“Gauge-invariant observables in perturbative quantum gravity”

Abstract:

It is well known that the diffeomorphism invariance of gravitational theories makes it impossible to define local and gauge-invariant observables in perturbative (quantum) gravity, except at linear order. While in flat space one can study the S-Matrix, which is a gauge-invariant global observable, no analogue exists in a general curved space. Relational observables (i.e., the value of one field at the point where a second field has a prescribed value) are natural candidates for observables in (quantum) gravity, but they are not local when constructed around flat space or around a cosmological (FLRW) background spacetime due to the high symmetry of the latter.

We present two different approaches to this problem: a) correlation functions at fixed geodesic distance, and b) a construction of invariant coordinates, for which explicit and fully renormalized results for one-graviton-loop corrections to two-point functions and coupling constants have been obtained.