Single field consistency relation for the 3-point function

Abstract

We point out the existence of a consistency relation involving the 3-point function of scalar perturbations which is valid in any inflationary model, independently of the inflaton Lagrangian under the assumption that the inflaton is the only dynamical field. The 3-point function in the limit in which one of the momenta is much smaller than the other two is fixed in terms of the power spectrum and its tilt. This relation, although very hard to verify experimentally, could be easily proved wrong by forecoming data, thus ruling out any scenario with a single dynamical field in a model independent way.

4 pages. v2: reference added, matches published version

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• The primordial non-Gaussianities for non-singular Horndeski cosmologies
• Viable Curvaton Models from the $f_{NL}$ Parameter
• Fundamental Physics in 2025: Status, Decisive Targets, and Path Forward
• Inflationary tensor fossils deformed by solid matter -- scalar field interaction
• The double-soft limit in cosmological correlation functions and graviton exchange effects
• Cosmological Geometric Phase From Pure Quantum States: A study without/with having Bell's inequality violation
• On higher spin symmetries in de Sitter QFTs
• The scalar-scalar-tensor inflationary three-point function in the axion monodromy model
• A Consistency Relation for the CMB B-mode Polarization in the Squeezed Limit
• An introduction to inflation after Planck: from theory to observations
• Bispectrum at NLO in single field inflation: conservation and squeezed limit
• Spatial anisotropies from long wavelength scalar and tensor modes
• Adiabatic Solutions in General Relativity and Boundary Symmetries
• Inflation: a quantum laboratory on cosmological scales
• Inflationary cross-correlations of a non-minimal spectator and their soft limits
• Non-linear effects in early Universe cosmology
• A (semi)-exact Hamiltonian for the curvature perturbation $\zeta$
• Infrared Logarithms in Minisuperspace Inflation
• A revisited Correction to the Halo Mass Function for local-type Primordial non-Gaussianity
• Primordial non-Gaussianity systematics from redshift mismatch with SPHEREx
• A Tail of Eternal Inflation
• Non-Gaussianity in the Squeezed Three-Point Correlation from the Relativistic Effects
• Quijote PNG: The information content of the halo power spectrum and bispectrum
• New leading contributions to non-gaussianity in single field inflation
• Searching for non-Gaussianity in the Planck data
• Enhancing Bispectrum Estimators for Galaxy Redshift Surveys with Velocities
• On the space of non-Gaussian fields with single-clock bispectra
• First constraints on the intrinsic CMB dipole and our velocity with Doppler and aberration
• Integrated Markov Chain Monte Carlo (MCMC) analysis of primordial non-Gaussianity (f_NL) in the recent CMB data
• Non-Gaussianity from explicit $U(1)$-breaking interactions
• The Black Hole Window on Cosmic Inflation
• Model-independent constraints on inflation and reheating