Soft limits in holographic cosmology

TL;DR

This paper derives the leading and subleading soft limits of cosmological correlators holographically, establishing a non-perturbative connection between quantum field theory Ward identities and inflationary consistency relations.

Contribution

It provides a holographic derivation of all leading and subleading consistency relations for cosmological 3-point functions from a general quantum field theory perspective.

Findings

Derivation of soft limits from Ward identities in dual QFT

Verification for slow-roll inflation and holographic cosmologies

Non-perturbative results applicable to general QFTs

Abstract

We study the soft limits of cosmological correlators from a holographic perspective, showing how the inflationary consistency relations arise from the diffeomorphism invariance of the dual quantum field theory. Starting from the corresponding Ward identity, by taking moments we derive the leading and subleading behaviour of the stress tensor 3-point function in the limit as one momentum vanishes. These results are non-perturbative and valid in quantum field theories of a very general nature. Exploiting the known mapping of correlators in the dual quantum field theory to those of the cosmology, we then obtain the leading and subleading soft behaviour of all cosmological 3-point correlators of curvature perturbations and gravitons. Our results thus provide a holographic derivation of all leading and subleading consistency relations for cosmological 3-point functions, and our method is easily generalised. We verify our results explicitly for slow-roll inflation and for strongly coupled holographic cosmologies with a perturbative dual description.