  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. However, we argue that this subclass
of observables is sufficient for measuring perturbations which vanish at
spatial infinity, which is in line with standard assumptions. Finally, we
comment on a recent observation that, upon standard quantization, the quantum
Bardeen potentials display a non-local behaviour and argue that a similar
phenomenon occurs in any local quantum field theory.
