Making classical and quantum canonical general relativity computable through a power series expansion in the inverse cosmological constant

Abstract

We consider general relativity with a cosmological constant as a perturbative expansion around a completely solvable diffeomorphism invariant field theory. This theory is the $\Lambda \to \infty$ limit of general relativity. This allows an explicit perturbative computational setup in which the quantum states of the theory and the classical observables can be explicitly computed. The zeroth order corresponds to highly degenerate space-times with vanishing volume. Perturbations give rise to space-times with non-vanishing volumes in a natural way. The spectrum of area- and volume-related observables constructed by coupling the theory to matter can be directly assessed. An unexpected relationship arises at a quantum level between the discrete spectrum of the volume operator and the allowed values of the cosmological constant.

5 pages, RevTeX with multicol and psfig

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• A generalized Hamiltonian Constraint Operator in Loop Quantum Gravity and its simplest Euclidean Matrix Elements
• A regularization of the hamiltonian constraint compatible with the spinfoam dynamics
• Wave function of the Universe and Chern-Simons Perturbation Theory
• The large cosmological constant approximation to classical and quantum gravity: model examples
• Bibliography of Publications related to Classical Self-dual variables and Loop Quantum Gravity
• Quantized cosmological constant in 1+1 dimensional quantum gravity with coupled scalar matter