One-particle-irreducible consistency relations for cosmological perturbations

We derive consistency relations for correlators of scalar cosmological perturbations that hold in the squeezed limit in which one or more of the external momenta become soft. Our results are formulated as relations between suitably defined one-particle-irreducible N-point and (N - 1)-point functions that follow from residual spatial conformal diffeomorphisms of the unitary gauge Lagrangian. As such, some of these relations are exact to all orders in perturbation theory and do not rely on approximate de Sitter invariance or other dynamical assumptions (e. g., properties of the operator product expansion or the behavior of modes at the horizon crossing). The consistency relations apply model-independently to cosmological scenarios in which the time evolution is driven by a single scalar field. Besides reproducing the known results for single-field inflation in the slow-roll limit, we verify that our consistency relations hold more generally, for instance, in ghost condensate models in flat space. We comment on possible extensions of our results to multifield models.