Consistency relations in multi-field inflation

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.

24 pages, version to appear in JCAP

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• Quantum non-linear evolution of inflationary tensor perturbations
• The Cosmological OTOC: A New Proposal for Quantifying Auto-Correlated Random Non-Chaotic Primordial Fluctuations
• Quantum nature of Wigner function for inflationary tensor perturbations
• The spatial gauge-dependence of single-field inflationary bispectra
• Cosmological Geometric Phase From Pure Quantum States: A study without/with having Bell's inequality violation
• Classical and quantum exact solutions for the anisotropic Bianchi type I in multi-scalar field cosmology with an exponential potential driven inflation