General Covariance Constraints on Cosmological Correlators
  We study the extent to which diffeomorphism invariance restricts the
properties of the primordial perturbations in single scalar field models. We
derive a set of identities that constrain the connected correlators of the
cosmological perturbations, as well as the one-particle-irreducible vertices of
the theory in any gauge. These identities are the analogues of Slavnov-Taylor
identities in gauge theories, and follow essentially from diffeomorphism
invariance alone. Yet because quantization requires diffeomorphism invariance
to be broken, they not only reflect invariance under diffeomorphisms, but also
how the latter has been broken by gauge fixing terms. In order to not lose the
symmetry altogether, we cannot simply set some fields to zero, as is usually
done in cosmological perturbation theory, but need to decouple them smoothly
and make sure that they do not contribute to cosmological correlators in the
decoupling limit. We use these identities to derive a set of consistency
relations between bispectra and power spectra of cosmological perturbations in
different gauges. Without additional assumptions, these consistency relations
just seem to reflect the redundancy implied by diffeomorphisms. But when
combined with analyticity, in a formulation of the theory in which auxiliary
fields have been integrated out, we recover novel and previously derived
relations that follow from invariance under both time and spatial
diffeomorphisms.
