"Observables" in de Sitter Quantum Gravity: in Perturbation Theory and Beyond

TL;DR

This paper reviews the conceptual issues in defining observables and energy in de Sitter quantum gravity, emphasizing the gauge nature of static de Sitter Hamiltonian and the challenges in measuring its eigenvalues.

Contribution

It clarifies misconceptions about the static de Sitter Hamiltonian and discusses the implications for quantum models of gravity in cosmological space-times.

Findings

Static de Sitter Hamiltonian is not conserved.

Static energy is an approximate property of meta-stable states.

Eigenvalues of a Hamiltonian, if it exists, are not locally measurable.

Abstract

A review of some errors made by the author and others in their search for quantum models of gravity in cosmological space-times that asymptote to de Sitter (dS) space in the future. The "static de Sitter Hamiltonian", which measures the energy of localized objects in a static patch, is not a conserved quantity. The static time translation diffeomorphism of eternal dS space is a gauge symmetry, and the static energy is an approximate property of meta-stable constrained states. It's not clear whether a theoretical model has to have a time independent Hamiltonian at all, but if it does, its eigenvalues are, {\it in principle}, not accessible to measurement by local detectors.