  We discuss the correlation function for the metric for homogeneous and
isotropic cosmologies. The exact propagator equation determines the correlation
function as the inverse of the second functional derivative of the quantum
effective action. This formulation relates the metric correlation function
employed in quantum gravity computations to cosmological observables as the
graviton power spectrum. In the Einstein-Hilbert approximation for the
effective action the on-shell graviton correlation function can be obtained
equivalently from a product of mode functions which solve the linearized
Einstein equations. In contrast, the product of mode functions, often employed
in the context of cosmology, does not yield the correlation function for the
vector and scalar components of the metric fluctuations. We divide the metric
fluctuations into "physical fluctuations", which couple to a conserved energy
momentum tensor, and gauge fluctuations. On the subspace of physical metric
fluctuations the relation to physical sources becomes invertible, such that the
effective action and its relation to correlation functions no longer needs to
involve a gauge fixing term. The physical metric fluctuations have a similar
status as the Bardeen potentials, while being formulated in a covariant way. We
compute the effective action for the physical metric fluctuations for
geometries corresponding to realistic cosmologies.
