Quantization of the linearised Einstein-Klein-Gordon system on arbitrary backgrounds and the special case of perturbations in Inflation

Understand

We quantize the linearised Einstein-Klein-Gordon system on arbitrary on-shell backgrounds in a manifestly covariant and gauge-invariant manner.

• For the special case of perturbations in Inflation, i.e.
• on-shell backgrounds of Friedmann-Lema\^itre-Robertson-Walker type, we compare our general quantization construction with the standard approach to the quantum theory of perturbations in Inflation.
• We find that not all local quantum observables of the linearised Einstein-Klein-Gordon system can be split into local observables of scalar and tensor type as in the standard approach.