QLO-QG · Quasi-local observables in quantum gravity

Quasi-local observables in quantum gravity

Although the theory of quantum gravity is unknown at the fundamental level, valid quantum gravitational predictions can be made at low energies and large distances compared to the Planck scale, which is about 10^(-33) cm where the precise theory of quantum gravity becomes relevant. At low energies, quantum gravity can be treated as an effective field theory by quantising metric fluctuations around a classical background (this approach is called “perturbative quantum gravity”, or pQG). Experimentally, quantum gravity effects manifest themselves in the cosmological microwave background, where one of the lowest-order predictions of pQG (the scalar power spectrum) has already been experimentally confirmed, and higher-order corrections are likely to be tested by next-generation experiments. An open issue in this context was the identification of suitable observables in pQG corresponding to experimentally observed quantities. In contrast to other well-known gauge theories where the gauge symmetry only concerns internal degrees of freedom, the gauge symmetry of pQG – diffeomorphisms – moves points on the underlying manifold, and local observables (defined at a fixed point of the background metric) are not gauge-invariant and hence unphysical. The primary objective of the project was the study of non-local observables in pQG, which contributes both to our understanding of the fundamental forces of nature, and to a correct interpretation of future experimental results. Besides advances in the mathematical description of these observables and the proof that a certain class of such observables are unsuitable from a physical point of view, the main result of the project is the construction of an observable that quantifies in a mathematically sound and gauge-invariant way the local expansion rate of the universe (the Hubble rate). Loop corrections to this observable were then calculated, which confirm a physical picture that was conjectured 25 years ago: the exponential expansion of spacetime during the inflationary period of the early universe produces large amounts of gravitons, whose mutual attraction then slows down the expansion.

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