Diffeomorphism invariant cosmological sector in loop quantum gravity

TL;DR

This paper develops a rigorous, diffeomorphism-invariant framework for homogeneous and isotropic cosmological sectors within loop quantum gravity, enabling detailed comparison with loop quantum cosmology.

Contribution

It formulates covariant conditions for symmetry in classical phase space and translates them into loop quantum gravity, establishing a basis for embedding and comparing with loop quantum cosmology.

Findings

Formulated covariant symmetry conditions for classical general relativity.

Translated symmetry conditions into loop quantum gravity framework.

Proposed embedding strategy for loop quantum cosmology states.

Abstract

In this paper we work out in detail a new proposal to define rigorously a sector of loop quantum gravity at the diffeomorphism invariant level corresponding to homogeneous and isotropic cosmologies, and propose how to compare in detail the physics of this sector with that of loop quantum cosmology. The key technical steps we have completed are (a) to formulate conditions for homogeneity and isotropy in a diffeomorphism covariant way on the classical phase space of general relativity, and (b) to translate these conditions consistently using well-understood techniques to loop quantum gravity. To impose the symmetry at the quantum level, on both the connection and its conjugate momentum, the method used necessarily has similiarities to the Gupta-Bleuler method of quantizing the electromagnetic field. Lastly, a strategy for embedding states of loop quantum cosmology into this new homogeneous isotropic sector, and using this embedding to compare the physics, is presented.