One-particle-irreducible consistency relations for cosmological perturbations

TL;DR

This paper derives exact consistency relations for scalar cosmological perturbations in the squeezed limit, applicable across various models, based on residual conformal symmetries, without relying on specific dynamical assumptions.

Contribution

It introduces model-independent consistency relations for cosmological correlators derived from residual conformal symmetries, valid to all orders in perturbation theory.

Findings

Relations hold in single-field models and beyond

Valid in flat space ghost condensate models

Exact to all orders in perturbation theory

Abstract

We derive consistency relations for correlators of scalar cosmological perturbations which 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 deSitter invariance or other dynamical assumptions (e.g., properties of the operator product expansion or the behavior of modes at horizon crossing). The consistency relations apply model-independently to cosmological scenarios where 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 multi-field models.