Diffeomorphism invariant cosmological symmetry in full quantum gravity

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.

8 pages, invited submission for special issue of Int. J. Mod. Phys. D; Remark added on use of intertwining condition to reduce quantization ambiguities, assumptions on matter model made clear, sign convention for complexification changed to match that of Thiemann, as well as minor corrections

References in corpus (5)

• Quantum Nature of the Big Bang: Improved dynamics
• Relating loop quantum cosmology to loop quantum gravity: Symmetric sectors and embeddings
• Quantum Reduced Loop Gravity: a realistic Universe
• A quantum reduction to Bianchi I models in loop quantum gravity
• Is classical flat Kasner spacetime flat in quantum gravity?

Cited by in corpus (12)

• Effective Quantum Extended Spacetime of Polymer Schwarzschild Black Hole
• (b,v)-type variables for black to white hole transitions in effective loop quantum gravity
• New Hamiltonians for loop quantum cosmology with arbitrary spin representations
• New Loop Quantum Cosmology Modifications from Gauge-covariant Fluxes
• Loop quantum cosmology: relation between theory and observations
• Diffeomorphism invariant cosmological sector in loop quantum gravity
• State refinements and coarse graining in a full theory embedding of loop quantum cosmology
• Orthogonal gauge fixing of first order gravity
• Quantum isotropy and the reduction of dynamics in Bianchi I
• Effective LQC model for k=+1 isotropic cosmologies from spatial discretisations
• Quantum surface holonomies for loop quantum gravity and their application to black hole horizons
• On the Role of Fiducial Structures in Minisuperspace Reduction and Quantum Fluctuations in LQC