  We make a proposal for gauge-invariant observables in perturbative quantum
gravity in cosmological spacetimes, building on the recent work of Brunetti et
al. [JHEP 08 (2016) 032]. These observables are relational, and are obtained by
evaluating the field operator in a field-dependent coordinate system. We show
that it is possible to define this coordinate system such that the
non-localities inherent in any higher-order observable in quantum gravity are
causal, i.e., the value of the gauge-invariant observable at a point $x$ only
depends on the metric and inflation perturbations in the past light cone of
$x$. We then construct propagators for the metric and inflaton perturbations in
a gauge adapted to that coordinate system, which simplifies the calculation of
loop corrections, and give explicit expressions for relevant cases: matter- and
radiation-dominated eras and slow-roll inflation.
