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

TL;DR

This paper introduces a perturbative approach to general relativity with a cosmological constant, enabling explicit calculations of quantum states and observables by expanding around a solvable limit as the cosmological constant becomes large.

Contribution

It develops a novel perturbative framework for quantum and classical general relativity using a power series expansion in the inverse cosmological constant, making the theory computationally accessible.

Findings

Explicit computation of quantum states and observables

Relationship between volume spectrum and cosmological constant

Perturbative method applicable to quantum gravity models

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.