Non-Trivial Checks of Novel Consistency Relations

Abstract

Single-field perturbations satisfy an infinite number of consistency relations constraining the squeezed limit of correlation functions at each order in the soft momentum. These can be understood as Ward identities for an infinite set of residual global symmetries, or equivalently as Slavnov-Taylor identities for spatial diffeomorphisms. In this paper, we perform a number of novel, non-trivial checks of the identities in the context of slow-roll single field inflationary models with arbitrary sound speed. We focus for concreteness on identities involving 3-point functions with a soft external mode, and consider all possible scalar and tensor combinations for the hard-momentum modes. In all these cases, we check the consistency relations up to and including cubic order in the soft momentum. For this purpose, we compute for the first time the 3-point functions involving 2 scalars and 1 tensor, as well as 2 tensors and 1 scalar, for arbitrary sound speed.

30 pages

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Cited by in corpus (22)

• Imprints of Massive Primordial Fields on Large-Scale Structure
• Inflationary tensor fossils in large-scale structure
• From Amplitudes to Contact Cosmological Correlators
• On the scalar consistency relation away from slow roll
• Multiple Soft Limits of Cosmological Correlation Functions
• Systematics of Adiabatic Modes: Flat Universes
• Double Soft Limits of Cosmological Correlations
• Examining the consistency relations describing the three-point functions involving tensors
• The squeezed limit of the bispectrum in multi-field inflation
• Soft limits in holographic cosmology
• Effective Field Theory of non-Attractor Inflation
• On the Initial State and Consistency Relations
• The Separate Universe Approach to Soft Limits
• Weinberg Soft Theorems from Weinberg Adiabatic Modes
• A Cosmological Slavnov-Taylor Identity
• An Effective Theory for Holographic RG Flows
• Soft theorems for boosts and other time symmetries
• Spatial Curvature at the Sound Horizon
• General Covariance Constraints on Cosmological Correlators
• Inflation in Flatland
• The double-soft limit in cosmological correlation functions and graviton exchange effects
• Inflationary cross-correlations of a non-minimal spectator and their soft limits