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arXiv · 1603.01128

Diffeomorphism invariant cosmological symmetry in full quantum gravity

Christopher Beetle·Jonathan S. Engle·Matthew E. Hogan·Phillip Mendonca
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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.

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Christopher Beetle, Jonathan S. Engle, Matthew E. Hogan, Phillip Mendonca. 2016-09-09. Diffeomorphism invariant cosmological symmetry in full quantum gravity. https://doi.org/10.1142/s0218271816420128

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