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

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, { in principle}, not accessible to measurement by local detectors.