduction constraints. An application of this reduction procedure to spherical symmetry is also sketched, with similar results, but only one canonical pair in (b, v) form.