Perturbative Quantum Gravity: Diffeomorphisms, Observables and Noncommutativity
Markus Fröb (U. Leipzig)

Perturbative Quantum Gravity (pQG), the effective quantum field theory of gravitational fluctuations around a given background, is currently the only experimentally accessible theory of quantum gravity. Its tree-level predictions, in the form of temperature fluctuations of the Cosmic Microwave Background, have been experimentally confirmed, and it is possible that loop corrections are accessible to future experiments. However, while the tree-level results are well understood also from a theoretical point of view, the diffeomorphism symmetry of gravity makes the construction of invariant observables very difficult beyond this. Only recently, this issue has been overcome, and a class of causal invariant observables has been constructed. I will discuss this construction and how it can be related to observations, and present some predictions of pQG for graviton loop corrections to the Newtonian gravitational potential and the Hubble rate, the local expansion rate of the universe. Lastly, I show that pQG also predicts that spacetime becomes non-commutative at the Planck scale, but in a different way from previous approaches. The talk is based (in particular) on the recent papers arXiv:1806.11124, 2108.11960, 2109.09753 and 2207.03345.