Vanishing of local non-Gaussianity in canonical single field inflation

Abstract

We study the production of observable primordial local non-Gaussianity in two opposite regimes of canonical single field inflation: attractor (standard single field slow-roll inflation) and non attractor (ultra slow-roll inflation). In the attractor regime, the standard derivation of the bispectrum's squeezed limit using co-moving coordinates gives the well known Maldacena's consistency relation $f_{NL}=5(1-n_s)/12$. On the other hand, in the non-attractor regime, the squeezed limit offers a substantial violation of this relation given by $f_{NL}=5/2$. In this work we argue that, independently of whether inflation is attractor or non-attractor, the size of the observable primordial local non-Gaussianity is predicted to be $f_{NL}^{obs}=0$ (a result that was already understood to hold in the case of attractor models). To show this, we follow the use of the so-called Conformal Fermi Coordinates (CFC), recently introduced in the literature. These coordinates parametrize the local environment of inertial observers in a perturbed FRW spacetime, allowing one to identify and compute gauge invariant quantities, such as $n$-point correlation functions. Concretely, we find that during inflation, after all the modes have exited the horizon, the squeezed limit of the 3-point correlation function of curvature perturbations vanishes in the CFC frame, regardless of the inflationary regime. We argue that such a cancellation should persist after inflation ends.

arXiv comment27 pages, v2:matches published version(JCAP)

References in corpus (44)

• Non-Gaussian features of primordial fluctuations in single field inflationary models
• Perturbations in k-inflation
• Observational Signatures and Non-Gaussianities of General Single Field Inflation
• A general proof of the conservation of the curvature perturbation
• Single field consistency relation for the 3-point function
• Planck 2015 results. XVII. Constraints on primordial non-Gaussianity
• Primordial non-gaussianities in single field inflation
• Non-Gaussianity of the primordial perturbation in the curvaton model
• Horizon crossing and inflation with large η
• Features of heavy physics in the CMB power spectrum
• New Perspective on Galaxy Clustering as a Cosmological Probe: General Relativistic Effects
• Ultra Slow-Roll Inflation and the non-Gaussianity Consistency Relation
• On Soft Limits of Inflationary Correlation Functions
• Violation of non-Gaussianity consistency relation in a single field inflationary model
• On the consistency relation of the 3-point function in single field inflation
• Conformal consistency relations for single-field inflation
• The Observed Squeezed Limit of Cosmological Three-Point Functions
• The Separate Universe Approach and the Evolution of Nonlinear Superhorizon Cosmological Perturbations
• Conformal Symmetries of Adiabatic Modes in Cosmology
• Galaxy Bias and non-Linear Structure Formation in General Relativity
• An Infinite Set of Ward Identities for Adiabatic Modes in Cosmology
• Improved Estimates of Cosmological Perturbations
• Ultra slow-roll inflation demystified
• A Single Field Inflation Model with Large Local Non-Gaussianity
• Conditions for large non-Gaussianity in two-field slow-roll inflation
• Dominance of gauge artifact in the consistency relation for the primordial bispectrum
• Constraints from Conformal Symmetry on the Three Point Scalar Correlator in Inflation
• Ward Identities for Scale and Special Conformal Transformations in Inflation
• A Note on the Consistency Condition of Primordial Fluctuations
• One-particle-irreducible consistency relations for cosmological perturbations
• Consistently violating the non-Gaussian consistency relation
• Soft Theorems For Shift-Symmetric Cosmologies
• How Gaussian can our Universe be?
• A new method for calculating the primordial bispectrum in the squeezed limit
• Conformal Fermi Coordinates
• Features from the non-attractor beginning of inflation
• The Physical Squeezed Limit: Consistency Relations at Order q^2
• On the squeezed limit of the bispectrum in general single field inflation
• Squeezed Bispectrum in the $\delta N$ Formalism: Local Observer Effect in Field Space
• Systematics of Adiabatic Modes: Flat Universes
• Global adiabaticity and non-Gaussianity consistency condition
• Adiabaticity and gravity theory independent conservation laws for cosmological perturbations
• Correlated primordial spectra in effective theory of inflation
• Single-Field Inflation and the Local Ansatz: Distinguishability and Consistency

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• Dynamical Analysis of Attractor Behavior in Constant Roll Inflation
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• Constraints on holographic multi-field inflation and models based on the Hamilton-Jacobi formalism
• The observed galaxy bispectrum from single-field inflation in the squeezed limit
• CMB B-mode non-Gaussianity: optimal bispectrum estimator and Fisher forecasts
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• A non-perturbative test of consistency relations and their violation
• Revisiting non-Gaussianity in non-attractor inflation models in the light of the cosmological soft theorem
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• Squeezing $f_{\mathrm{NL}}$ out of the matter bispectrum with consistency relations
• Primordial non-Guassianity in inflation with gravitationally enhanced friction
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• Unifying attractor and non-attractor models of inflation under a single soft theorem
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• The Physical Content of Long Tensor Modes in Cosmology
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