Diffeomorphism invariant cosmological symmetry in full quantum gravity

TL;DR

This paper proposes a rigorous way to identify and analyze homogeneous and isotropic cosmological sectors within full loop quantum gravity, enabling better comparison with loop quantum cosmology results.

Contribution

It formulates covariant conditions for homogeneity and isotropy in classical and quantum gravity, advancing the connection between full loop quantum gravity and cosmological models.

Findings

Formulated covariant conditions for cosmological symmetry in classical phase space.

Translated symmetry conditions into the language of loop quantum gravity.

Presented a proof of concept embedding of LQC into the Bianchi I model.

Abstract

This paper summarizes a new proposal to define rigorously a sector of loop quantum gravity at the diffeomorphism invariant level corresponding to homogeneous and isotropic cosmologies, thereby enabling a detailed comparison of results in loop quantum gravity and 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. Some additional steps, such as constructing a specific embedding of the Hilbert space of loop quantum cosmology into a space of (distributional) states in the full theory, remain incomplete. However, we also describe, as a proof of concept, a complete analysis of an analogous embedding of homogeneous and isotropic loop quantum cosmology into the quantum Bianchi I model of Ashtekar and Wilson-Ewing. Details will appear in a pair of forthcoming papers.