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

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.

20 pages; v2: journal version, clarifications and comments added

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• On the canonical structure of general relativity with a limiting curvature and its relation to loop quantum gravity
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• Challenges in recovering a consistent cosmology from the effective dynamics of loop quantum gravity
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• Critical Insight into the Cosmological Sector of Loop Quantum Gravity
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• Symmetry restriction and its application to gravity
• The Physical Relevance of the Fiducial Cell in Loop Quantum Cosmology
• Quantum isotropy and the reduction of dynamics in Bianchi I
• Effective LQC model for k=+1 isotropic cosmologies from spatial discretisations
• On the Role of Fiducial Structures in Minisuperspace Reduction and Quantum Fluctuations in LQC