Consistency relations in multi-field inflation

TL;DR

This paper derives consistency relations for cosmological perturbations in multi-field inflation, showing that certain relations hold regardless of the matter sector details, based on symmetry considerations.

Contribution

It introduces a novel derivation of consistency relations in multi-field inflation using symmetry and gauge invariance principles.

Findings

Consistency relations are independent of matter sector details.

Dilatation symmetry leads to quantum-protected identities.

Explicit lowest-order relations are derived.

Abstract

We study the consequences of spatial coordinate transformation in multi-field inflation. Among the spontaneously broken de Sitter isometries, only dilatation in the comoving gauge preserves the form of the metric and thus results in quantum-protected Slavnov-Taylor identities. We derive the corresponding consistency relations between correlation functions of cosmological perturbations in two different ways, by the connected and one-particle-irreducible Green's functions. The lowest-order consistency relations are explicitly given, and we find that even in multi-field inflation the consistency relations in the soft limit are independent of the detail of the matter sector.